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Merge remote-tracking branch 'upstream/master'

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Adrian Mariano 2023-06-16 19:12:32 -04:00
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4
.openscad_docsgen_rc
View File

@ -5,10 +5,11 @@ GenerateDocs: Files, TOC, Index, Topics, CheatSheet, Sidebar
UsePNGAnimations: Yes
IgnoreFiles:
affine.scad
foo.scad
metric_screws.scad
std.scad
bosl1compat.scad
builtins.scad
foo.scad
tmp_*.scad
PrioritizeFiles:
constants.scad
@ -73,6 +74,7 @@ DefineSynTags:
Path = Can return a Path.
PathList = Can return a list of Paths.
Region = Can return a Region.
RegList = Can return a list of Regions.
Trans = Can transform children.
VNF = Can return a VNF.

2
README.md
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@ -10,7 +10,7 @@ Requires OpenSCAD 2021.01 or later.
- **NOTE:** BOSL2 IS BETA CODE. THE CODE IS STILL BEING REORGANIZED.
- **NOTE2:** CODE WRITTEN FOR BOSLv1 PROBABLY WON'T WORK WITH BOSL2!
[![Join the chat at https://gitter.im/BelfrySCAD/BOSL2](https://badges.gitter.im/BelfrySCAD/BOSL2.svg)](https://gitter.im/BelfrySCAD/BOSL2?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
[![Join the chat at https://gitter.im/revarbat/BOSL2](https://badges.gitter.im/revarbat/BOSL2.svg)](https://gitter.im/revarbat/BOSL2?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
## Documentation

331
attachments.scad
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@ -464,6 +464,7 @@ _ANCHOR_TYPES = ["intersect","hull"];
// Module: position()
// Synopsis: Attaches children to a parent object at an anchor point.
// SynTags: Trans
// Topics: Attachments
// See Also: attachable(), attach(), orient()
// Usage:
@ -473,6 +474,7 @@ _ANCHOR_TYPES = ["intersect","hull"];
// of attachments, see the [Attachments Tutorial](Tutorial-Attachments).
// Arguments:
// from = The vector, or name of the parent anchor point to attach to.
// from = The vector, or name of the parent anchor point to attach to.
// Side Effects:
// `$attach_anchor` for each `from=` anchor given, this is set to the `[ANCHOR, POSITION, ORIENT, SPIN]` information for that anchor.
// `$attach_to` is set to `undef`.
@ -535,14 +537,13 @@ module position(from)
// Module: orient()
// Synopsis: Orients children's tops in the directon of the specified anchor.
// SynTags: Trans
// Topics: Attachments
// See Also: attachable(), attach(), orient()
// Usage:
// PARENT() orient(anchor, [spin]) CHILDREN;
// Description:
// Orients children such that their top is tilted in the direction of the specified parent anchor point.
// The `$align` variable can help you anchor the child, aligned with the edges of the parent, based
// on the position specified by a parent {{position()}} module. See {{position()}} for examples using `$align`.
// For a step-by-step explanation of attachments, see the [Attachments Tutorial](Tutorial-Attachments).
// Arguments:
// anchor = The anchor on the parent which you want to match the orientation of.
@ -599,9 +600,9 @@ module orient(anchor, spin) {
// Module: attach()
// Synopsis: Attaches children to a parent object at an anchor point and orientation.
// SynTags: Trans
// Topics: Attachments
// See Also: attachable(), position(), face_profile(), edge_profile(), corner_profile()
// Usage:
@ -1429,6 +1430,7 @@ module show_int(tags)
// Module: face_mask()
// Synopsis: Ataches a 3d mask shape to the given faces of the parent.
// SynTags: Trans
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), edge_mask(), corner_mask(), face_profile(), edge_profile(), corner_profile()
// Usage:
@ -1472,6 +1474,7 @@ module face_mask(faces=[LEFT,RIGHT,FRONT,BACK,BOT,TOP]) {
// Module: edge_mask()
// Synopsis: Attaches a 3D mask shape to the given edges of the parent.
// SynTags: Trans
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), face_mask(), corner_mask(), face_profile(), edge_profile(), corner_profile()
// Usage:
@ -1536,6 +1539,7 @@ module edge_mask(edges=EDGES_ALL, except=[]) {
// Module: corner_mask()
// Synopsis: Attaches a 3d mask shape to the given corners of the parent.
// SynTags: Trans
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), face_mask(), edge_mask(), face_profile(), edge_profile(), corner_profile()
// Usage:
@ -1586,6 +1590,7 @@ module corner_mask(corners=CORNERS_ALL, except=[]) {
// Module: face_profile()
// Synopsis: Extrudes a 2D edge profile into a mask for all edges and corners of the given faces on the parent.
// SynTags: Geom
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), edge_profile(), corner_profile(), face_mask(), edge_mask(), corner_mask()
// Usage:
@ -1625,8 +1630,9 @@ module face_profile(faces=[], r, d, excess=0.01, convexity=10) {
// Module: edge_profile()
// Synopsis: Extrudes a 2d edge profile into a mask on the given edges of the parent.
// SynTags: Geom
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), face_profile(), corner_profile(), edge_mask(), face_mask(), corner_mask()
// See Also: attachable(), position(), attach(), face_profile(), edge_profile_asym(), corner_profile(), edge_mask(), face_mask(), corner_mask()
// Usage:
// PARENT() edge_profile([edges], [except], [convexity]) CHILDREN;
// Description:
@ -1651,19 +1657,20 @@ module face_profile(faces=[], r, d, excess=0.01, convexity=10) {
// cube([50,60,70],center=true)
// edge_profile([TOP,"Z"],except=[BACK,TOP+LEFT])
// mask2d_roundover(r=10, inset=2);
module edge_profile(edges=EDGES_ALL, except=[], excess=0.01, convexity=10) {
req_children($children);
assert($parent_geom != undef, "No object to attach to!");
check1 = assert($parent_geom != undef, "No object to attach to!");
edges = _edges(edges, except=except);
vecs = [
for (i = [0:3], axis=[0:2])
if (edges[axis][i]>0)
EDGE_OFFSETS[axis][i]
];
all_vecs_are_edges = all([for (vec = vecs) sum(v_abs(vec))==2]);
check2 = assert(all_vecs_are_edges, "All vectors must be edges.");
for ($idx = idx(vecs)) {
vec = vecs[$idx];
vcount = (vec.x?1:0) + (vec.y?1:0) + (vec.z?1:0);
dummy=assert(vcount == 2, "Not an edge vector!");
anch = _find_anchor(vec, $parent_geom);
$attach_to = undef;
$attach_anchor = anch;
@ -1687,8 +1694,295 @@ module edge_profile(edges=EDGES_ALL, except=[], excess=0.01, convexity=10) {
}
}
// Module: edge_profile_asym()
// Synopsis: Extrudes an asymmetric 2D profile into a mask on the given edges and corners of the parent.
// SynTags: Geom
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), face_profile(), edge_profile(), corner_profile(), edge_mask(), face_mask(), corner_mask()
// Usage:
// PARENT() edge_profile([edges], [except=], [convexity=], [flip=], [corner_type=]) CHILDREN;
// Description:
// Takes an asymmetric 2D mask shape and attaches it to the selected edges and corners, with the appropriate
// orientation and extruded length to be `diff()`ed away, to give the edges and corners a matching profile.
// If no tag is set then `edge_profile_asym()` sets the tag for children to "remove" so that it will work
// with the default {{diff()}} tag. For details on specifying the edges to mask see [Specifying Edges](attachments.scad#subsection-specifying-edges).
// For a step-by-step explanation of attachments, see the [Attachments Tutorial](Tutorial-Attachments).
// Profile orientation will be made consistent for all connected edges and corners. This prohibits having three
// edges meeting at any one corner. You can intert the orientations of all edges with `flip=true`.
// Arguments:
// edges = Edges to mask. See [Specifying Edges](attachments.scad#subsection-specifying-edges). Default: All edges.
// except = Edges to explicitly NOT mask. See [Specifying Edges](attachments.scad#subsection-specifying-edges). Default: No edges.
// excess = Excess length to extrude the profile to make edge masks. Default: 0.01
// convexity = Max number of times a line could intersect the perimeter of the mask shape. Default: 10
// flip = If true, reverses the orientation of any external profile parts at each edge. Default false
// corner_type = Specifies how exterior corners should be formed. Must be one of `"none"`, `"chamfer"`, `"round"`, or `"sharp"`. Default: `"none"`
// Side Effects:
// Tags the children with "remove" (and hence sets `$tag`) if no tag is already set.
// `$idx` is set to the index number of each edge.
// `$attach_anchor` is set for each edge given, to the `[ANCHOR, POSITION, ORIENT, SPIN]` information for that anchor.
// `$profile_type` is set to `"edge"`.
// Example:
// ogee = [
// "xstep",1, "ystep",1, // Starting shoulder.
// "fillet",5, "round",5, // S-curve.
// "ystep",1, "xstep",1 // Ending shoulder.
// ];
// diff()
// cuboid(50) {
// edge_profile_asym(FRONT)
// mask2d_ogee(ogee);
// }
// Example: Flipped
// ogee = [
// "xstep",1, "ystep",1, // Starting shoulder.
// "fillet",5, "round",5, // S-curve.
// "ystep",1, "xstep",1 // Ending shoulder.
// ];
// diff()
// cuboid(50) {
// edge_profile_asym(FRONT, flip=true)
// mask2d_ogee(ogee);
// }
// Example: Negative Chamfering
// cuboid(50) {
// edge_profile_asym(FWD, flip=false)
// xflip() mask2d_chamfer(10);
// edge_profile_asym(BACK, flip=true, corner_type="sharp")
// xflip() mask2d_chamfer(10);
// }
// Example: Negative Roundings
// cuboid(50) {
// edge_profile_asym(FWD, flip=false)
// xflip() mask2d_roundover(10);
// edge_profile_asym(BACK, flip=true, corner_type="round")
// xflip() mask2d_roundover(10);
// }
// Example: Cornerless
// cuboid(50) {
// edge_profile_asym(
// "ALL", except=[TOP+FWD+RIGHT, BOT+BACK+LEFT]
// ) xflip() mask2d_roundover(10);
// }
// Example: More complicated edge sets
// cuboid(50) {
// edge_profile_asym(
// "ALL", except=[TOP+FWD+RIGHT, BOT+BACK+LEFT],
// corner_type="chamfer"
// ) xflip() mask2d_roundover(10);
// }
module edge_profile_asym(edges=EDGES_ALL, except=[], excess=0.01, convexity=10, flip=false, corner_type="none") {
function _corner_orientation(pos,pvec) =
let(
j = [for (i=[0:2]) if (pvec[i]) i][0],
T =
(pos.x>0? xflip() : ident(4)) *
(pos.y>0? yflip() : ident(4)) *
(pos.z>0? zflip() : ident(4)) *
rot(-120*(2-j), v=[1,1,1])
) T;
function _default_edge_orientation(edge) =
edge.z < 0? [[-edge.x,-edge.y,0], UP] :
edge.z > 0? [[-edge.x,-edge.y,0], DOWN] :
edge.y < 0? [[-edge.x,0,0], BACK] :
[[-edge.x,0,0], FWD] ;
function _edge_transition_needs_flip(from,to) =
let(
flip_edges = [
[BOT+FWD, [FWD+LEFT, FWD+RIGHT]],
[BOT+BACK, [BACK+LEFT, BACK+RIGHT]],
[BOT+LEFT, []],
[BOT+RIGHT, []],
[TOP+FWD, [FWD+LEFT, FWD+RIGHT]],
[TOP+BACK, [BACK+LEFT, BACK+RIGHT]],
[TOP+LEFT, []],
[TOP+RIGHT, []],
[FWD+LEFT, [TOP+FWD, BOT+FWD]],
[FWD+RIGHT, [TOP+FWD, BOT+FWD]],
[BACK+LEFT, [TOP+BACK, BOT+BACK]],
[BACK+RIGHT, [TOP+BACK, BOT+BACK]],
],
i = search([from], flip_edges, num_returns_per_match=1)[0],
check = assert(i!=[], "Bad edge vector.")
) in_list(to,flip_edges[i][1]);
function _edge_corner_numbers(vec) =
let(
v2 = [for (i=idx(vec)) vec[i]? (vec[i]+1)/2*pow(2,i) : 0],
off = v2.x + v2.y + v2.z,
xs = [0, if (!vec.x) 1],
ys = [0, if (!vec.y) 2],
zs = [0, if (!vec.z) 4]
) [for (x=xs, y=ys, z=zs) x+y+z + off];
function _gather_contiguous_edges(edge_corners) =
let(
no_tri_corners = all([for(cn = [0:7]) len([for (ec=edge_corners) if(in_list(cn,ec[1])) 1])<3]),
check = assert(no_tri_corners, "Cannot have three edges that meet at the same corner.")
)
_gather_contiguous_edges_r(
[for (i=idx(edge_corners)) if(i) edge_corners[i]],
edge_corners[0][1],
[edge_corners[0][0]], []);
function _gather_contiguous_edges_r(edge_corners, ecns, curr, out) =
len(edge_corners)==0? [each out, curr] :
let(
i1 = [
for (i = idx(edge_corners))
if (in_list(ecns[0], edge_corners[i][1]))
i
],
i2 = [
for (i = idx(edge_corners))
if (in_list(ecns[1], edge_corners[i][1]))
i
]
) !i1 && !i2? _gather_contiguous_edges_r(
[for (i=idx(edge_corners)) if(i) edge_corners[i]],
edge_corners[0][1],
[edge_corners[0][0]],
[each out, curr]
) : let(
nu_curr = [
if (i1) edge_corners[i1[0]][0],
each curr,
if (i2) edge_corners[i2[0]][0],
],
nu_ecns = [
if (!i1) ecns[0] else [
for (ecn = edge_corners[i1[0]][1])
if (ecn != ecns[0]) ecn
][0],
if (!i2) ecns[1] else [
for (ecn = edge_corners[i2[0]][1])
if (ecn != ecns[1]) ecn
][0],
],
rem = [
for (i = idx(edge_corners))
if (i != i1[0] && i != i2[0])
edge_corners[i]
]
)
_gather_contiguous_edges_r(rem, nu_ecns, nu_curr, out);
function _edge_transition_inversions(edge_string) =
let(
// boolean cumulative sum
bcs = function(list, i=0, inv=false, out=[])
i>=len(list)? out :
let( nu_inv = list[i]? !inv : inv )
bcs(list, i+1, nu_inv, [each out, nu_inv]),
inverts = bcs([
false,
for(i = idx(edge_string)) if (i)
_edge_transition_needs_flip(
edge_string[i-1],
edge_string[i]
)
]),
boti = [for(i = idx(edge_string)) if (edge_string[i].z<0) i],
topi = [for(i = idx(edge_string)) if (edge_string[i].z>0) i],
lfti = [for(i = idx(edge_string)) if (edge_string[i].x<0) i],
rgti = [for(i = idx(edge_string)) if (edge_string[i].x>0) i],
idx = [for (m = [boti, topi, lfti, rgti]) if(m) m[0]][0],
rinverts = inverts[idx] == false? inverts : [for (x = inverts) !x]
) rinverts;
function _is_closed_edge_loop(edge_string) =
let(
e1 = edge_string[0],
e2 = last(edge_string)
)
len([for (i=[0:2]) if (abs(e1[i])==1 && e1[i]==e2[i]) 1]) == 1 &&
len([for (i=[0:2]) if (e1[i]==0 && abs(e2[i])==1) 1]) == 1 &&
len([for (i=[0:2]) if (e2[i]==0 && abs(e1[i])==1) 1]) == 1;
function _edge_pair_perp_vec(e1,e2) =
[for (i=[0:2]) if (abs(e1[i])==1 && e1[i]==e2[i]) -e1[i] else 0];
req_children($children);
check1 = assert($parent_geom != undef, "No object to attach to!")
assert(in_list(corner_type, ["none", "round", "chamfer", "sharp"]))
assert(is_bool(flip));
edges = _edges(edges, except=except);
vecs = [
for (i = [0:3], axis=[0:2])
if (edges[axis][i]>0)
EDGE_OFFSETS[axis][i]
];
all_vecs_are_edges = all([for (vec = vecs) sum(v_abs(vec))==2]);
check2 = assert(all_vecs_are_edges, "All vectors must be edges.");
edge_corners = [for (vec = vecs) [vec, _edge_corner_numbers(vec)]];
edge_strings = _gather_contiguous_edges(edge_corners);
for (edge_string = edge_strings) {
inverts = _edge_transition_inversions(edge_string);
flipverts = [for (x = inverts) flip? !x : x];
vecpairs = [
for (i = idx(edge_string))
let (p = _default_edge_orientation(edge_string[i]))
flipverts[i]? [p.y,p.x] : p
];
is_loop = _is_closed_edge_loop(edge_string);
for (i = idx(edge_string)) {
if (corner_type!="none" && (i || is_loop)) {
e1 = select(edge_string,i-1);
e2 = select(edge_string,i);
vp1 = select(vecpairs,i-1);
vp2 = select(vecpairs,i);
pvec = _edge_pair_perp_vec(e1,e2);
pos = [for (i=[0:2]) e1[i]? e1[i] : e2[i]];
if (vp1.y == vp2.y) {
default_tag("remove")
position(pos) {
mirT = _corner_orientation(pos, pvec);
multmatrix(mirT) {
if (corner_type=="chamfer") {
fn = $fn;
rotate_extrude(angle=90, $fn=4)
right_half(planar=true, $fn=fn)
children();
rotate_extrude(angle=90, $fn=4)
left_half(planar=true, $fn=fn)
children();
} else if (corner_type=="round") {
rotate_extrude(angle=90)
right_half(planar=true)
children();
rotate_extrude(angle=90)
left_half(planar=true)
children();
} else { //corner_type == "sharp"
intersection() {
rot([90,0, 0]) linear_extrude(height=100,center=true,convexity=convexity) children();
rot([90,0,90]) linear_extrude(height=100,center=true,convexity=convexity) children();
}
}
}
}
}
}
}
for (i = idx(edge_string)) {
edge_profile(edge_string[i], excess=excess, convexity=convexity) {
if (flipverts[i]) {
mirror([-1,1]) children();
} else {
children();
}
}
}
}
}
// Module: corner_profile()
// Synopsis: Rotationally extrudes a 2d edge profile into corner mask on the given corners of the parent.
// SynTags: Geom
// Topics: Attachments, Masking
// See Also: attachable(), position(), attach(), face_profile(), edge_profile(), corner_mask(), face_mask(), edge_mask()
// Usage:
@ -1718,15 +2012,15 @@ module edge_profile(edges=EDGES_ALL, except=[], excess=0.01, convexity=10) {
// mask2d_teardrop(r=10, angle=40);
// }
module corner_profile(corners=CORNERS_ALL, except=[], r, d, convexity=10) {
assert($parent_geom != undef, "No object to attach to!");
check1 = assert($parent_geom != undef, "No object to attach to!");
r = max(0.01, get_radius(r=r, d=d, dflt=undef));
assert(is_num(r));
check2 = assert(is_num(r), "Bad r/d argument.");
corners = _corners(corners, except=except);
vecs = [for (i = [0:7]) if (corners[i]>0) CORNER_OFFSETS[i]];
all_vecs_are_corners = all([for (vec = vecs) sum(v_abs(vec))==3]);
check3 = assert(all_vecs_are_corners, "All vectors must be corners.");
for ($idx = idx(vecs)) {
vec = vecs[$idx];
vcount = (vec.x?1:0) + (vec.y?1:0) + (vec.z?1:0);
dummy=assert(vcount == 3, "Not an edge vector!");
anch = _find_anchor(vec, $parent_geom);
$attach_to = undef;
$attach_anchor = anch;
@ -2074,6 +2368,7 @@ module attachable(
// Function: reorient()
// Synopsis: Calculates the transformation matrix needed to reorient an object.
// SynTags: Trans, Path, VNF
// Topics: Attachments
// See Also: reorient(), attachable()
// Usage: Square/Trapezoid Geometry
@ -2090,25 +2385,25 @@ module attachable(
// pts = reorient(anchor, spin, [orient], two_d=true, region=, [extent=], p=, ...);
// Usage: Cubical/Prismoidal Geometry
// mat = reorient(anchor, spin, [orient], size=, [size2=], [shift=], ...);
// pts = reorient(anchor, spin, [orient], size=, [size2=], [shift=], p=, ...);
// vnf = reorient(anchor, spin, [orient], size=, [size2=], [shift=], p=, ...);
// Usage: Cylindrical Geometry
// mat = reorient(anchor, spin, [orient], r=|d=, l=, [axis=], ...);
// pts = reorient(anchor, spin, [orient], r=|d=, l=, [axis=], p=, ...);
// vnf = reorient(anchor, spin, [orient], r=|d=, l=, [axis=], p=, ...);
// Usage: Conical Geometry
// mat = reorient(anchor, spin, [orient], r1=|d1=, r2=|d2=, l=, [axis=], ...);
// pts = reorient(anchor, spin, [orient], r1=|d1=, r2=|d2=, l=, [axis=], p=, ...);
// vnf = reorient(anchor, spin, [orient], r1=|d1=, r2=|d2=, l=, [axis=], p=, ...);
// Usage: Spheroid/Ovoid Geometry
// mat = reorient(anchor, spin, [orient], r|d=, ...);
// pts = reorient(anchor, spin, [orient], r|d=, p=, ...);
// vnf = reorient(anchor, spin, [orient], r|d=, p=, ...);
// Usage: Extruded Path/Polygon Geometry
// mat = reorient(anchor, spin, [orient], path=, l=|h=, [extent=], ...);
// pts = reorient(anchor, spin, [orient], path=, l=|h=, [extent=], p=, ...);
// vnf = reorient(anchor, spin, [orient], path=, l=|h=, [extent=], p=, ...);
// Usage: Extruded Region Geometry
// mat = reorient(anchor, spin, [orient], region=, l=|h=, [extent=], ...);
// pts = reorient(anchor, spin, [orient], region=, l=|h=, [extent=], p=, ...);
// vnf = reorient(anchor, spin, [orient], region=, l=|h=, [extent=], p=, ...);
// Usage: VNF Geometry
// mat = reorient(anchor, spin, [orient], vnf, [extent], ...);
// pts = reorient(anchor, spin, [orient], vnf, [extent], p=, ...);
// vnf = reorient(anchor, spin, [orient], vnf, [extent], p=, ...);
//
// Description:
// Given anchor, spin, orient, and general geometry info for a managed volume, this calculates

6
comparisons.scad
View File

@ -241,7 +241,7 @@ function are_ends_equal(list, eps=EPSILON) =
// Usage:
// bool = is_increasing(list, [strict]);
// Description:
// Returns true if the list is (non-strictly) increasing, or strictly increasing if strict is set to true.
// Returns true if the list is (non-strictly) increasing, or strictly increasing if `strict=true`.
// The list can be a list of any items that OpenSCAD can compare, or it can be a string which will be
// evaluated character by character.
// Arguments:
@ -266,7 +266,7 @@ function is_increasing(list,strict=false) =
// Usage:
// bool = is_decreasing(list, [strict]);
// Description:
// Returns true if the list is (non-strictly) decreasing, or strictly decreasing if strict is set to true.
// Returns true if the list is (non-strictly) decreasing, or strictly decreasing if `strict=true`.
// The list can be a list of any items that OpenSCAD can compare, or it can be a string which will be
// evaluated character by character.
// Arguments:
@ -532,7 +532,7 @@ function close_path(list,eps=EPSILON) =
list_wrap(list,eps);
// Function: list_unwrap()
// Synopsis: Removes the last item of a list if it's first and last values are equal.
// Synopsis: Removes the last item of a list if its first and last values are equal.
// Topics: List Handling, Paths
// See Also: list_wrap(), deduplicate()
// Usage:

1
constants.scad
View File

@ -130,6 +130,7 @@ INCH = 25.4;
// Constant: IDENT
// Synopsis: A constant containing the 3D identity transformation matrix.
// SynTags: Mat
// Topics: Constants, Affine, Matrices, Transforms
// See Also: ident()
// Description: Identity transformation matrix for three-dimensional transforms. Equal to `ident(4)`.

110
coords.scad
View File

@ -12,11 +12,11 @@
// Section: Coordinate Manipulation
// Function: point2d()
// Usage:
// pt = point2d(p, [fill]);
// Synopsis: Convert a vector to 2D.
// Topics: Coordinates, Points
// See Also: path2d(), point3d(), path3d()
// Synopsis: Convert a vector to 2d.
// Usage:
// pt = point2d(p, [fill]);
// Description:
// Returns a 2D vector/point from a 2D or 3D vector. If given a 3D point, removes the Z coordinate.
// Arguments:
@ -26,11 +26,12 @@ function point2d(p, fill=0) = assert(is_list(p)) [for (i=[0:1]) (p[i]==undef)? f
// Function: path2d()
// Usage:
// pts = path2d(points);
// Synopsis: Convert a path to 2D.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: point2d(), point3d(), path3d()
// Synopsis: Convert a path to 2d.
// Usage:
// pts = path2d(points);
// Description:
// Returns a list of 2D vectors/points from a list of 2D, 3D or higher dimensional vectors/points.
// Removes the extra coordinates from higher dimensional points. The input must be a path, where
@ -45,11 +46,11 @@ function path2d(points) =
// Function: point3d()
// Usage:
// pt = point3d(p, [fill]);
// Synopsis: Convert a vector to 3D.
// Topics: Coordinates, Points
// See Also: path2d(), point2d(), path3d()
// Synopsis: Convert a vector to 3d.
// Usage:
// pt = point3d(p, [fill]);
// Description:
// Returns a 3D vector/point from a 2D or 3D vector.
// Arguments:
@ -61,11 +62,12 @@ function point3d(p, fill=0) =
// Function: path3d()
// Synopsis: Convert a path to 3D.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: point2d(), path2d(), point3d()
// Usage:
// pts = path3d(points, [fill]);
// Topics: Coordinates, Points, Paths
// Synopsis: Convert a path to 3d.
// See Also: point2d(), path2d(), point3d()
// Description:
// Returns a list of 3D vectors/points from a list of 2D or higher dimensional vectors/points
// by removing extra coordinates or adding the z coordinate.
@ -86,11 +88,11 @@ function path3d(points, fill=0) =
// Function: point4d()
// Synopsis: Convert a vector to 4d.
// Topics: Coordinates, Points
// See Also: point2d(), path2d(), point3d(), path3d(), path4d()
// Usage:
// pt = point4d(p, [fill]);
// Topics: Coordinates, Points
// Synopsis: Convert a vector to 4d.
// See Also: point2d(), path2d(), point3d(), path3d(), path4d()
// Description:
// Returns a 4D vector/point from a 2D or 3D vector.
// Arguments:
@ -101,11 +103,12 @@ function point4d(p, fill=0) = assert(is_list(p))
// Function: path4d()
// Usage:
// pt = path4d(points, [fill]);
// Synopsis: Convert a path to 4d.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: point2d(), path2d(), point3d(), path3d(), point4d()
// Synopsis: Convert a path to 4d.
// Usage:
// pt = path4d(points, [fill]);
// Description:
// Returns a list of 4D vectors/points from a list of 2D or 3D vectors/points.
// Arguments:
@ -134,13 +137,14 @@ function path4d(points, fill=0) =
// Section: Coordinate Systems
// Function: polar_to_xy()
// Synopsis: Convert 2D polar coordinates to cartesian coordinates.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: xy_to_polar(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Usage:
// pt = polar_to_xy(r, theta);
// pt = polar_to_xy([R, THETA]);
// pts = polar_to_xy([[R,THETA], [R,THETA], ...]);
// Topics: Coordinates, Points, Paths
// Synopsis: Convert 2d polar coordinates to cartesian coordinates.
// See Also: xy_to_polar(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Description:
// Called with two arguments, converts the `r` and `theta` 2D polar coordinate into an `[X,Y]` cartesian coordinate.
// Called with one `[R,THETA]` vector argument, converts the 2D polar coordinate into an `[X,Y]` cartesian coordinate.
@ -172,13 +176,13 @@ function polar_to_xy(r,theta) =
// Function: xy_to_polar()
// Synopsis: Convert 2D cartesian coordinates to polar coordinates (radius and angle)
// Topics: Coordinates, Points, Paths
// See Also: polar_to_xy(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Usage:
// r_theta = xy_to_polar(x,y);
// r_theta = xy_to_polar([X,Y]);
// r_thetas = xy_to_polar([[X,Y], [X,Y], ...]);
// Topics: Coordinates, Points, Paths
// Synopsis: Convert 2d cartesian coordinates to polar coordinates (radius and angle)
// See Also: polar_to_xy(), xyz_to_cylindrical(), cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz()
// Description:
// Called with two arguments, converts the `x` and `y` 2D cartesian coordinate into a `[RADIUS,THETA]` polar coordinate.
// Called with one `[X,Y]` vector argument, converts the 2D cartesian coordinate into a `[RADIUS,THETA]` polar coordinate.
@ -209,16 +213,19 @@ function xy_to_polar(x, y) =
// Function: project_plane()
// Synopsis: Project a set of points onto a specified plane, returning 2D points.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: lift_plane()
// Usage:
// xy = project_plane(plane, p);
// Usage: To get a transform matrix
// M = project_plane(plane)
// Synopsis: Project a set of points onto a specified plane, returning 2d points.
// Description:
// Maps the provided 3d point(s) from 3D coordinates to a 2d coordinate system defined by `plane`. Points that are not
// Maps the provided 3D point(s) from 3D coordinates to a 2D coordinate system defined by `plane`. Points that are not
// on the specified plane will be projected orthogonally onto the plane. This coordinate system is useful if you need
// to perform 2d operations on a coplanar set of data. After those operations are done you can return the data
// to 3d with `lift_plane()`. You could also use this to force approximately coplanar data to be exactly coplanar.
// to perform 2D operations on a coplanar set of data. After those operations are done you can return the data
// to 3D with `lift_plane()`. You could also use this to force approximately coplanar data to be exactly coplanar.
// The parameter p can be a point, path, region, bezier patch or VNF.
// The plane can be specified as
// - A list of three points. The planar coordinate system will have [0,0] at plane[0], and plane[1] will lie on the Y+ axis.
@ -227,7 +234,6 @@ function xy_to_polar(x, y) =
// .
// If you omit the point specification then `project_plane()` returns a rotation matrix that maps the specified plane to the XY plane.
// Note that if you apply this transformation to data lying on the plane it will produce 3D points with the Z coordinate of zero.
// Topics: Coordinates, Points, Paths
// Arguments:
// plane = plane specification or point list defining the plane
// p = 3D point, path, region, VNF or bezier patch to project
@ -271,7 +277,7 @@ function project_plane(plane,p) =
is_vnf(p) ? [project_plane(plane,p[0]), p[1]]
: is_list(p) && is_list(p[0]) && is_vector(p[0][0],3) ? // bezier patch or region
[for(plist=p) project_plane(plane,plist)]
: assert(is_vector(p,3) || is_path(p,3),str("Data must be a 3d point, path, region, vnf or bezier patch",p))
: assert(is_vector(p,3) || is_path(p,3),str("Data must be a 3D point, path, region, vnf or bezier patch",p))
is_matrix(plane,3,3) ?
assert(!is_collinear(plane),"Points defining the plane must not be collinear")
let(
@ -285,13 +291,14 @@ function project_plane(plane,p) =
// Function: lift_plane()
// Synopsis: Map a list of 2D points onto a plane in 3D.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: project_plane()
// Usage:
// xyz = lift_plane(plane, p);
// Usage: to get transform matrix
// M = lift_plane(plane);
// Synopsis: Map a list of 2d points onto a plane in 3d.
// Topics: Coordinates, Points, Paths
// See Also: project_plane()
// Description:
// Converts the given 2D point on the plane to 3D coordinates of the specified plane.
// The parameter p can be a point, path, region, bezier patch or VNF.
@ -327,7 +334,7 @@ function lift_plane(plane, p) =
: is_vnf(p) ? [lift_plane(plane,p[0]), p[1]]
: is_list(p) && is_list(p[0]) && is_vector(p[0][0],3) ? // bezier patch or region
[for(plist=p) lift_plane(plane,plist)]
: assert(is_vector(p,2) || is_path(p,2),"Data must be a 2d point, path, region, vnf or bezier patch")
: assert(is_vector(p,2) || is_path(p,2),"Data must be a 2D point, path, region, vnf or bezier patch")
is_matrix(plane,3,3) ?
let(
v = plane[2]-plane[0],
@ -338,13 +345,14 @@ function lift_plane(plane, p) =
// Function: cylindrical_to_xyz()
// Synopsis: Convert cylindrical coordinates to cartesian coordinates.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: xyz_to_cylindrical(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Usage:
// pt = cylindrical_to_xyz(r, theta, z);
// pt = cylindrical_to_xyz([RADIUS,THETA,Z]);
// pts = cylindrical_to_xyz([[RADIUS,THETA,Z], [RADIUS,THETA,Z], ...]);
// Topics: Coordinates, Points, Paths
// See Also: xyz_to_cylindrical(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Synopsis: Convert cylindrical coordinates to cartesian coordinates.
// Description:
// Called with three arguments, converts the `r`, `theta`, and 'z' 3D cylindrical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with one `[RADIUS,THETA,Z]` vector argument, converts the 3D cylindrical coordinate into an `[X,Y,Z]` cartesian coordinate.
@ -368,13 +376,13 @@ function cylindrical_to_xyz(r,theta,z) =
// Function: xyz_to_cylindrical()
// Synopsis: Convert 3D cartesian coordinates to cylindrical coordinates.
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Usage:
// rtz = xyz_to_cylindrical(x,y,z);
// rtz = xyz_to_cylindrical([X,Y,Z]);
// rtzs = xyz_to_cylindrical([[X,Y,Z], [X,Y,Z], ...]);
// Topics: Coordinates, Points, Paths
// Synopsis: Convert 3d cartesian coordinates to cylindrical coordinates.
// See Also: cylindrical_to_xyz(), xy_to_polar(), polar_to_xy(), xyz_to_spherical(), spherical_to_xyz()
// Description:
// Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into a `[RADIUS,THETA,Z]` cylindrical coordinate.
// Called with one `[X,Y,Z]` vector argument, converts the 3D cartesian coordinate into a `[RADIUS,THETA,Z]` cylindrical coordinate.
@ -399,6 +407,10 @@ function xyz_to_cylindrical(x,y,z) =
// Function: spherical_to_xyz()
// Synopsis: Convert spherical coordinates to 3D cartesian coordinates.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz()
// Usage:
// pt = spherical_to_xyz(r, theta, phi);
// pt = spherical_to_xyz([RADIUS,THETA,PHI]);
@ -408,9 +420,6 @@ function xyz_to_cylindrical(x,y,z) =
// Called with one `[RADIUS,THETA,PHI]` vector argument, converts the 3D spherical coordinate into an `[X,Y,Z]` cartesian coordinate.
// Called with a list of `[RADIUS,THETA,PHI]` vector arguments, converts each 3D spherical coordinate into `[X,Y,Z]` cartesian coordinates.
// Theta is the angle counter-clockwise of X+ on the XY plane. Phi is the angle down from the Z+ pole.
// Synopsis: Convert spherical coordinates to 3d cartesian coordinates.
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz()
// Arguments:
// r = distance from origin.
// theta = angle in degrees, counter-clockwise of X+ on the XY plane.
@ -435,7 +444,7 @@ function spherical_to_xyz(r,theta,phi) =
// r_theta_phi = xyz_to_spherical([X,Y,Z])
// r_theta_phis = xyz_to_spherical([[X,Y,Z], [X,Y,Z], ...])
// Topics: Coordinates, Points, Paths
// Synopsis: Convert 3d cartesian coordinates to spherical coordinates.
// Synopsis: Convert 3D cartesian coordinates to spherical coordinates.
// See Also: cylindrical_to_xyz(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz(), xyz_to_altaz()
// Description:
// Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into a `[RADIUS,THETA,PHI]` spherical coordinate.
@ -461,13 +470,14 @@ function xyz_to_spherical(x,y,z) =
// Function: altaz_to_xyz()
// Synopsis: Convert altitude/azimuth/range to 3D cartesian coordinates.
// SynTags: Path
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), xyz_to_altaz()
// Usage:
// pt = altaz_to_xyz(alt, az, r);
// pt = altaz_to_xyz([ALT,AZ,R]);
// pts = altaz_to_xyz([[ALT,AZ,R], [ALT,AZ,R], ...]);
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), xyz_to_altaz()
// Synopsis: Convert altitude/azimuth/range to 3d cartesian coordinates.
// Description:
// Convert altitude/azimuth/range coordinates to 3D cartesian coordinates.
// Called with three arguments, converts the `alt`, `az`, and 'r' 3D altitude-azimuth coordinate into an `[X,Y,Z]` cartesian coordinate.
@ -493,13 +503,13 @@ function altaz_to_xyz(alt,az,r) =
// Function: xyz_to_altaz()
// Synopsis: Convert 3D cartesian coordinates to [altitude,azimuth,range].
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz()
// Usage:
// alt_az_r = xyz_to_altaz(x,y,z);
// alt_az_r = xyz_to_altaz([X,Y,Z]);
// alt_az_rs = xyz_to_altaz([[X,Y,Z], [X,Y,Z], ...]);
// Topics: Coordinates, Points, Paths
// See Also: cylindrical_to_xyz(), xyz_to_spherical(), spherical_to_xyz(), xyz_to_cylindrical(), altaz_to_xyz()
// Synopsis: Convert 3d cartesian coordinates to [altitude,azimuth,range].
// Description:
// Converts 3D cartesian coordinates to altitude/azimuth/range coordinates.
// Called with three arguments, converts the `x`, `y`, and `z` 3D cartesian coordinate into an `[ALTITUDE,AZIMUTH,RANGE]` coordinate.

17
cubetruss.scad
View File

@ -18,6 +18,7 @@ $cubetruss_clip_thickness = 1.6;
// Module: cubetruss()
// Synopsis: Creates a multi-cube straight cubetruss shape.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -35,7 +36,6 @@ $cubetruss_clip_thickness = 1.6;
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss(extents=3);
// cubetruss(extents=3, clips=FRONT);
@ -91,6 +91,7 @@ module cubetruss(extents=6, clips=[], bracing, size, strut, clipthick, anchor=CE
// Module: cubetruss_corner()
// Synopsis: Creates a multi-cube corner cubetruss shape.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -108,7 +109,6 @@ module cubetruss(extents=6, clips=[], bracing, size, strut, clipthick, anchor=CE
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_corner(extents=2);
// cubetruss_corner(extents=2, h=2);
@ -167,6 +167,7 @@ module cubetruss_corner(h=1, extents=[1,1,0,0,1], bracing, size, strut, clipthic
// Module: cubetruss_support()
// Synopsis: Creates a cubetruss support structure shape.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -181,7 +182,6 @@ module cubetruss_corner(h=1, extents=[1,1,0,0,1], bracing, size, strut, clipthic
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Example(VPT=[0,0,0],VPD=150):
// cubetruss_support();
// Example(VPT=[0,0,0],VPD=200):
@ -234,6 +234,7 @@ module cubetruss_support(size, strut, extents=1, anchor=CENTER, spin=0, orient=U
// Module: cubetruss_foot()
// Synopsis: Creates a foot that can connect two cubetrusses.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -250,7 +251,6 @@ module cubetruss_support(size, strut, extents=1, anchor=CENTER, spin=0, orient=U
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_foot(w=1);
// cubetruss_foot(w=3);
@ -314,6 +314,7 @@ module cubetruss_foot(w=1, size, strut, clipthick, anchor=CENTER, spin=0, orient
// Module: cubetruss_joiner()
// Synopsis: Creates a joiner that can connect two cubetrusses end-to-end.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -331,7 +332,6 @@ module cubetruss_foot(w=1, size, strut, clipthick, anchor=CENTER, spin=0, orient
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_joiner(w=1, vert=false);
// cubetruss_joiner(w=1, vert=true);
@ -385,6 +385,7 @@ module cubetruss_joiner(w=1, vert=true, size, strut, clipthick, anchor=CENTER, s
// Module: cubetruss_uclip()
// Synopsis: Creates a joiner that can connect two cubetrusses end-to-end.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -401,7 +402,6 @@ module cubetruss_joiner(w=1, vert=true, size, strut, clipthick, anchor=CENTER, s
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_uclip(dual=false);
// cubetruss_uclip(dual=true);
@ -437,6 +437,7 @@ module cubetruss_uclip(dual=true, size, strut, clipthick, anchor=CENTER, spin=0,
// Module: cubetruss_segment()
// Synopsis: Creates a single cubetruss cube.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -451,7 +452,6 @@ module cubetruss_uclip(dual=true, size, strut, clipthick, anchor=CENTER, spin=0,
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_segment(bracing=false);
// cubetruss_segment(bracing=true);
@ -509,6 +509,7 @@ module cubetruss_segment(size, strut, bracing, anchor=CENTER, spin=0, orient=UP)
// Module: cubetruss_clip()
// Synopsis: Creates a clip for the end of a cubetruss to snap-lock it to another cubetruss.
// SynTags: Geom
// Topics: Trusses, CubeTruss, FDM Optimized, Parts
// See Also: cubetruss_segment(), cubetruss_support(), cubetruss(), cubetruss_corner()
// Usage:
@ -525,7 +526,6 @@ module cubetruss_segment(size, strut, bracing, anchor=CENTER, spin=0, orient=UP)
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Topics: Attachable, Trusses
// Examples:
// cubetruss_clip(extents=2);
// cubetruss_clip(extents=1);
@ -588,7 +588,6 @@ module cubetruss_clip(extents=1, size, strut, clipthick, anchor=CENTER, spin=0,
// gaps = The number of extra strut widths to add in, corresponding to each time a truss butts up against another.
// size = The length of each side of the cubetruss cubes. Default: `$cubetruss_size` (usually 30)
// strut = The width of the struts on the cubetruss cubes. Default: `$cubetruss_strut_size` (usually 3)
// Topics: Trusses
function cubetruss_dist(cubes=0, gaps=0, size, strut) =
let(
size = is_undef(size)? $cubetruss_size : size,

62
distributors.scad
View File

@ -93,6 +93,7 @@
// Function&Module: move_copies()
// Synopsis: Translates copies of all children.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xcopies(), ycopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -145,6 +146,7 @@ function move_copies(a=[[0,0,0]],p=_NO_ARG) =
// Function&Module: xcopies()
// Synopsis: Places copies of children along the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), ycopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -230,6 +232,7 @@ function xcopies(spacing, n, l, sp, p=_NO_ARG) =
// Function&Module: ycopies()
// Synopsis: Places copies of children along the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), zcopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -315,6 +318,7 @@ function ycopies(spacing, n, l, sp, p=_NO_ARG) =
// Function&Module: zcopies()
// Synopsis: Places copies of children along the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), line_copies(), grid_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -415,6 +419,7 @@ function zcopies(spacing, n, l, sp, p=_NO_ARG) =
// Function&Module: line_copies()
// Synopsis: Places copies of children along an arbitrary line.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), zcopies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -548,6 +553,7 @@ function line_copies(spacing, n, l, p1, p2, p=_NO_ARG) =
// Function&Module: grid_copies()
// Synopsis: Places copies of children in an [X,Y] grid.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies()
//
@ -771,6 +777,7 @@ function grid_copies(spacing, n, size, stagger=false, inside=undef, nonzero, p=_
// Function&Module: rot_copies()
// Synopsis: Rotates copies of children.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -895,6 +902,7 @@ function rot_copies(rots=[], v, cp=[0,0,0], n, sa=0, offset=0, delta=[0,0,0], su
// Function&Module: xrot_copies()
// Synopsis: Rotates copies of children around the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -974,6 +982,7 @@ function xrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG)
// Function&Module: yrot_copies()
// Synopsis: Rotates copies of children around the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1053,6 +1062,7 @@ function yrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG)
// Function&Module: zrot_copies()
// Synopsis: Rotates copies of children around the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1132,6 +1142,7 @@ function zrot_copies(rots=[], cp=[0,0,0], n, sa=0, r, d, subrot=true, p=_NO_ARG)
// Function&Module: arc_copies()
// Synopsis: Distributes duplicates of children along an arc.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), sphere_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1256,6 +1267,7 @@ function arc_copies(
// Function&Module: sphere_copies()
// Synopsis: Distributes copies of children over the surface of a sphere.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Rotation, Copiers
// See Also: rot_copies(), xrot_copies(), yrot_copies(), zrot_copies(), arc_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1363,6 +1375,7 @@ function sphere_copies(n=100, r=undef, d=undef, cone_ang=90, scale=[1,1,1], perp
// Function&Module: path_copies()
// Synopsis: Uniformly distributes copies of children along a path.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Copiers
// See Also: line_copies(), move_copies(), xcopies(), ycopies(), zcopies(), grid_copies(), xflip_copy(), yflip_copy(), zflip_copy(), mirror_copy()
//
@ -1576,6 +1589,7 @@ function path_copies(path, n, spacing, sp=undef, dist, rotate_children=true, dis
// Function&Module: xflip_copy()
// Synopsis: Makes a copy of children mirrored across the X axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: yflip_copy(), zflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1626,6 +1640,7 @@ function xflip_copy(offset=0, x=0, p=_NO_ARG) =
// Function&Module: yflip_copy()
// Synopsis: Makes a copy of children mirrored across the Y axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), zflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1676,6 +1691,7 @@ function yflip_copy(offset=0, y=0, p=_NO_ARG) =
// Function&Module: zflip_copy()
// Synopsis: Makes a copy of children mirrored across the Z axis.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), yflip_copy(), mirror_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1726,6 +1742,7 @@ function zflip_copy(offset=0, z=0, p=_NO_ARG) =
// Function&Module: mirror_copy()
// Synopsis: Makes a copy of children mirrored across a given plane.
// SynTags: MatList, Trans
// Topics: Transformations, Distributors, Translation, Copiers
// See Also: xflip_copy(), yflip_copy(), zflip_copy(), path_copies(), move_copies(), xcopies(), ycopies(), zcopies(), line_copies(), grid_copies()
//
@ -1815,6 +1832,14 @@ function mirror_copy(v=[0,0,1], offset=0, cp, p=_NO_ARG) =
// Section: Distributing children individually along a line
///////////////////
// Module: xdistribute()
// Synopsis: Distributes each child, individually, out along the X axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// xdistribute(spacing, [sizes]) CHILDREN;
// xdistribute(l=, [sizes=]) CHILDREN;
//
//
// Description:
// Spreads out the children individually along the X axis.
@ -1822,10 +1847,6 @@ function mirror_copy(v=[0,0,1], offset=0, cp, p=_NO_ARG) =
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// xdistribute(spacing, [sizes]) CHILDREN;
// xdistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
@ -1861,6 +1882,13 @@ module xdistribute(spacing=10, sizes=undef, l=undef)
// Module: ydistribute()
// Synopsis: Distributes each child, individually, out along the Y axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// ydistribute(spacing, [sizes]) CHILDREN;
// ydistribute(l=, [sizes=]) CHILDREN;
//
// Description:
// Spreads out the children individually along the Y axis.
@ -1868,10 +1896,6 @@ module xdistribute(spacing=10, sizes=undef, l=undef)
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// ydistribute(spacing, [sizes]) CHILDREN;
// ydistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
@ -1907,6 +1931,13 @@ module ydistribute(spacing=10, sizes=undef, l=undef)
// Module: zdistribute()
// Synopsis: Distributes each child, individually, out along the Z axis.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// zdistribute(spacing, [sizes]) CHILDREN;
// zdistribute(l=, [sizes=]) CHILDREN;
//
// Description:
// Spreads out each individual child along the Z axis.
@ -1914,10 +1945,6 @@ module ydistribute(spacing=10, sizes=undef, l=undef)
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// zdistribute(spacing, [sizes]) CHILDREN;
// zdistribute(l=, [sizes=]) CHILDREN;
//
// Arguments:
// spacing = spacing between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.
@ -1954,6 +1981,13 @@ module zdistribute(spacing=10, sizes=undef, l=undef)
// Module: distribute()
// Synopsis: Distributes each child, individually, out along an arbitrary line.
// SynTags: Trans
// See Also: xdistribute(), ydistribute(), zdistribute(), distribute()
//
// Usage:
// distribute(spacing, sizes, dir) CHILDREN;
// distribute(l=, [sizes=], [dir=]) CHILDREN;
//
// Description:
// Spreads out the children individually along the direction `dir`.
@ -1961,10 +1995,6 @@ module zdistribute(spacing=10, sizes=undef, l=undef)
// This is useful for laying out groups of disparate objects
// where you only really care about the spacing between them.
//
// Usage:
// distribute(spacing, sizes, dir) CHILDREN;
// distribute(l=, [sizes=], [dir=]) CHILDREN;
//
// Arguments:
// spacing = Spacing to add between each child. (Default: 10.0)
// sizes = Array containing how much space each child will need.

18
drawing.scad
View File

@ -18,6 +18,7 @@
// Module: stroke()
// Synopsis: Draws a line along a path or region boundry.
// SynTags: Geom
// Topics: Paths (2D), Paths (3D), Drawing Tools
// See Also: offset_stroke(), path_sweep()
// Usage:
@ -588,6 +589,7 @@ module stroke(
// Function&Module: dashed_stroke()
// Synopsis: Draws a dashed line along a path or region boundry.
// SynTags: Geom, PathList
// Topics: Paths, Drawing Tools
// See Also: stroke(), path_cut()
// Usage: As a Module
@ -665,8 +667,10 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, round
// Section: Computing paths
// Function&Module: arc()
// Synopsis: Draws a 2d pie-slice or returns 2D or 3D path forming an arc.
// Topics: Shapes (2D), Path Generators (2D)
// Synopsis: Draws a 2D pie-slice or returns 2D or 3D path forming an arc.
// SynTags: Geom, Path
// Topics: Paths (2D), Paths (3D), Shapes (2D), Path Generators
// See Also: pie_slice(), stroke()
//
// Usage: 2D arc from 0º to `angle` degrees.
// path=arc(n, r|d=, angle);
@ -684,7 +688,6 @@ module dashed_stroke(path, dashpat=[3,3], width=1, closed=false, fit=true, round
// path=arc(n, corner=[P0,P1,P2], r=);
// Usage: as module
// arc(...) [ATTACHMENTS];
// Topics: Paths (2D), Paths (3D), Shapes (2D), Path Generators
// Description:
// If called as a function, returns a 2D or 3D path forming an arc.
// If called as a module, creates a 2D arc polygon or pie slice shape.
@ -861,7 +864,9 @@ module arc(n, r, angle, d, cp, points, corner, width, thickness, start, wedge=fa
// Function: helix()
// Synopsis: Creates a 2d spiral or 3d helical path.
// SynTags: Path
// Topics: Path Generators, Paths, Drawing Tools
// See Also: pie_slice(), stroke(), thread_helix(), path_sweep()
//
// Usage:
// path = helix(l|h, [turns=], [angle=], r=|r1=|r2=, d=|d1=|d2=);
@ -916,10 +921,11 @@ function _normal_segment(p1,p2) =
// Function: turtle()
// Synopsis: Uses [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) to generate a 2D path.
// SynTags: Path
// Topics: Shapes (2D), Path Generators (2D), Mini-Language
// See Also: turtle3d()
// See Also: turtle3d(), stroke(), path_sweep()
// Usage:
// turtle(commands, [state], [full_state=], [repeat=])
// path = turtle(commands, [state], [full_state=], [repeat=])
// Description:
// Use a sequence of [turtle graphics]{https://en.wikipedia.org/wiki/Turtle_graphics} commands to generate a path. The parameter `commands` is a list of
// turtle commands and optional parameters for each command. The turtle state has a position, movement direction,
@ -1179,7 +1185,9 @@ function _turtle_command(command, parm, parm2, state, index) =
// Module: debug_polygon()
// Synopsis: Draws an annotated polygon.
// SynTags: Geom
// Topics: Shapes (2D)
// See Also: debug_vnf(), debug_bezier()
//
// Usage:
// debug_polygon(points, paths, [vertices=], [edges=], [convexity=], [size=]);

7
gears.scad
View File

@ -27,6 +27,7 @@
// Function&Module: spur_gear()
// Synopsis: Creates a spur gear shape.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
@ -193,6 +194,7 @@ module spur_gear(
// Function&Module: spur_gear2d()
// Synopsis: Creates a 2D spur gear shape.
// SynTags: Geom, Path
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As Module
@ -294,6 +296,7 @@ module spur_gear2d(
// Function&Module: rack()
// Synopsis: Creates a gear rack shape.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack2d(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
@ -443,6 +446,7 @@ function rack(
// Function&Module: rack2d()
// Synopsis: Creates a 2D gear rack shape.
// SynTags: Geom, Path
// Topics: Gears, Parts
// See Also: rack(), spur_gear(), spur_gear2d(), bevel_gear()
// Usage: As a Module
@ -566,6 +570,7 @@ module rack2d(
// Function&Module: bevel_gear()
// Synopsis: Creates a possibly spiral beveled gear shape.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear()
// Usage: As a Module
@ -826,6 +831,7 @@ module bevel_gear(
// Function&Module: worm()
// Synopsis: Creates a worm shape that will mate with a worm gear.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: worm(), worm_gear(), rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear()
// Usage: As a Module
@ -946,6 +952,7 @@ module worm(
// Function&Module: worm_gear()
// Synopsis: Creates a worm gear shape that will mate with a worm.
// SynTags: Geom, VNF
// Topics: Gears, Parts
// See Also: worm(), worm_gear(), rack(), rack2d(), spur_gear(), spur_gear2d(), bevel_pitch_angle(), bevel_gear()
// Usage: As a Module

259
geometry.scad
View File

@ -15,10 +15,11 @@
// Section: Lines, Rays, and Segments
// Function: is_point_on_line()
// Synopsis: Determine if a point is on a line, ray or segment.
// Topics: Geometry, Points, Segments
// See Also: is_collinear(), is_point_on_line(), point_line_distance(), line_from_points()
// Usage:
// pt = is_point_on_line(point, line, [bounded], [eps]);
// Topics: Geometry, Points, Segments
// Synopsis: Determine if a point is on a line, ray or segment.
// Description:
// Determine if the point is on the line segment, ray or segment defined by the two between two points.
// Returns true if yes, and false if not. If bounded is set to true it specifies a segment, with
@ -140,10 +141,11 @@ function _point_left_of_line2d(point, line, eps=EPSILON) =
// Function: is_collinear()
// Synopsis: Determine if points are collinear.
// Topics: Geometry, Points, Collinearity
// See Also: is_collinear(), is_point_on_line(), point_line_distance(), line_from_points()
// Usage:
// bool = is_collinear(a, [b, c], [eps]);
// Synopsis: Determine if a points are collinear.
// Topics: Geometry, Points, Collinearity
// Description:
// Returns true if the points `a`, `b` and `c` are co-linear or if the list of points `a` is collinear.
// Arguments:
@ -162,10 +164,11 @@ function is_collinear(a, b, c, eps=EPSILON) =
// Function: point_line_distance()
// Synopsis: Find shortest distance from point to a line, segment or ray.
// Topics: Geometry, Points, Lines, Distance
// See Also: is_collinear(), is_point_on_line(), point_line_distance(), line_from_points()
// Usage:
// dist = point_line_distance(line, pt, [bounded]);
// Topics: Geometry, Points, Lines, Distance
// Synopsis: Find shortest distance from point to a line, segment or ray.
// Description:
// Finds the shortest distance from the point `pt` to the specified line, segment or ray.
// The bounded parameter specifies the whether the endpoints give a ray or segment.
@ -187,11 +190,11 @@ function point_line_distance(pt, line, bounded=false) =
// Function: segment_distance()
// Usage:
// dist = segment_distance(seg1, seg2, [eps]);
// Synopsis: Find smallest distance between two line semgnets.
// Topics: Geometry, Segments, Distance
// See Also: convex_collision(), convex_distance()
// Synopsis: Find smallest distance between two line semgnets.
// Usage:
// dist = segment_distance(seg1, seg2, [eps]);
// Description:
// Returns the smallest distance of the points on two given line segments.
// Arguments:
@ -207,13 +210,14 @@ function segment_distance(seg1, seg2,eps=EPSILON) =
// Function: line_normal()
// Synopsis: Return normal vector to given line.
// Topics: Geometry, Lines
// See Also: line_intersection(), line_from_points()
// Usage:
// vec = line_normal([P1,P2])
// vec = line_normal(p1,p2)
// Topics: Geometry, Lines
// Description:
// Returns the 2D normal vector to the given 2D line. This is otherwise known as the perpendicular vector counter-clockwise to the given ray.
// Synopsis: Return normal vector to given line.
// Arguments:
// p1 = First point on 2D line.
// p2 = Second point on 2D line.
@ -255,9 +259,11 @@ function _general_line_intersection(s1,s2,eps=EPSILON) =
// Function: line_intersection()
// Synopsis: Compute intersection of two lines, segments or rays.
// Topics: Geometry, Lines
// See Also: line_normal(), line_from_points()
// Usage:
// pt = line_intersection(line1, line2, [bounded1], [bounded2], [bounded=], [eps=]);
// Synopsis: Compute intersection of two lines, segments or rays.
// Description:
// Returns the intersection point of any two 2D lines, segments or rays. Returns undef
// if they do not intersect. You specify a line by giving two distinct points on the
@ -316,10 +322,11 @@ function line_intersection(line1, line2, bounded1, bounded2, bounded, eps=EPSILO
// Function: line_closest_point()
// Synopsis: Find point on given line, segment or ray that is closest to a given point.
// Topics: Geometry, Lines, Distance
// See Also: line_normal(), point_line_distance()
// Usage:
// pt = line_closest_point(line, pt, [bounded]);
// Topics: Geometry, Lines, Distance
// Synopsis: Find point on given line, segment or ray that is closest to a given point.
// Description:
// Returns the point on the given line, segment or ray that is closest to the given point `pt`.
// The inputs `line` and `pt` args should be of the same dimension. The parameter bounded indicates
@ -401,10 +408,10 @@ function line_closest_point(line, pt, bounded=false) =
// Function: line_from_points()
// Usage:
// line = line_from_points(points, [fast], [eps]);
// Synopsis: Given a list of collinear points, return the line they define.
// Topics: Geometry, Lines, Points
// Usage:
// line = line_from_points(points, [fast], [eps]);
// Description:
// Given a list of 2 or more collinear points, returns two points defining a line containing them.
// If `fast` is false and the points are coincident or non-collinear, then `undef` is returned.
@ -428,10 +435,11 @@ function line_from_points(points, fast=false, eps=EPSILON) =
// Function: is_coplanar()
// Synopsis: Check if 3d points are coplanar and not collinear.
// Topics: Geometry, Coplanarity
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// bool = is_coplanar(points,[eps]);
// Topics: Geometry, Coplanarity
// Synopsis: Check if 3d points are coplanar and not collinear.
// Description:
// Returns true if the given 3D points are non-collinear and are on a plane.
// Arguments:
@ -449,11 +457,12 @@ function is_coplanar(points, eps=EPSILON) =
// Function: plane3pt()
// Synopsis: Return a plane from 3 points.
// Topics: Geometry, Planes
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// plane = plane3pt(p1, p2, p3);
// plane = plane3pt([p1, p2, p3]);
// Topics: Geometry, Planes
// Synopsis: Return a plane from 3 points.
// Description:
// Generates the normalized cartesian equation of a plane from three 3d points.
// Returns [A,B,C,D] where Ax + By + Cz = D is the equation of a plane.
@ -474,10 +483,11 @@ function plane3pt(p1, p2, p3) =
// Function: plane3pt_indexed()
// Synopsis: Given list of 3d points and 3 indices, return the plane they define.
// Topics: Geometry, Planes
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// plane = plane3pt_indexed(points, i1, i2, i3);
// Topics: Geometry, Planes
// Synopsis: Given list of 3d points and 3 indices, return the plane they define.
// Description:
// Given a list of 3d points, and the indices of three of those points,
// generates the normalized cartesian equation of a plane that those points all
@ -503,10 +513,11 @@ function plane3pt_indexed(points, i1, i2, i3) =
// Function: plane_from_normal()
// Usage:
// plane = plane_from_normal(normal, [pt])
// Synopsis: Return plane defined by normal vector and a point.
// Topics: Geometry, Planes
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// plane = plane_from_normal(normal, [pt])
// Description:
// Returns a plane defined by a normal vector and a point. If you omit `pt` you will get a plane
// passing through the origin.
@ -564,11 +575,11 @@ function _covariance_evec_eval(points) =
// Function: plane_from_points()
// Usage:
// plane = plane_from_points(points, [fast], [eps]);
// Synopsis: Return plane defined by a set of coplanar 3d points, with arbitrary normal direction.
// Topics: Geometry, Planes, Points
// See Also: plane_from_polygon()
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// plane = plane_from_points(points, [fast], [eps]);
// Description:
// Given a list of 3 or more coplanar 3D points, returns the coefficients of the normalized cartesian equation of a plane,
// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane and norm([A,B,C])=1.
@ -603,11 +614,11 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
// Function: plane_from_polygon()
// Usage:
// plane = plane_from_polygon(points, [fast], [eps]);
// Synopsis: Given a 3d planar polygon, returns directed plane.
// Topics: Geometry, Planes, Polygons
// See Also: plane_from_points()
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon()
// Usage:
// plane = plane_from_polygon(points, [fast], [eps]);
// Description:
// Given a 3D planar polygon, returns the normalized cartesian equation of its plane.
// Returns [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1.
@ -640,10 +651,11 @@ function plane_from_polygon(poly, fast=false, eps=EPSILON) =
// Function: plane_normal()
// Synopsis: Returns the normal vector to a plane.
// Topics: Geometry, Planes
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon(), plane_normal(), plane_offset()
// Usage:
// vec = plane_normal(plane);
// Topics: Geometry, Planes
// Synopsis: Returns the normal vector to a plane.
// Description:
// Returns the unit length normal vector for the given plane.
// Arguments:
@ -654,10 +666,11 @@ function plane_normal(plane) =
// Function: plane_offset()
// Synopsis: Returns the signed offset of the plane from the origin.
// Topics: Geometry, Planes
// See Also: plane3pt(), plane3pt_indexed(), plane_from_normal(), plane_from_points(), plane_from_polygon(), plane_normal(), plane_offset()
// Usage:
// d = plane_offset(plane);
// Topics: Geometry, Planes
// Synopsis: Returns the signed offset of the plane from the origin.
// Description:
// Returns coeficient D of the normalized plane equation `Ax+By+Cz=D`, or the scalar offset of the plane from the origin.
// This value may be negative.
@ -686,21 +699,22 @@ function _general_plane_line_intersection(plane, line, eps=EPSILON) =
/// Internal Function: normalize_plane()
// Usage:
// nplane = normalize_plane(plane);
/// Usage:
/// nplane = normalize_plane(plane);
/// Topics: Geometry, Planes
// Description:
// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one.
/// Description:
/// Returns a new representation [A,B,C,D] of `plane` where norm([A,B,C]) is equal to one.
function _normalize_plane(plane) =
assert( _valid_plane(plane), str("Invalid plane. ",plane ) )
plane/norm(point3d(plane));
// Function: plane_line_intersection()
// Synopsis: Returns the intersection of a plane and 3d line, segment or ray.
// Topics: Geometry, Planes, Lines, Intersection
// See Also: plane3pt(), plane_from_normal(), plane_from_points(), plane_from_polygon(), line_intersection()
// Usage:
// pt = plane_line_intersection(plane, line, [bounded], [eps]);
// Topics: Geometry, Planes, Lines, Intersection
// Synopsis: Returns the intersection of a plane and 3d line, segment or ray.
// Description:
// Takes a line, and a plane [A,B,C,D] where the equation of that plane is `Ax+By+Cz=D`.
// If `line` intersects `plane` at one point, then that intersection point is returned.
@ -727,11 +741,12 @@ function plane_line_intersection(plane, line, bounded=false, eps=EPSILON) =
// Function: plane_intersection()
// Synopsis: Returns the intersection of two or three planes.
// Topics: Geometry, Planes, Intersection
// See Also: plane3pt(), plane_from_normal(), plane_from_points(), plane_from_polygon(), line_intersection()
// Usage:
// line = plane_intersection(plane1, plane2)
// pt = plane_intersection(plane1, plane2, plane3)
// Topics: Geometry, Planes, Intersection
// Synopsis: Returns the intersection of two or three planes.
// Description:
// Compute the point which is the intersection of the three planes, or the line intersection of two planes.
// If you give three planes the intersection is returned as a point. If you give two planes the intersection
@ -763,10 +778,11 @@ function plane_intersection(plane1,plane2,plane3) =
// Function: plane_line_angle()
// Synopsis: Returns the angle between a plane and a 3d line.
// Topics: Geometry, Planes, Lines, Angle
// See Also: plane3pt(), plane_from_normal(), plane_from_points(), plane_from_polygon(), plane_intersection(), line_intersection(), vector_angle()
// Usage:
// angle = plane_line_angle(plane,line);
// Topics: Geometry, Planes, Lines, Angle
// Synopsis: Returns the angle between a plane and a 3d line.
// Description:
// Compute the angle between a plane [A, B, C, D] and a 3d line, specified as a pair of 3d points [p1,p2].
// The resulting angle is signed, with the sign positive if the vector p2-p1 lies above the plane, on
@ -784,10 +800,11 @@ function plane_line_angle(plane, line) =
// Function: plane_closest_point()
// Synopsis: Returns the orthogonal projection of points onto a plane.
// Topics: Geometry, Planes, Projection
// See Also: plane3pt(), line_closest_point(), point_plane_distance()
// Usage:
// pts = plane_closest_point(plane, points);
// Topics: Geometry, Planes, Projection
// Synopsis: Returns the orthogonal projection of points onto a plane.
// Description:
// Given a plane definition `[A,B,C,D]`, where `Ax+By+Cz=D`, and a list of 2d or
// 3d points, return the closest 3D orthogonal projection of the points on the plane.
@ -820,10 +837,11 @@ function plane_closest_point(plane, points) =
// Function: point_plane_distance()
// Synopsis: Determine distance between a point and plane.
// Topics: Geometry, Planes, Distance
// See Also: plane3pt(), line_closest_point(), plane_closest_point()
// Usage:
// dist = point_plane_distance(plane, point)
// Topics: Geometry, Planes, Distance
// Synopsis: Determine distance between a point and plane.
// Description:
// Given a plane as [A,B,C,D] where the cartesian equation for that plane
// is Ax+By+Cz=D, determines how far from that plane the given point is.
@ -852,10 +870,11 @@ function _pointlist_greatest_distance(points,plane) =
// Function: are_points_on_plane()
// Synopsis: Determine if all of the listed points are on a plane.
// Topics: Geometry, Planes, Points
// See Also: plane3pt(), line_closest_point(), plane_closest_point(), is_coplanar()
// Usage:
// bool = are_points_on_plane(points, plane, [eps]);
// Topics: Geometry, Planes, Points
// Synopsis: Determine if all of the listed points are on a plane.
// Description:
// Returns true if the given 3D points are on the given plane.
// Arguments:
@ -889,10 +908,11 @@ function _is_point_above_plane(plane, point) =
// Section: Circle Calculations
// Function: circle_line_intersection()
// Usage:
// pts = circle_line_intersection(r|d=, cp, line, [bounded], [eps=]);
// Synopsis: Find the intersection points between a 2d circle and a line, ray or segment.
// Topics: Geometry, Circles, Lines, Intersection
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// pts = circle_line_intersection(r|d=, cp, line, [bounded], [eps=]);
// Description:
// Find intersection points between a 2D circle and a line, ray or segment specified by two points.
// By default the line is unbounded. Returns the list of zero or more intersection points.
@ -963,10 +983,11 @@ function _circle_or_sphere_line_intersection(r, cp, line, bounded=false, d, eps=
// Function: circle_circle_intersection()
// Usage:
// pts = circle_circle_intersection(r1|d1=, cp1, r2|d2=, cp2, [eps]);
// Synopsis: Find the intersection points of two 2d circles.
// Topics: Geometry, Circles
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// pts = circle_circle_intersection(r1|d1=, cp1, r2|d2=, cp2, [eps]);
// Description:
// Compute the intersection points of two circles. Returns a list of the intersection points, which
// will contain two points in the general case, one point for tangent circles, or will be empty
@ -1030,11 +1051,12 @@ function circle_circle_intersection(r1, cp1, r2, cp2, eps=EPSILON, d1, d2) =
// Function: circle_2tangents()
// Synopsis: Given two 2d or 3d rays, find a circle tangent to both.
// Topics: Geometry, Circles, Tangents
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// circ = circle_2tangents(r|d=, pt1, pt2, pt3, [tangents=]);
// circ = circle_2tangents(r|d=, [PT1, PT2, PT3], [tangents=]);
// Topics: Geometry, Circles, Tangents
// Synopsis: Given two 2d or 3d rays, find a circle tangent to both.
// Description:
// Given a pair of 2d or 3d rays with a common origin, and a known circle radius/diameter, finds
// the centerpoint for the circle of that size that touches both rays tangentally.
@ -1108,7 +1130,7 @@ function circle_2tangents(r, pt1, pt2, pt3, tangents=false, d) =
assert(r!=undef, "Must specify either r or d.")
assert( ( is_path(pt1) && len(pt1)==3 && is_undef(pt2) && is_undef(pt3))
|| (is_matrix([pt1,pt2,pt3]) && (len(pt1)==2 || len(pt1)==3) ),
"Invalid input points." )
str("Invalid input points. pt1=",pt1,", pt2=",pt2,", pt3=",pt3))
is_undef(pt2)
? circle_2tangents(r, pt1[0], pt1[1], pt1[2], tangents=tangents)
: is_collinear(pt1, pt2, pt3)? undef :
@ -1131,11 +1153,12 @@ function circle_2tangents(r, pt1, pt2, pt3, tangents=false, d) =
// Function: circle_3points()
// Synopsis: Find a circle passing through three 2d or 3d points.
// Topics: Geometry, Circles
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// circ = circle_3points(pt1, pt2, pt3);
// circ = circle_3points([PT1, PT2, PT3]);
// Topics: Geometry, Circles
// Synopsis: Find a circle passing through three 2d or 3d points.
// Description:
// Returns the [CENTERPOINT, RADIUS, NORMAL] of the circle that passes through three non-collinear
// points where NORMAL is the normal vector of the plane that the circle is on (UP or DOWN if the points are 2D).
@ -1183,10 +1206,11 @@ function circle_3points(pt1, pt2, pt3) =
// Function: circle_point_tangents()
// Synopsis: Given a circle and point, find tangents to circle passing through the point.
// Topics: Geometry, Circles, Tangents
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// tangents = circle_point_tangents(r|d=, cp, pt);
// Topics: Geometry, Circles, Tangents
// Synopsis: Given a circle and point, find tangents to circle passing through the point.
// Description:
// Given a 2d circle and a 2d point outside that circle, finds the 2d tangent point(s) on the circle for a
// line passing through the point. Returns a list of zero or more 2D tangent points.
@ -1220,10 +1244,11 @@ function circle_point_tangents(r, cp, pt, d) =
// Function: circle_circle_tangents()
// Synopsis: Find tangents to a pair of circles in 2d.
// Topics: Geometry, Circles, Tangents
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// segs = circle_circle_tangents(r1|d1=, cp1, r2|d2=, cp2);
// Topics: Geometry, Circles, Tangents
// Synopsis: Find tangents to a pair of circles in 2d.
// Description:
// Computes 2d lines tangents to a pair of circles in 2d. Returns a list of line endpoints [p1,p2] where
// p1 is the tangent point on circle 1 and p2 is the tangent point on circle 2.
@ -1346,10 +1371,11 @@ function _noncollinear_triple(points,error=true,eps=EPSILON) =
// Function: sphere_line_intersection()
// Synopsis: Find intersection between a sphere and line, ray or segment.
// Topics: Geometry, Spheres, Lines, Intersection
// See Also: circle_line_intersection(), circle_circle_intersection(), circle_2tangents(), circle_3points(), circle_point_tangents(), circle_circle_tangents()
// Usage:
// isect = sphere_line_intersection(r|d=, cp, line, [bounded], [eps=]);
// Topics: Geometry, Spheres, Lines, Intersection
// Synopsis: Find intersection between a sphere and line, ray or segment.
// Description:
// Find intersection points between a sphere and a line, ray or segment specified by two points.
// By default the line is unbounded.
@ -1379,10 +1405,11 @@ function sphere_line_intersection(r, cp, line, bounded=false, d, eps=EPSILON) =
// Section: Polygons
// Function: polygon_area()
// Synopsis: Calculate area of a 2d or 3d polygon.
// Topics: Geometry, Polygons, Area
// See Also: polygon_area(), centroid(), polygon_normal(), point_in_polygon(), polygon_line_intersection()
// Usage:
// area = polygon_area(poly, [signed]);
// Topics: Geometry, Polygons, Area
// Synopsis: Calculate area of a 2d or 3d polygon.
// Description:
// Given a 2D or 3D simple planar polygon, returns the area of that polygon.
// If the polygon is non-planar the result is `undef.` If the polygon is self-intersecting
@ -1414,10 +1441,11 @@ function polygon_area(poly, signed=false) =
// Function: centroid()
// Synopsis: Compute centroid of a 2d or 3d polygon or a VNF.
// Topics: Geometry, Polygons, Centroid
// See Also: polygon_area(), centroid(), polygon_normal(), point_in_polygon(), polygon_line_intersection()
// Usage:
// c = centroid(object, [eps]);
// Topics: Geometry, Polygons, Centroid
// Synopsis: Compute centroid of a 2d or 3d polygon or a VNF.
// Description:
// Given a simple 2D polygon, returns the 2D coordinates of the polygon's centroid.
// Given a simple 3D planar polygon, returns the 3D coordinates of the polygon's centroid.
@ -1500,10 +1528,11 @@ function _polygon_centroid(poly, eps=EPSILON) =
// Function: polygon_normal()
// Synopsis: Return normal to a polygon.
// Topics: Geometry, Polygons
// See Also: polygon_area(), centroid(), polygon_normal(), point_in_polygon(), polygon_line_intersection()
// Usage:
// vec = polygon_normal(poly);
// Topics: Geometry, Polygons
// Synopsis: Return normal to a polygon.
// Description:
// Given a 3D simple planar polygon, returns a unit normal vector for the polygon. The vector
// is oriented so that if the normal points towards the viewer, the polygon winds in the clockwise
@ -1529,10 +1558,11 @@ function polygon_normal(poly) =
// Function: point_in_polygon()
// Synopsis: Checks if a 2d point is inside or on the boundary of a 2d polygon.
// Topics: Geometry, Polygons
// See Also: polygon_area(), centroid(), polygon_normal(), point_in_polygon(), polygon_line_intersection()
// Usage:
// bool = point_in_polygon(point, poly, [nonzero], [eps])
// Topics: Geometry, Polygons
// Synopsis: Checks if a 2d point is inside or on the boundary of a 2d polygon.
// Description:
// This function tests whether the given 2D point is inside, outside or on the boundary of
// the specified 2D polygon.
@ -1673,10 +1703,11 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
// Function: polygon_line_intersection()
// Synopsis: Find intersection between 2d or 3d polygon and a line, segment or ray.
// Topics: Geometry, Polygons, Lines, Intersection
// See Also: polygon_area(), centroid(), polygon_normal(), point_in_polygon(), polygon_line_intersection()
// Usage:
// pt = polygon_line_intersection(poly, line, [bounded], [nonzero], [eps]);
// Topics: Geometry, Polygons, Lines, Intersection
// Synopsis: Find intersection between 2d or 3d polygon and a line, segment or ray.
// Description:
// Takes a possibly bounded line, and a 2D or 3D planar polygon, and finds their intersection. Note the polygon is
// treated as its boundary and interior, so the intersection may include both points and line segments.
@ -1860,9 +1891,11 @@ function _merge_segments(insegs,outsegs, eps, i=1) =
// Function: polygon_triangulate()
// Synopsis: Divide a polygon into triangles.
// Topics: Geometry, Triangulation
// See Also: vnf_triangulate()
// Usage:
// triangles = polygon_triangulate(poly, [ind], [error], [eps])
// Synopsis: Divide a polygon into triangles.
// Description:
// Given a simple polygon in 2D or 3D, triangulates it and returns a list
// of triples indexing into the polygon vertices. When the optional argument `ind` is
@ -2049,11 +2082,11 @@ function _none_inside(idxs,poly,p0,p1,p2,eps,i=0) =
// Function: is_polygon_clockwise()
// Usage:
// bool = is_polygon_clockwise(poly);
// Synopsis: Determine if a 2d polygon winds clockwise.
// Topics: Geometry, Polygons, Clockwise
// See Also: clockwise_polygon(), ccw_polygon(), reverse_polygon()
// Synopsis: Determine if a 2d polygon winds clockwise.
// Usage:
// bool = is_polygon_clockwise(poly);
// Description:
// Return true if the given 2D simple polygon is in clockwise order, false otherwise.
// Results for complex (self-intersecting) polygon are indeterminate.
@ -2076,11 +2109,11 @@ function is_polygon_clockwise(poly) =
// Function: clockwise_polygon()
// Synopsis: Return clockwise version of a polygon.
// Topics: Geometry, Polygons, Clockwise
// See Also: is_polygon_clockwise(), ccw_polygon(), reverse_polygon()
// Usage:
// newpoly = clockwise_polygon(poly);
// Topics: Geometry, Polygons, Clockwise
// Synopsis: Return clockwise version of a polygon.
// See Also: is_polygon_clockwise(), ccw_polygon(), reverse_polygon()
// Description:
// Given a 2D polygon path, returns the clockwise winding version of that path.
// Arguments:
@ -2091,11 +2124,11 @@ function clockwise_polygon(poly) =
// Function: ccw_polygon()
// Synopsis: Return counter-clockwise version of a polygon.
// Topics: Geometry, Polygons, Clockwise
// See Also: is_polygon_clockwise(), clockwise_polygon(), reverse_polygon()
// Usage:
// newpoly = ccw_polygon(poly);
// Synopsis: Return counter-clockwise version of a polygon.
// See Also: is_polygon_clockwise(), clockwise_polygon(), reverse_polygon()
// Topics: Geometry, Polygons, Clockwise
// Description:
// Given a 2D polygon poly, returns the counter-clockwise winding version of that poly.
// Arguments:
@ -2106,11 +2139,11 @@ function ccw_polygon(poly) =
// Function: reverse_polygon()
// Usage:
// newpoly = reverse_polygon(poly)
// Synopsis: Reverse winding direction of polygon.
// Topics: Geometry, Polygons, Clockwise
// See Also: is_polygon_clockwise(), ccw_polygon(), clockwise_polygon()
// Usage:
// newpoly = reverse_polygon(poly)
// Description:
// Reverses a polygon's winding direction, while still using the same start point.
// Arguments:
@ -2122,10 +2155,11 @@ function reverse_polygon(poly) =
// Function: reindex_polygon()
// Usage:
// newpoly = reindex_polygon(reference, poly);
// Synopsis: Adjust point indexing of polygon to minimize pointwise distance to a reference polygon.
// Topics: Geometry, Polygons
// See Also: reindex_polygon(), align_polygon(), are_polygons_equal()
// Usage:
// newpoly = reindex_polygon(reference, poly);
// Description:
// Rotates and possibly reverses the point order of a 2d or 3d polygon path to optimize its pairwise point
// association with a reference polygon. The two polygons must have the same number of vertices and be the same dimension.
@ -2177,10 +2211,11 @@ function reindex_polygon(reference, poly, return_error=false) =
// Function: align_polygon()
// Synopsis: Find best alignment of a 2d polygon to a reference 2d polygon over a set of transformations.
// Topics: Geometry, Polygons
// See Also: reindex_polygon(), align_polygon(), are_polygons_equal()
// Usage:
// newpoly = align_polygon(reference, poly, [angles], [cp], [tran], [return_ind]);
// Topics: Geometry, Polygons
// Synopsis: Find best alignment of a 2d polygon to a reference 2d polygon over a set of transformations.
// Description:
// Find the best alignment of a specified 2D polygon with a reference 2D polygon over a set of
// transformations. You can specify a list or range of angles and a centerpoint or you can
@ -2245,12 +2280,14 @@ function align_polygon(reference, poly, angles, cp, trans, return_ind=false) =
// Function: are_polygons_equal()
// Synopsis: Check if two polygons (not necessarily in the same point order) are equal.
// Topics: Geometry, Polygons, Comparators
// See Also: reindex_polygon(), align_polygon(), are_polygons_equal()
// Usage:
// bool = are_polygons_equal(poly1, poly2, [eps])
// Description:
// Returns true if poly1 and poly2 are the same polongs
// within given epsilon tolerance.
// Synopsis: Check if two polygons (not necessarily in the same point order) are equal.
// Arguments:
// poly1 = first polygon
// poly2 = second polygon
@ -2301,9 +2338,11 @@ function ___is_polygon_in_list(poly, polys, i) =
// Function: hull()
// Synopsis: Convex hull of a list of 2d or 3d points.
// Topics: Geometry, Hulling
// See Also: hull(), hull_points(), hull2d_path(), hull3d_faces()
// Usage:
// face_list_or_index_list = hull(points);
// Synopsis: Convex hull of a list of 2d or 3d points.
// Description:
// Takes a list of 2D or 3D points (but not both in the same list) and returns either the list of
// indexes into `points` that forms the 2D convex hull perimeter path, or the list of faces that
@ -2322,9 +2361,11 @@ function hull(points) =
// Module: hull_points()
// Synopsis: Convex hull of a list of 2d or 3d points.
// Topics: Geometry, Hulling
// See Also: hull(), hull_points(), hull2d_path(), hull3d_faces()
// Usage:
// hull_points(points, [fast]);
// Synopsis: Convex hull of a list of 2d or 3d points.
// Description:
// If given a list of 2D points, creates a 2D convex hull polygon that encloses all those points.
// If given a list of 3D points, creates a 3D polyhedron that encloses all the points. This should
@ -2380,13 +2421,15 @@ function _is_cw(a,b,c,all) =
// Function: hull2d_path()
// Synopsis: Convex hull of a list of 2d points.
// Topics: Geometry, Hulling
// See Also: hull(), hull_points(), hull2d_path(), hull3d_faces()
// Usage:
// index_list = hull2d_path(points,all)
// Description:
// Takes a list of arbitrary 2D points, and finds the convex hull polygon to enclose them.
// Returns a path as a list of indices into `points`.
// When all==true, returns extra points that are on edges of the hull.
// Synopsis: Convex hull of a list of 2d points.
// Arguments:
// points = list of 2d points to get the hull of.
// all = when true, includes all points on the edges of the convex hull. Default: false.
@ -2443,9 +2486,11 @@ function _hull_collinear(points) =
// Function: hull3d_faces()
// Synopsis: Convex hull of a list of 3d points.
// Topics: Geometry, Hulling
// See Also: hull(), hull_points(), hull2d_path(), hull3d_faces()
// Usage:
// faces = hull3d_faces(points)
// Synopsis: Convex hull of a list of 3d points.
// Description:
// Takes a list of arbitrary 3D points, and finds the convex hull polyhedron to enclose
// them. Returns a list of triangular faces, where each face is a list of indexes into the given `points`
@ -2555,10 +2600,11 @@ function _find_first_noncoplanar(plane, points, i=0) =
// Function: is_polygon_convex()
// Usage:
// bool = is_polygon_convex(poly, [eps]);
// Synopsis: Check if a polygon is convex.
// Topics: Geometry, Convexity, Test
// See Also: clockwise_polygon(), ccw_polygon()
// Usage:
// bool = is_polygon_convex(poly, [eps]);
// Description:
// Returns true if the given 2D or 3D polygon is convex.
// The result is meaningless if the polygon is not simple (self-crossing) or non coplanar.
@ -2601,12 +2647,11 @@ function is_polygon_convex(poly,eps=EPSILON) =
// Function: convex_distance()
// Usage:
// dist = convex_distance(points1, points2,eps);
// Synopsis: Compute distance between convex hull of two point lists.
// Topics: Geometry, Convexity, Distance
// See also:
// convex_collision(), hull()
// See also: convex_collision(), hull()
// Usage:
// dist = convex_distance(points1, points2,eps);
// Description:
// Returns the smallest distance between a point in convex hull of `points1`
// and a point in the convex hull of `points2`. All the points in the lists
@ -2661,12 +2706,12 @@ function _GJK_distance(points1, points2, eps=EPSILON, lbd, d, simplex=[]) =
// Function: convex_collision()
// Usage:
// bool = convex_collision(points1, points2, [eps]);
// Synopsis: Check whether the convex hulls of two point lists intersect.
// Topics: Geometry, Convexity, Collision, Intersection
// See also:
// convex_distance(), hull()
// Synopsis: Check whether the convex hulls of two point lists intersect.
// Usage:
// bool = convex_collision(points1, points2, [eps]);
// Description:
// Returns `true` if the convex hull of `points1` intersects the convex hull of `points2`
// otherwise, `false`.
@ -2812,10 +2857,10 @@ function _support_diff(p1,p2,d) =
// Section: Rotation Decoding
// Function: rot_decode()
// Usage:
// info = rot_decode(rotation,[long]); // Returns: [angle,axis,cp,translation]
// Synopsis: Extract axis and rotation angle from a rotation matrix.
// Topics: Affine, Matrices, Transforms
// Usage:
// info = rot_decode(rotation,[long]); // Returns: [angle,axis,cp,translation]
// Description:
// Given an input 3D rigid transformation operator (one composed of just rotations and translations) represented
// as a 4x4 matrix, compute the rotation and translation parameters of the operator. Returns a list of the

5
hinges.scad
View File

@ -15,6 +15,7 @@ include <screws.scad>
// Module: knuckle_hinge()
// Synopsis: Creates a knuckle-hinge shape.
// SynTags: Geom
// Topics: Hinges, Parts
// See Also: living_hinge_mask(), snap_lock(), snap_socket()
// Usage:
@ -346,6 +347,7 @@ module _knuckle_hinge_profile(offset, arm_height, arm_angle=45, knuckle_diam=4,
// Module: living_hinge_mask()
// Synopsis: Creates a mask to make a folding "living" hinge.
// SynTags: Geom
// Topics: Hinges, Parts
// See Also: knuckle_hinge(), living_hinge_mask(), snap_lock(), snap_socket(), apply_folding_hinges_and_snaps()
// Usage:
@ -391,6 +393,7 @@ module folding_hinge_mask(l, thick, layerheight=0.2, foldangle=90, hingegap=unde
// Module: apply_folding_hinges_and_snaps()
// Synopsis: Adds snap shapes and removes living hinges from a child shape.
// SynTags: Geom
// Topics: Hinges, Parts
// See Also: knuckle_hinge(), living_hinge_mask(), snap_lock(), snap_socket()
// Usage:
@ -476,6 +479,7 @@ module apply_folding_hinges_and_snaps(thick, foldangle=90, hinges=[], snaps=[],
// Module: snap_lock()
// Synopsis: Creates a snap-lock shape.
// SynTags: Geom
// Topics: Hinges, Parts
// See Also: knuckle_hinge(), living_hinge_mask(), snap_lock(), snap_socket()
// Usage:
@ -515,6 +519,7 @@ module snap_lock(thick, snaplen=5, snapdiam=5, layerheight=0.2, foldangle=90, hi
// Module: snap_socket()
// Synopsis: Creates a snap-lock socket shape.
// SynTags: Geom
// Topics: Hinges, Parts
// See Also: knuckle_hinge(), living_hinge_mask(), snap_lock(), snap_socket()
// Usage:

9
joiners.scad
View File

@ -17,6 +17,7 @@ include <rounding.scad>
// Function&Module: half_joiner_clear()
// Synopsis: Creates a mask to clear space for a {{half_joiner()}}.
// SynTags: Geom, VNF
// Topics: Joiners, Parts
// See Also: half_joiner_clear(), half_joiner(), half_joiner2(), joiner_clear(), joiner(), snap_pin(), rabbit_clip(), dovetail()
// Usage: As Module
@ -62,6 +63,7 @@ module half_joiner_clear(l=20, w=10, ang=30, clearance=0, overlap=0.01, anchor=C
// Function&Module: half_joiner()
// Synopsis: Creates a half-joiner shape to mate with a {{half_joiner2()}} shape..
// SynTags: Geom, VNF
// Topics: Joiners, Parts
// See Also: half_joiner_clear(), half_joiner(), half_joiner2(), joiner_clear(), joiner(), snap_pin(), rabbit_clip(), dovetail()
// Usage: As Module
@ -244,6 +246,7 @@ module half_joiner(l=20, w=10, base=10, ang=30, screwsize, anchor=CENTER, spin=0
// Function&Module: half_joiner2()
// Synopsis: Creates a half_joiner2 shape to mate with a {{half_joiner()}} shape..
// SynTags: Geom, VNF
// Topics: Joiners, Parts
// See Also: half_joiner_clear(), half_joiner(), half_joiner2(), joiner_clear(), joiner(), snap_pin(), rabbit_clip(), dovetail()
// Usage: As Module
@ -459,6 +462,7 @@ module half_joiner2(l=20, w=10, base=10, ang=30, screwsize, anchor=CENTER, spin=
// Module: joiner_clear()
// Synopsis: Creates a mask to clear space for a {{joiner()}} shape.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: half_joiner_clear(), half_joiner(), half_joiner2(), joiner_clear(), joiner(), snap_pin(), rabbit_clip(), dovetail()
// Description:
@ -498,6 +502,7 @@ module joiner_clear(l=40, w=10, ang=30, clearance=0, overlap=0.01, anchor=CENTER
// Module: joiner()
// Synopsis: Creates a joiner shape that can mate with another rotated joiner shape.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: half_joiner_clear(), half_joiner(), half_joiner2(), joiner_clear(), joiner(), snap_pin(), rabbit_clip(), dovetail()
// Usage:
@ -549,6 +554,7 @@ module joiner(l=40, w=10, base=10, ang=30, screwsize, anchor=CENTER, spin=0, ori
// Module: dovetail()
// Synopsis: Creates a possibly tapered dovetail shape.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: joiner(), snap_pin(), rabbit_clip()
//
@ -819,6 +825,7 @@ function _pin_size(size) =
// Module: snap_pin()
// Synopsis: Creates a snap-pin that can slot into a {{snap_pin_socket()}} to join two parts.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: snap_pin_socket(), joiner(), dovetail(), snap_pin(), rabbit_clip()
// Usage:
@ -892,6 +899,7 @@ module snap_pin(size,r,radius,d,diameter, l,length, nub_depth, snap, thickness,
// Module: snap_pin_socket()
// Synopsis: Creates a snap-pin socket for a {{snap_pin()}} to slot into.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: snap_pin(), joiner(), dovetail(), snap_pin(), rabbit_clip()
// Usage:
@ -965,6 +973,7 @@ module snap_pin_socket(size, r, radius, l,length, d,diameter,nub_depth, snap, fi
// Module: rabbit_clip()
// Synopsis: Creates a rabbit-eared clip that can snap into a slot.
// SynTags: Geom
// Topics: Joiners, Parts
// See Also: snap_pin(), joiner(), dovetail(), snap_pin(), rabbit_clip()
// Usage:

142
linalg.scad
View File

@ -31,10 +31,11 @@
// Section: Matrix testing and display
// Function: is_matrix()
// Synopsis: Check if input is a numeric matrix, optionally of specified size
// Topics: Matrices
// See Also: is_matrix_symmetric(), is_rotation()
// Usage:
// test = is_matrix(A, [m], [n], [square])
// Topics: Matrices
// Synopsis: Check if input is a numeric matrix, optionally of specified size
// Description:
// Returns true if A is a numeric matrix of height m and width n with finite entries. If m or n
// are omitted or set to undef then true is returned for any positive dimension.
@ -52,13 +53,14 @@ function is_matrix(A,m,n,square=false) =
// Function: is_matrix_symmetric()
// Synopsis: Checks if matrix is symmetric
// Topics: Matrices
// See Also: is_matrix(), is_rotation()
// Usage:
// b = is_matrix_symmetric(A, [eps])
// Topics: Matrices
// Description:
// Returns true if the input matrix is symmetric, meaning it approximately equals its transpose.
// The matrix can have arbitrary entries.
// Synopsis: Checks if matrix is symmetric
// Arguments:
// A = matrix to test
// eps = epsilon for comparing equality. Default: 1e-12
@ -67,15 +69,16 @@ function is_matrix_symmetric(A,eps=1e-12) =
// Function: is_rotation()
// Synopsis: Check if a transformation matrix represents a rotation.
// Topics: Affine, Matrices, Transforms
// See Also: is_matrix(), is_matrix_symmetric(), is_rotation()
// Usage:
// b = is_rotation(A, [dim], [centered])
// Topics: Affine, Matrices, Transforms
// Description:
// Returns true if the input matrix is a square affine matrix that is a rotation around any point,
// or around the origin if `centered` is true.
// The matrix must be 3x3 (representing a 2d transformation) or 4x4 (representing a 3d transformation).
// You can set `dim` to 2 to require a 2d transform (3x3 matrix) or to 3 to require a 3d transform (4x4 matrix).
// Synopsis: Check if a transformation matrix represents a rotation.
// Arguments:
// A = matrix to test
// dim = if set, specify dimension in which the transform operates (2 or 3)
@ -96,11 +99,12 @@ function is_rotation(A,dim,centered=false) =
// Function&Module: echo_matrix()
// Synopsis: Print a matrix neatly to the console.
// Topics: Matrices
// See Also: is_matrix(), is_matrix_symmetric(), is_rotation()
// Usage:
// echo_matrix(M, [description], [sig], [sep], [eps]);
// dummy = echo_matrix(M, [description], [sig], [sep], [eps]),
// Topics: Matrices
// Synopsis: Print a matrix neatly to the console.
// Description:
// Display a numerical matrix in a readable columnar format with `sig` significant
// digits. Values smaller than eps display as zero. If you give a description
@ -135,14 +139,14 @@ module echo_matrix(M,description,sig=4,sep=1,eps=1e-9)
// Section: Matrix indexing
// Function: column()
// Usage:
// list = column(M, i);
// Synopsis: Extract a column from a matrix.
// Topics: Matrices, List Handling, Arrays
// See Also: select(), slice()
// Usage:
// list = column(M, i);
// Description:
// Extracts entry `i` from each list in M, or equivalently column i from the matrix M, and returns it as a vector.
// This function will return `undef` at all entry positions indexed by i not found in M.
// Synopsis: Extract a column from a matrix.
// Arguments:
// M = The given list of lists.
// i = The index to fetch
@ -162,11 +166,11 @@ function column(M, i) =
// Function: submatrix()
// Usage:
// mat = submatrix(M, idx1, idx2);
// Synopsis: Extract a submatrix from a matrix
// Topics: Matrices, Arrays
// See Also: column(), block_matrix(), submatrix_set()
// Synopsis: Extract a submatrix from a matrix
// Usage:
// mat = submatrix(M, idx1, idx2);
// Description:
// The input must be a list of lists (a matrix or 2d array). Returns a submatrix by selecting the rows listed in idx1 and columns listed in idx2.
// Arguments:
@ -196,12 +200,13 @@ function submatrix(M,idx1,idx2) =
// Section: Matrix construction and modification
// Function: ident()
// Synopsis: Return identity matrix.
// Topics: Affine, Matrices, Transforms
// See Also: IDENT, submatrix(), column()
// Usage:
// mat = ident(n);
// Topics: Affine, Matrices, Transforms
// Description:
// Create an `n` by `n` square identity matrix.
// Synopsis: Return identity matrix.
// Arguments:
// n = The size of the identity matrix square, `n` by `n`.
// Example:
@ -229,15 +234,15 @@ function ident(n) = [
// Function: diagonal_matrix()
// Usage:
// mat = diagonal_matrix(diag, [offdiag]);
// Synopsis: Make a diagonal matrix.
// Topics: Affine, Matrices
// See Also: column(), submatrix()
// Usage:
// mat = diagonal_matrix(diag, [offdiag]);
// Description:
// Creates a square matrix with the items in the list `diag` on
// its diagonal. The off diagonal entries are set to offdiag,
// which is zero by default.
// Synopsis: Make a diagonal matrix.
// Arguments:
// diag = A list of items to put in the diagnal cells of the matrix.
// offdiag = Value to put in non-diagonal matrix cells.
@ -247,11 +252,11 @@ function diagonal_matrix(diag, offdiag=0) =
// Function: transpose()
// Synopsis: Transpose a matrix
// Topics: Linear Algebra, Matrices
// See Also: submatrix(), block_matrix(), hstack(), flatten()
// Usage:
// M = transpose(M, [reverse]);
// Topics: Linear Algebra, Matrices
// Synopsis: Transpose a matrix
// See Also: submatrix(), block_matrix(), hstack(), flatten()
// Description:
// Returns the transpose of the given input matrix. The input can be a matrix with arbitrary entries or
// a numerical vector. If you give a vector then transpose returns it unchanged.
@ -326,10 +331,11 @@ function transpose(M, reverse=false) =
// Function: outer_product()
// Synopsis: Compute the outer product of two vectors.
// Topics: Linear Algebra, Matrices
// See Also: submatrix(), determinant()
// Usage:
// x = outer_product(u,v);
// Topics: Linear Algebra, Matrices
// Synopsis: Compute the outer product of two vectors.
// Description:
// Compute the outer product of two vectors, which is a matrix.
// Usage:
@ -339,11 +345,11 @@ function outer_product(u,v) =
[for(ui=u) ui*v];
// Function: submatrix_set()
// Usage:
// mat = submatrix_set(M, A, [m], [n]);
// Synopsis: Takes a matrix as input and change values in a submatrix.
// Topics: Matrices, Arrays
// See Also: column(), submatrix()
// Synopsis: Takes a matrix as input and change values in a submatrix.
// Usage:
// mat = submatrix_set(M, A, [m], [n]);
// Description:
// Sets a submatrix of M equal to the matrix A. By default the top left corner of M is set to A, but
// you can specify offset coordinates m and n. If A (as adjusted by m and n) extends beyond the bounds
@ -368,13 +374,13 @@ function submatrix_set(M,A,m=0,n=0) =
// Function: hstack()
// Synopsis: Make a new matrix by stacking matrices horizontally.
// Topics: Matrices, Arrays
// See Also: column(), submatrix(), block_matrix()
// Usage:
// A = hstack(M1, M2)
// A = hstack(M1, M2, M3)
// A = hstack([M1, M2, M3, ...])
// Synopsis: Make a new matrix by stacking matrices horizontally.
// Topics: Matrices, Arrays
// See Also: column(), submatrix(), block_matrix()
// Description:
// Constructs a matrix by horizontally "stacking" together compatible matrices or vectors. Vectors are treated as columsn in the stack.
// This command is the inverse of `column`. Note: strings given in vectors are broken apart into lists of characters. Strings given
@ -423,11 +429,11 @@ function hstack(M1, M2, M3) =
// Function: block_matrix()
// Usage:
// bmat = block_matrix([[M11, M12,...],[M21, M22,...], ... ]);
// Synopsis: Make a new matrix from a block of matrices.
// Topics: Matrices, Arrays
// See Also: column(), submatrix()
// Synopsis: Make a new matrix from a block of matrices.
// Usage:
// bmat = block_matrix([[M11, M12,...],[M21, M22,...], ... ]);
// Description:
// Create a block matrix by supplying a matrix of matrices, which will
// be combined into one unified matrix. Every matrix in one row
@ -471,10 +477,11 @@ function block_matrix(M) =
// Section: Solving Linear Equations and Matrix Factorizations
// Function: linear_solve()
// Synopsis: Solve Ax=b or, for overdetermined case, solve the least square problem.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// solv = linear_solve(A,b,[pivot])
// Topics: Matrices, Linear Algebra
// Synopsis: Solve Ax=b or, for overdetermined case, solve the least square problem.
// Description:
// Solves the linear system Ax=b. If `A` is square and non-singular the unique solution is returned. If `A` is overdetermined
// the least squares solution is returned. If `A` is underdetermined, the minimal norm solution is returned.
@ -509,10 +516,11 @@ function linear_solve(A,b,pivot=true) =
// Function: linear_solve3()
// Synopsis: Fast solution to Ax=b where A is 3x3.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// x = linear_solve3(A,b)
// Topics: Matrices, Linear Algebra
// Synopsis: Fast solution to Ax=b where A is 3x3.
// Description:
// Fast solution to a 3x3 linear system using Cramer's rule (which appears to be the fastest
// method in OpenSCAD). The input `A` must be a 3x3 matrix. Returns undef if `A` is singular.
@ -535,10 +543,11 @@ function linear_solve3(A,b) =
// Function: matrix_inverse()
// Synopsis: General matrix inverse.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// mat = matrix_inverse(A)
// Topics: Matrices, Linear Algebra
// Synopsis: General matrix inverse.
// Description:
// Compute the matrix inverse of the square matrix `A`. If `A` is singular, returns `undef`.
// Note that if you just want to solve a linear system of equations you should NOT use this function.
@ -550,10 +559,11 @@ function matrix_inverse(A) =
// Function: rot_inverse()
// Usage:
// B = rot_inverse(A)
// Synopsis: Invert 2d or 3d rotation transformations.
// Topics: Matrices, Linear Algebra, Affine
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// B = rot_inverse(A)
// Description:
// Inverts a 2d (3x3) or 3d (4x4) rotation matrix. The matrix can be a rotation around any center,
// so it may include a translation. This is faster and likely to be more accurate than using `matrix_inverse()`.
@ -572,10 +582,11 @@ function rot_inverse(T) =
// Function: null_space()
// Synopsis: Return basis for the null space of A.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// x = null_space(A)
// Topics: Matrices, Linear Algebra
// Synopsis: Return basis for the null space of A.
// Description:
// Returns an orthonormal basis for the null space of `A`, namely the vectors {x} such that Ax=0.
// If the null space is just the origin then returns an empty list.
@ -590,10 +601,11 @@ function null_space(A,eps=1e-12) =
select(transpose(Q_R[0]), zrows);
// Function: qr_factor()
// Synopsis: Compute QR factorization of a matrix.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// qr = qr_factor(A,[pivot]);
// Topics: Matrices, Linear Algebra
// Synopsis: Compute QR factorization of a matrix.
// Description:
// Calculates the QR factorization of the input matrix A and returns it as the list [Q,R,P]. This factorization can be
// used to solve linear systems of equations. The factorization is `A = Q*R*transpose(P)`. If pivot is false (the default)
@ -642,10 +654,11 @@ function _swap_matrix(n,i,j) =
// Function: back_substitute()
// Synopsis: Solve an upper triangular system, Rx=b.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// x = back_substitute(R, b, [transpose]);
// Topics: Matrices, Linear Algebra
// Synopsis: Solve an upper triangular system, Rx=b.
// Description:
// Solves the problem Rx=b where R is an upper triangular square matrix. The lower triangular entries of R are
// ignored. If transpose==true then instead solve transpose(R)*x=b.
@ -675,10 +688,11 @@ function _back_substitute(R, b, x=[]) =
// Function: cholesky()
// Synopsis: Compute the Cholesky factorization of a matrix.
// Topics: Matrices, Linear Algebra
// See Also: linear_solve(), linear_solve3(), matrix_inverse(), rot_inverse(), back_substitute(), cholesky()
// Usage:
// L = cholesky(A);
// Topics: Matrices, Linear Algebra
// Synopsis: Compute the Cholesky factorization of a matrix.
// Description:
// Compute the cholesky factor, L, of the symmetric positive definite matrix A.
// The matrix L is lower triangular and `L * transpose(L) = A`. If the A is
@ -712,10 +726,11 @@ function _cholesky(A,L,n) =
// Section: Matrix Properties: Determinants, Norm, Trace
// Function: det2()
// Synopsis: Compute determinant of 2x2 matrix.
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// d = det2(M);
// Topics: Matrices, Linear Algebra
// Synopsis: Compute determinant of 2x2 matrix.
// Description:
// Rturns the determinant for the given 2x2 matrix.
// Arguments:
@ -729,10 +744,11 @@ function det2(M) =
// Function: det3()
// Synopsis: Compute determinant of 3x3 matrix.
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// d = det3(M);
// Topics: Matrices, Linear Algebra
// Synopsis: Compute determinant of 3x3 matrix.
// Description:
// Returns the determinant for the given 3x3 matrix.
// Arguments:
@ -747,10 +763,11 @@ function det3(M) =
M[2][0] * (M[0][1]*M[1][2]-M[1][1]*M[0][2]);
// Function: det4()
// Synopsis: Compute determinant of 4x4 matrix.
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// d = det4(M);
// Topics: Matrices, Linear Algebra
// Synopsis: Compute determinant of 4x4 matrix.
// Description:
// Returns the determinant for the given 4x4 matrix.
// Arguments:
@ -770,12 +787,13 @@ function det4(M) =
- M[0][3]*M[1][0]*M[2][1]*M[3][2] - M[0][3]*M[1][1]*M[2][2]*M[3][0] - M[0][3]*M[1][2]*M[2][0]*M[3][1];
// Function: determinant()
// Synopsis: compute determinant of an arbitrary square matrix.
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// d = determinant(M);
// Topics: Matrices, Linear Algebra
// Description:
// Returns the determinant for the given square matrix.
// Synopsis: compute determinant of an arbitrary square matrix.
// Arguments:
// M = The NxN square matrix to get the determinant of.
// Example:
@ -804,10 +822,11 @@ function determinant(M) =
// Function: norm_fro()
// Synopsis: Compute Frobenius norm of a matrix
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// norm_fro(A)
// Topics: Matrices, Linear Algebra
// Synopsis: Compute Frobenius norm of a matrix
// Description:
// Computes frobenius norm of input matrix. The frobenius norm is the square root of the sum of the
// squares of all of the entries of the matrix. On vectors it is the same as the usual 2-norm.
@ -818,10 +837,11 @@ function norm_fro(A) =
// Function: matrix_trace()
// Synopsis: Compute the trace of a square matrix.
// Topics: Matrices, Linear Algebra
// See Also: det2(), det3(), det4(), determinant(), norm_fro(), matrix_trace()
// Usage:
// matrix_trace(M)
// Topics: Matrices, Linear Algebra
// Synopsis: Compute the trace of a square matrix.
// Description:
// Computes the trace of a square matrix, the sum of the entries on the diagonal.
function matrix_trace(M) =

23
linear_bearings.scad
View File

@ -8,14 +8,14 @@
// FileSummary: Mounts for LMxUU style linear bearings.
//////////////////////////////////////////////////////////////////////
include <metric_screws.scad>
include <screws.scad>
// Section: Generic Linear Bearings
// Module: linear_bearing_housing()
// Synopsis: Creates a generic linear bearing mount clamp.
// SynTags: Geom
// Topics: Parts, Bearings
// See Also: linear_bearing(), lmXuu_info(), ball_bearing()
// Usage:
@ -25,7 +25,7 @@ include <metric_screws.scad>
// Arguments:
// d = Diameter of linear bearing. (Default: 15)
// l = Length of linear bearing. (Default: 24)
// tab = Clamp tab height. (Default: 7)
// tab = Clamp tab height. (Default: 8)
// tabwall = Clamp Tab thickness. (Default: 5)
// wall = Wall thickness of clamp housing. (Default: 3)
// gap = Gap in clamp. (Default: 5)
@ -35,12 +35,12 @@ include <metric_screws.scad>
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Example:
// linear_bearing_housing(d=19, l=29, wall=2, tab=6, screwsize=2.5);
module linear_bearing_housing(d=15, l=24, tab=7, gap=5, wall=3, tabwall=5, screwsize=3, anchor=BOTTOM, spin=0, orient=UP)
// linear_bearing_housing(d=19, l=29, wall=2, tab=8, screwsize=2.5);
module linear_bearing_housing(d=15, l=24, tab=8, gap=5, wall=3, tabwall=5, screwsize=3, anchor=BOTTOM, spin=0, orient=UP)
{
od = d+2*wall;
ogap = gap+2*tabwall;
tabh = tab/2+od/2*sqrt(2)-ogap/2;
tabh = tab/2+od/2*sqrt(2)-ogap/2-1;
h = od+tab/2;
anchors = [
named_anchor("axis", [0,0,-tab/2/2]),
@ -68,11 +68,15 @@ module linear_bearing_housing(d=15, l=24, tab=7, gap=5, wall=3, tabwall=5, screw
cube([l+0.05,gap,od], anchor=BOTTOM);
up(tabh) {
screwsize = is_string(screwsize)? screwsize : str("M",screwsize);
// Screwhole
fwd(ogap/2-2+0.01) generic_screw(screwsize=screwsize*1.06, screwlen=ogap, headsize=screwsize*2, headlen=10, orient=FWD);
fwd(ogap/2-2+0.01)
screw_hole(str(screwsize,",",ogap), head="socket", counterbore=3, anchor="head_bot", orient=FWD, $fn=12);
// Nut holder
back(ogap/2-2+0.01) metric_nut(size=screwsize, hole=false, anchor=BOTTOM, orient=BACK);
back(ogap/2-2+0.01)
nut_trap_inline(tabwall, screwsize, orient=BACK);
}
}
children();
@ -82,6 +86,7 @@ module linear_bearing_housing(d=15, l=24, tab=7, gap=5, wall=3, tabwall=5, screw
// Module: linear_bearing()
// Synopsis: Creates a generic linear bearing cartridge.
// SynTags: Geom
// Topics: Parts, Bearings
// See Also: linear_bearing_housing(), lmXuu_info(), ball_bearing()
// Usage:
@ -116,6 +121,7 @@ module linear_bearing(l, od=15, id=8, length, anchor=CTR, spin=0, orient=UP) {
// Module: lmXuu_housing()
// Synopsis: Creates a standardized LM*UU linear bearing mount clamp.
// SynTags: Geom
// Topics: Parts, Bearings
// See Also: linear_bearing(), linear_bearing_housing(), lmXuu_info(), lmXuu_bearing(), lmXuu_housing(), ball_bearing()
// Usage:
@ -146,6 +152,7 @@ module lmXuu_housing(size=8, tab=7, gap=5, wall=3, tabwall=5, screwsize=3, ancho
// Module: lmXuu_bearing()
// Synopsis: Creates a standardized LM*UU linear bearing cartridge.
// SynTags: Geom
// Topics: Parts, Bearings
// See Also: linear_bearing(), linear_bearing_housing(), lmXuu_info(), lmXuu_bearing(), lmXuu_housing(), ball_bearing()
// Usage:

1
lists.scad
View File

@ -268,6 +268,7 @@ function slice(list,start=0,end=-1) =
)
[if (start<=end && end>=0 && start<=l) for (i=[max(start,0):1:min(end,l-1)]) list[i]];
// Function: last()
// Synopsis: Returns the last item of a list.
// Topics: List Handling

13
masks3d.scad
View File

@ -17,7 +17,7 @@
// Synopsis: Creates a shape to chamfer a 90° edge.
// SynTags: Geom
// Topics: Masking, Chamfers, Shapes (3D)
// See Also: chamfer_corner_mask()
// See Also: chamfer_corner_mask(), chamfer_cylinder_mask(), chamfer_edge_mask()
// Usage:
// chamfer_edge_mask(l|h=|length=|height=, chamfer, [excess]) [ATTACHMENTS];
// Description:
@ -59,7 +59,7 @@ module chamfer_edge_mask(l, chamfer=1, excess=0.1, h, length, height, anchor=CEN
// Synopsis: Creates a shape to chamfer a 90° corner.
// SynTags: Geom
// Topics: Masking, Chamfers, Shapes (3D)
// See Also: chamfer_edge_mask()
// See Also: chamfer_corner_mask(), chamfer_cylinder_mask(), chamfer_edge_mask()
// Usage:
// chamfer_corner_mask(chamfer) [ATTACHMENTS];
// Description:
@ -98,6 +98,7 @@ module chamfer_corner_mask(chamfer=1, anchor=CENTER, spin=0, orient=UP) {
// Synopsis: Creates a shape to chamfer the end of a cylinder.
// SynTags: Geom
// Topics: Masking, Chamfers, Cylinders
// See Also: chamfer_corner_mask(), chamfer_cylinder_mask(), chamfer_edge_mask()
// Usage:
// chamfer_cylinder_mask(r|d=, chamfer, [ang], [from_end]) [ATTACHMENTS];
// Description:
@ -419,7 +420,7 @@ module rounding_angled_corner_mask(r, ang=90, d, anchor=CENTER, spin=0, orient=U
// Synopsis: Creates a shape to round the end of a cylinder.
// SynTags: Geom
// Topics: Masking, Rounding, Cylinders
// See Also: rounding_hole_mask()
// See Also: rounding_hole_mask(), rounding_angled_edge_mask(), rounding_corner_mask(), rounding_angled_corner_mask()
// Usage:
// rounding_cylinder_mask(r|d=, rounding);
// Description:
@ -471,7 +472,7 @@ module rounding_cylinder_mask(r, rounding, d, anchor=CENTER, spin=0, orient=UP)
// Synopsis: Creates a shape to round the edge of a round hole.
// SynTags: Geom
// Topics: Masking, Rounding
// See Also: rounding_cylinder_mask()
// See Also: rounding_cylinder_mask(), rounding_hole_mask(), rounding_angled_edge_mask(), rounding_corner_mask(), rounding_angled_corner_mask()
// Usage:
// rounding_hole_mask(r|d, rounding, [excess]) [ATTACHMENTS];
// Description:
@ -524,7 +525,7 @@ module rounding_hole_mask(r, rounding, excess=0.1, d, anchor=CENTER, spin=0, ori
// Synopsis: Creates a shape to round a 90° edge but limit the angle of overhang.
// SynTags: Geom
// Topics: Masking, Rounding, Shapes (3D), FDM Optimized
// See Also: teardrop_corner_mask()
// See Also: teardrop_corner_mask(), teardrop_edge_mask()
// Usage:
// teardrop_edge_mask(l|h=|length=|height=, r|d=, [angle], [excess], [anchor], [spin], [orient]) [ATTACHMENTS];
// Description:
@ -567,7 +568,7 @@ module teardrop_edge_mask(l, r, angle=45, excess=0.1, d, anchor=CTR, spin=0, ori
// Synopsis: Creates a shape to round a 90° corner but limit the angle of overhang.
// SynTags: Geom
// Topics: Masking, Rounding, Shapes (3D), FDM Optimized
// See Also: teardrop_edge_mask()
// See Also: teardrop_corner_mask(), teardrop_edge_mask()
// Usage:
// teardrop_corner_mask(r|d=, [angle], [excess], [anchor], [spin], [orient]) [ATTACHMENTS];
// Description:

2
metric_screws.scad
View File

@ -12,6 +12,8 @@
include <threading.scad>
include <screw_drive.scad>
warn = echo("*** WARNING: metric_screws.scad is deprecated and may be removed in the future. Use screws.scad instead. ***");
// Section: Functions

20
modular_hose.scad
View File

@ -10,7 +10,7 @@
// Section: Modular Hose Parts
_small_end = [
_modhose_small_end = [
turtle([
"left", 90-38.5, // 1/4" hose
"arcsteps", 12,
@ -57,7 +57,7 @@ _small_end = [
];
_big_end = [
_modhose_big_end = [
turtle([ // 1/4" hose
"left", 90-22,
"move", 6.5,
@ -116,7 +116,7 @@ _big_end = [
];
_hose_waist = [1.7698, 1.8251, 3.95998];
_modhose_waist = [1.7698, 1.8251, 3.95998];
// Module: modular_hose()
@ -159,14 +159,14 @@ module modular_hose(size, type, clearance=0, waist_len, anchor=BOTTOM, spin=0,or
ind = search([size],[1/4, 1/2, 3/4])[0];
sbound =
assert(ind!=[], "Must specify size as 1/4, 1/2 or 3/4")
pointlist_bounds(_small_end[ind]);
bbound = pointlist_bounds(_big_end[ind]);
pointlist_bounds(_modhose_small_end[ind]);
bbound = pointlist_bounds(_modhose_big_end[ind]);
smallend =
assert(is_vector(clearance,2), "Clearance must be a scalar or length 2 vector")
move([-clearance[0],-sbound[0].y],p=_small_end[ind]);
bigend = move([clearance[1], -bbound[0].y], p=_big_end[ind]);
move([-clearance[0],-sbound[0].y],p=_modhose_small_end[ind]);
bigend = move([clearance[1], -bbound[0].y], p=_modhose_big_end[ind]);
midlength = first_defined([waist_len, _hose_waist[ind]]);
midlength = first_defined([waist_len, _modhose_waist[ind]]);
dummy = assert(midlength>=0,"midlength must be nonnegative");
goodtypes = ["small","big","segment","socket","ball"];
@ -221,8 +221,8 @@ function modular_hose_radius(size, outer=false) =
)
assert(ind!=[], "Must specify size as 1/4, 1/2 or 3/4")
let(
b = select(_big_end[ind], [0,-1]),
s = select(_small_end[ind], [0,-1])
b = select(_modhose_big_end[ind], [0,-1]),
s = select(_modhose_small_end[ind], [0,-1])
)
outer ? b[1][0] : b[0][0];

14
mutators.scad
View File

@ -14,6 +14,7 @@
// Module: bounding_box()
// Synopsis: Creates the smallest bounding box that contains all the children.
// SynTags: Geom
// Topics: Mutators, Bounds, Bounding Boxes
// See Also: pointlist_bounds()
// Usage:
@ -109,6 +110,7 @@ module bounding_box(excess=0, planar=false) {
// Module: chain_hull()
// Synopsis: Performs the union of hull operations between consecutive pairs of children.
// SynTags: Geom
// Topics: Mutators
// See Also: hull()
// Usage:
@ -162,6 +164,7 @@ module chain_hull()
// Module: path_extrude2d()
// Synopsis: Extrudes 2D children along a 2D path.
// SynTags: Geom
// Topics: Mutators, Extrusion
// See Also: path_sweep(), path_extrude()
// Usage:
@ -284,6 +287,7 @@ module path_extrude2d(path, caps=false, closed=false, s, convexity=10) {
// Module: cylindrical_extrude()
// Synopsis: Extrudes 2D children outwards around a cylinder.
// SynTags: Geom
// Topics: Mutators, Extrusion, Rotation
// See Also: heightfield(), cylindrical_heightfield(), cyl()
// Usage:
@ -349,7 +353,8 @@ module cylindrical_extrude(ir, or, od, id, size=1000, convexity=10, spin=0, orie
// Module: extrude_from_to()
// Extrudes 2D children between two points in 3D space.
// Synopsis: Extrudes 2D children between two points in 3D space.
// SynTags: Geom
// Topics: Extrusion, Mutators
// See Also: path_sweep(), path_extrude2d()
// Usage:
@ -396,9 +401,11 @@ module extrude_from_to(pt1, pt2, convexity, twist, scale, slices) {
// Module: path_extrude()
// Synopsis: Extrudes 2D children along a 3D path.
// SynTags: Geom
// Topics: Paths, Extrusion, Mutators
// See Also: path_sweep(), path_extrude2d()
// Usage: path_extrude(path, [convexity], [clipsize]) 2D-CHILDREN;
// Usage:
// path_extrude(path, [convexity], [clipsize]) 2D-CHILDREN;
// Description:
// Extrudes 2D children along a 3D path. This may be slow and can have problems with twisting.
// Arguments:
@ -461,6 +468,7 @@ module path_extrude(path, convexity=10, clipsize=100) {
// Module: minkowski_difference()
// Synopsis: Removes diff shapes from base shape surface.
// SynTags: Geom
// Topics: Mutators
// See Also: offset3d()
// Usage:
@ -504,6 +512,7 @@ module minkowski_difference(planar=false) {
// Module: offset3d()
// Synopsis: Expands or contracts the surface of a 3D object.
// SynTags: Geom
// Topics: Mutators
// See Also: minkowski_difference(), round3d()
// Usage:
@ -550,6 +559,7 @@ module offset3d(r, size=100, convexity=10) {
// Module: round3d()
// Synopsis: Rounds arbitrary 3d objects.
// SynTags: Geom
// Topics: Rounding, Mutators
// See Also: offset3d(), minkowski_difference()
// Usage:

2
nema_steppers.scad
View File

@ -14,6 +14,7 @@
// Module: nema_stepper_motor()
// Synopsis: Creates a NEMA standard stepper motor model.
// SynTags: Geom
// Topics: Parts, Motors
// See Also: nema_stepper_motor(), nema_mount_mask()
// Usage:
@ -119,6 +120,7 @@ module nema_stepper_motor(size=17, h=24, shaft_len=20, details=true, atype="body
// Module: nema_mount_mask()
// Synopsis: Creates a standard NEMA mount holes mask.
// SynTags: Geom
// Topics: Parts, Motors
// See Also: nema_stepper_motor(), nema_mount_mask()
// Usage:

66
partitions.scad
View File

@ -15,7 +15,7 @@
// Synopsis: Masks half of an object at a cut plane.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: back_half(), front_half(), left_half(), right_half(), top_half(), bottom_half()
// See Also: back_half(), front_half(), left_half(), right_half(), top_half(), bottom_half(), intersection()
//
// Usage: as module
// half_of(v, [cp], [s], [planar]) CHILDREN;
@ -23,12 +23,13 @@
// result = half_of(p,v,[cp]);
//
// Description:
// Slices an object at a cut plane, and masks away everything that is on one side. The v parameter is either a plane specification or
// a normal vector. The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// When called as a function, you must supply a vnf, path or region in p. If planar is set to true for the module version the operation
// is performed in 2D and UP and DOWN are treated as equivalent to BACK and FWD respectively.
// Slices an object at a cut plane, and masks away everything that is on one side. The v parameter
// is either a plane specification or a normal vector. The `s` parameter is needed for the module
// version to control the size of the masking cube. If `s` is too large then the preview display
// will flip around and display the wrong half, but if it is too small it won't fully mask your
// model. When called as a function, you must supply a vnf, path or region in p. If planar is set
// to true for the module version the operation is performed in 2D and UP and DOWN are treated as
// equivalent to BACK and FWD respectively.
//
// Arguments:
// p = path, region or VNF to slice. (Function version)
@ -125,7 +126,7 @@ function half_of(p, v=UP, cp) =
// Synopsis: Masks the right half of an object along the Y-Z plane, leaving the left half.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: back_half(), front_half(), right_half(), top_half(), bottom_half(), half_of()
// See Also: back_half(), front_half(), right_half(), top_half(), bottom_half(), half_of(), intersection()
//
// Usage: as module
// left_half([s], [x]) CHILDREN;
@ -135,9 +136,9 @@ function half_of(p, v=UP, cp) =
//
// Description:
// Slices an object at a vertical Y-Z cut plane, and masks away everything that is right of it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
//
// Arguments:
// p = VNF, region or path to slice (function version)
@ -172,7 +173,7 @@ function left_half(p,x=0) = half_of(p, LEFT, [x,0,0]);
// SynTags: Geom, VNF, Path, Region
// Synopsis: Masks the left half of an object along the Y-Z plane, leaving the right half.
// Topics: Partitions, Masking
// See Also: back_half(), front_half(), left_half(), top_half(), bottom_half(), half_of()
// See Also: back_half(), front_half(), left_half(), top_half(), bottom_half(), half_of(), intersection()
//
// Usage: as module
// right_half([s=], [x=]) CHILDREN;
@ -182,9 +183,9 @@ function left_half(p,x=0) = half_of(p, LEFT, [x,0,0]);
//
// Description:
// Slices an object at a vertical Y-Z cut plane, and masks away everything that is left of it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may display the wrong half. (Module version) Default: 100
@ -217,7 +218,7 @@ function right_half(p,x=0) = half_of(p, RIGHT, [x,0,0]);
// Synopsis: Masks the back half of an object along the X-Z plane, leaving the front half.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: back_half(), left_half(), right_half(), top_half(), bottom_half(), half_of()
// See Also: back_half(), left_half(), right_half(), top_half(), bottom_half(), half_of(), intersection()
//
// Usage:
// front_half([s], [y]) CHILDREN;
@ -227,9 +228,9 @@ function right_half(p,x=0) = half_of(p, RIGHT, [x,0,0]);
//
// Description:
// Slices an object at a vertical X-Z cut plane, and masks away everything that is behind it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may display the wrong half. (Module version) Default: 100
@ -263,7 +264,7 @@ function front_half(p,y=0) = half_of(p, FRONT, [0,y,0]);
// Synopsis: Masks the front half of an object along the X-Z plane, leaving the back half.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: front_half(), left_half(), right_half(), top_half(), bottom_half(), half_of()
// See Also: front_half(), left_half(), right_half(), top_half(), bottom_half(), half_of(), intersection()
//
// Usage:
// back_half([s], [y]) CHILDREN;
@ -273,9 +274,9 @@ function front_half(p,y=0) = half_of(p, FRONT, [0,y,0]);
//
// Description:
// Slices an object at a vertical X-Z cut plane, and masks away everything that is in front of it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may display the wrong half. (Module version) Default: 100
@ -309,7 +310,7 @@ function back_half(p,y=0) = half_of(p, BACK, [0,y,0]);
// Synopsis: Masks the top half of an object along the X-Y plane, leaving the bottom half.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: back_half(), front_half(), left_half(), right_half(), top_half(), half_of()
// See Also: back_half(), front_half(), left_half(), right_half(), top_half(), half_of(), intersection()
//
// Usage:
// bottom_half([s], [z]) CHILDREN;
@ -318,9 +319,9 @@ function back_half(p,y=0) = half_of(p, BACK, [0,y,0]);
//
// Description:
// Slices an object at a horizontal X-Y cut plane, and masks away everything that is above it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may display the wrong half. (Module version) Default: 100
@ -347,7 +348,7 @@ function bottom_half(p,z=0) = half_of(p,BOTTOM,[0,0,z]);
// Synopsis: Masks the bottom half of an object along the X-Y plane, leaving the top half.
// SynTags: Geom, VNF, Path, Region
// Topics: Partitions, Masking
// See Also: back_half(), front_half(), left_half(), right_half(), bottom_half(), half_of()
// See Also: back_half(), front_half(), left_half(), right_half(), bottom_half(), half_of(), intersection()
//
// Usage: as module
// top_half([s], [z]) CHILDREN;
@ -356,9 +357,9 @@ function bottom_half(p,z=0) = half_of(p,BOTTOM,[0,0,z]);
//
// Description:
// Slices an object at a horizontal X-Y cut plane, and masks away everything that is below it.
// The s parameter is needed for the module
// version to control the size of the masking cube. If s is too large then the preview display will flip around and display the
// wrong half, but if it is too small it won't fully mask your model.
// The `s` parameter is needed for the module version to control the size of the masking cube.
// If `s` is too large then the preview display will flip around and display the wrong half,
// but if it is too small it won't fully mask your model.
// Arguments:
// p = VNF, region or path to slice (function version)
// s = Mask size to use. Use a number larger than twice your object's largest axis. If you make this too large, OpenSCAD's preview rendering may display the wrong half. (Module version) Default: 100
@ -433,7 +434,8 @@ function _partition_cutpath(l, h, cutsize, cutpath, gap) =
// Usage:
// partition_mask(l, w, h, [cutsize], [cutpath], [gap], [inverse], [$slop=], [anchor=], [spin=], [orient=]) [ATTACHMENTS];
// Description:
// Creates a mask that you can use to difference or intersect with an object to remove half of it, leaving behind a side designed to allow assembly of the sub-parts.
// Creates a mask that you can use to difference or intersect with an object to remove half of it,
// leaving behind a side designed to allow assembly of the sub-parts.
// Arguments:
// l = The length of the cut axis.
// w = The width of the part to be masked, back from the cut plane.

14
paths.scad
View File

@ -78,14 +78,16 @@ function is_1region(path, name="path") =
// Function: force_path()
// Synopsis: Checks that path is a region with one component.
// SynTags: Path
// Topics: Paths, Regions
// See Also: is_1region()
// Usage:
// outpath = force_path(path, [name])
// Description:
// If `path` is a region with one component (a 1-region) then return that component as a path. If path is a region with more components
// then display an error message about the parameter `name` requiring a path or a single component region. If the input
// is not a region then return the input without any checks. This function helps path functions accept 1-regions.
// If `path` is a region with one component (a 1-region) then returns that component as a path.
// If path is a region with more components then displays an error message about the parameter
// `name` requiring a path or a single component region. If the input is not a region then
// returns the input without any checks. This function helps path functions accept 1-regions.
// Arguments:
// path = input to process
// name = name of parameter to use in error message. Default: "path"
@ -129,6 +131,7 @@ function _path_select(path, s1, u1, s2, u2, closed=false) =
// Function: path_merge_collinear()
// Synopsis: Removes unnecessary points from a path.
// SynTags: Path
// Topics: Paths, Regions
// Description:
// Takes a path and removes unnecessary sequential collinear points.
@ -316,6 +319,7 @@ function _sum_preserving_round(data, index=0) =
// Function: subdivide_path()
// Synopsis: Subdivides a path to produce a more finely sampled path.
// SynTags: Path
// Topics: Paths, Path Subdivision
// See Also: subdivide_and_slice(), resample_path(), jittered_poly()
// Usage:
@ -461,6 +465,7 @@ function subdivide_path(path, n, refine, maxlen, closed=true, exact, method) =
// Function: resample_path()
// Synopsis: Returns an equidistant set of points along a path.
// SynTags: Path
// Topics: Paths
// See Also: subdivide_path()
// Usage:
@ -730,6 +735,7 @@ function path_torsion(path, closed=false) =
// Function: path_cut()
// Synopsis: Cuts a path into subpaths at various points.
// SynTags: PathList
// Topics: Paths, Path Subdivision
// See Also: split_path_at_self_crossings(), path_cut_points()
// Usage:
@ -929,6 +935,7 @@ function _cut_to_seg_u_form(pathcut, path, closed) =
// Function: split_path_at_self_crossings()
// Synopsis: Split a 2D path wherever it crosses itself.
// SynTags: PathList
// Topics: Paths, Path Subdivision
// See Also: path_cut(), path_cut_points()
// Usage:
@ -999,6 +1006,7 @@ function _tag_self_crossing_subpaths(path, nonzero, closed=true, eps=EPSILON) =
// Function: polygon_parts()
// Synopsis: Parses a self-intersecting polygon into a list of non-intersecting polygons.
// SynTags: PathList
// Topics: Paths, Polygons
// See Also: split_path_at_self_crossings(), path_cut(), path_cut_points()
// Usage:

1
polyhedra.scad
View File

@ -38,6 +38,7 @@ function _unique_groups(m) = [
// Module: regular_polyhedron()
// Synopsis: Creates a regular polyhedron with optional rounding.
// SynTags: Geom
// Topics: Polyhedra, Shapes, Parts
// See Also: regular_polyhedron_info()
// Usage: Selecting a polyhedron

9
regions.scad
View File

@ -248,6 +248,7 @@ function is_region_simple(region, eps=EPSILON) =
// Function: make_region()
// Synopsis: Converts lists of intersecting polygons into valid regions.
// SynTags: Region
// Topics: Regions, Paths, Polygons, List Handling
// See Also: force_region(), region()
//
@ -281,6 +282,7 @@ function make_region(polys,nonzero=false,eps=EPSILON) =
// Function: force_region()
// Synopsis: Given a polygon returns a region.
// SynTags: Region
// Topics: Regions, Paths, Polygons, List Handling
// See Also: make_region(), region()
// Usage:
@ -296,6 +298,7 @@ function force_region(poly) = is_path(poly) ? [poly] : poly;
// Module: region()
// Synopsis: Creates the 2D polygons described by the given region or list of polygons.
// SynTags: Geom
// Topics: Regions, Paths, Polygons, List Handling
// See Also: make_region(), region()
// Usage:
@ -576,6 +579,7 @@ function split_region_at_region_crossings(region1, region2, closed1=true, closed
// Function: region_parts()
// Synopsis: Splits a region into a list of regions.
// SynTags: RegList
// Topics: Regions, List Handling
// See Also: split_region_at_region_crossings()
// Usage:
@ -739,6 +743,7 @@ function _point_dist(path,pathseg_unit,pathseg_len,pt) =
// Function: offset()
// Synopsis: Takes a 2D path, polygon or region and returns a path offset by an amount.
// SynTags: Path, Region
// Topics: Paths, Polygons, Regions
// Usage:
// offsetpath = offset(path, [r=|delta=], [chamfer=], [closed=], [check_valid=], [quality=], [same_length=])
@ -1044,6 +1049,7 @@ function _list_three(a,b,c) =
// Function&Module: union()
// Synopsis: Performs a Boolean union operation.
// SynTags: Geom, Region
// Topics: Boolean Operations, Regions, Polygons, Shapes2D, Shapes3D
// See Also: difference(), intersection(), diff(), intersect(), exclusive_or()
// Usage:
@ -1077,6 +1083,7 @@ function union(regions=[],b=undef,c=undef,eps=EPSILON) =
// Function&Module: difference()
// Synopsis: Performs a Boolean difference operation.
// SynTags: Geom, Region
// Topics: Boolean Operations, Regions, Polygons, Shapes2D, Shapes3D
// See Also: union(), intersection(), diff(), intersect(), exclusive_or()
// Usage:
@ -1112,6 +1119,7 @@ function difference(regions=[],b=undef,c=undef,eps=EPSILON) =
// Function&Module: intersection()
// Synopsis: Performs a Boolean intersection operation.
// SynTags: Geom, Region
// Topics: Boolean Operations, Regions, Polygons, Shapes2D, Shapes3D
// See Also: difference(), union(), diff(), intersect(), exclusive_or()
// Usage:
@ -1146,6 +1154,7 @@ function intersection(regions=[],b=undef,c=undef,eps=EPSILON) =
// Function&Module: exclusive_or()
// Synopsis: Performs a Boolean exclusive-or operation.
// SynTags: Geom, Region
// Topics: Boolean Operations, Regions, Polygons, Shapes2D, Shapes3D
// See Also: union(), difference(), intersection(), diff(), intersect()
// Usage:

9
rounding.scad
View File

@ -135,6 +135,7 @@ include <structs.scad>
// Function: round_corners()
// Synopsis: Round or chamfer the corners of a path (clipping them off).
// SynTags: Path
// Topics: Rounding, Paths
// See Also: round_corners(), smooth_path(), path_join(), offset_stroke()
// Usage:
@ -597,6 +598,7 @@ function _rounding_offsets(edgespec,z_dir=1) =
// Function: smooth_path()
// Synopsis: Create smoothed path that passes through all the points of a given path.
// SynTags: Path
// Topics: Rounding, Paths
// See Also: round_corners(), smooth_path(), path_join(), offset_stroke()
// Usage:
@ -695,6 +697,7 @@ function _scalar_to_vector(value,length,varname) =
// Function: path_join()
// Synopsis: Join paths end to end with optional rounding.
// SynTags: Path
// Topics: Rounding, Paths
// See Also: round_corners(), smooth_path(), path_join(), offset_stroke()
// Usage:
@ -883,6 +886,7 @@ function _path_join(paths,joint,k=0.5,i=0,result=[],relocate=true,closed=false)
// Function&Module: offset_stroke()
// Synopsis: Draws a line along a path with options to specify angles and roundings at the ends.
// SynTags: Path, Region
// Topics: Rounding, Paths
// See Also: round_corners(), smooth_path(), path_join(), offset_stroke()
// Usage: as module
@ -1263,6 +1267,7 @@ module offset_stroke(path, width=1, rounded=true, start, end, check_valid=true,
// Function&Module: offset_sweep()
// Synopsis: Make a solid from a polygon with offset that changes along its length.
// SynTags: Geom, VNF
// Topics: Rounding, Offsets
// See Also: offset_sweep(), convex_offset_extrude(), rounded_prism(), bent_cutout_mask(), join_prism()
// Usage: most common module arguments. See Arguments list below for more.
@ -1732,6 +1737,7 @@ function os_mask(mask, out=false, extra,check_valid, quality, offset) =
// Module: convex_offset_extrude()
// Synopsis: Make a solid from geometry where offset changes along the object's length.
// SynTags: Geom
// Topics: Rounding, Offsets
// See Also: offset_sweep(), convex_offset_extrude(), rounded_prism(), bent_cutout_mask(), join_prism()
// Usage: Basic usage. See below for full options
@ -1969,6 +1975,7 @@ function _rp_compute_patches(top, bot, rtop, rsides, ktop, ksides, concave) =
// Function&Module: rounded_prism()
// Synopsis: Make a rounded 3d object by connecting two polygons with the same vertex count.
// SynTags: Geom, VNF
// Topics: Rounding, Offsets
// See Also: offset_sweep(), convex_offset_extrude(), rounded_prism(), bent_cutout_mask(), join_prism()
// Usage: as a module
@ -2285,6 +2292,7 @@ function _circle_mask(r) =
// Module: bent_cutout_mask()
// Synopsis: Create a mask for making a round-edged cutout in a cylindrical shell.
// SynTags: Geom
// Topics: Rounding, Offsets
// See Also: offset_sweep(), convex_offset_extrude(), rounded_prism(), bent_cutout_mask(), join_prism()
// Usage:
@ -2513,6 +2521,7 @@ Access to the derivative smoothing parameter?
// Function&Module: join_prism()
// Synopsis: Join an arbitrary prism to a plane, sphere, cylinder or another arbitrary prism with a fillet.
// SynTags: Geom, VNF
// Topics: Rounding, Offsets
// See Also: offset_sweep(), convex_offset_extrude(), rounded_prism(), bent_cutout_mask(), join_prism()
// Usage: The two main forms with most common options

5
screw_drive.scad
View File

@ -15,6 +15,7 @@ include <structs.scad>
// Module: phillips_mask()
// Synopsis: Creates a mask for a Philips screw drive.
// SynTags: Geom
// Topics: Screws, Masks
// See Also: hex_drive_mask(), phillips_depth(), phillips_diam(), torx_mask(), robertson_mask()
// Usage:
@ -139,6 +140,7 @@ function phillips_diam(size, depth) =
// Module: hex_drive_mask()
// Synopsis: Creates a mask for a hex drive recess.
// SynTags: Geom
// Topics: Screws, Masks
// See Also: phillips_mask(), hex_drive_mask(), torx_mask(), phillips_depth(), phillips_diam(), robertson_mask()
// Usage:
@ -161,6 +163,7 @@ function hex_drive_mask(size,length,l,h,height,anchor,spin,orient) = no_function
// Module: torx_mask()
// Synopsis: Creates a mask for a torx drive recess.
// SynTags: Geom
// Topics: Screws, Masks
// See Also: phillips_mask(), hex_drive_mask(), torx_mask(), phillips_depth(), phillips_diam(), robertson_mask()
// Usage:
@ -191,6 +194,7 @@ module torx_mask(size, l=5, center, anchor, spin=0, orient=UP) {
// Module: torx_mask2d()
// Synopsis: Creates the 2D cross section for a torx drive recess.
// SynTags: Geom
// Topics: Screws, Masks
// See Also: phillips_mask(), hex_drive_mask(), torx_mask(), phillips_depth(), phillips_diam(), torx_info(), robertson_mask()
// Usage:
@ -313,6 +317,7 @@ function torx_depth(size) = torx_info(size)[2];
// Module: robertson_mask()
// Synopsis: Creates a mask for a Robertson/Square drive recess.
// SynTags: Geom
// Topics: Screws, Masks
// See Also: phillips_mask(), hex_drive_mask(), torx_mask(), phillips_depth(), phillips_diam(), torx_info(), robertson_mask()
// Usage:

9
screws.scad
View File

@ -200,6 +200,7 @@ Torx values: https://www.stanleyengineeredfastening.com/-/media/web/sef/resourc
// Module: screw()
// Synopsis: Creates a standard screw with optional tolerances.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw_hole(), shoulder_screw()
// Usage:
@ -733,6 +734,7 @@ fdsa= echo(pitch=pitch);
// Module: screw_hole()
// Synopsis: Creates a screw hole.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw()
// Usage:
@ -990,6 +992,7 @@ module screw_hole(spec, head, thread, oversize, hole_oversize, head_oversize,
// Module: shoulder_screw()
// Synopsis: Creates a shoulder screw.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw(), screw_hole()
// Usage:
@ -1403,6 +1406,7 @@ function _parse_drive(drive=undef, drive_size=undef) =
// Module: screw_head()
// Synopsis: Creates a screw head.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw(), screw_hole()
// Usage:
@ -1506,6 +1510,7 @@ module screw_head(screw_info,details=false, counterbore=0,flat_height,teardrop=f
// Module: nut()
// Synopsis: Creates a standard nut.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw(), screw_hole()
// Usage:
@ -1628,6 +1633,7 @@ module nut(spec, shape, thickness, nutwidth, thread, tolerance, hole_oversize,
// Module: nut_trap_side()
// Synopsis: Creates a side nut trap mask.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw(), screw_hole()
// Usage:
@ -1718,6 +1724,7 @@ module nut_trap_side(trap_width, spec, shape, thickness, nutwidth, anchor=BOT, o
// Module: nut_trap_inline()
// Synopsis: Creates an inline nut trap mask.
// SynTags: Geom
// Topics: Threading, Screws
// See Also: screw(), screw_hole()
// Usage:
@ -1897,7 +1904,7 @@ function screw_info(name, head, drive, thread, drive_size, shaft_oversize, head_
// .
// Field | What it is
// ------------------ | ---------------
// "type" | Always set to "screw_info"
// "type" | Always set to "nut_info"
// "system" | Either `"UTS"` or `"ISO"` (used for correct tolerance computation).
// "origin" | Module that created the structure
// "name" | Name used to specify threading, such as "M6" or "#8"

55
shapes3d.scad
View File

@ -90,7 +90,7 @@ function cube(size=1, center, anchor, spin=0, orient=UP) =
// Module: cuboid()
// Synopsis: Creates a cube with chamfering and roundovers.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Shapes (3D), Attachable, VNF Generators
// See Also: prismoid(), rounded_prism()
// Usage: Standard Cubes
@ -604,7 +604,7 @@ function cuboid(
// chamfer = The chamfer size for the vertical-ish edges of the prismoid. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-]. Default: 0 (no chamfer)
// chamfer1 = The chamfer size for the bottom of the vertical-ish edges of the prismoid. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-].
// chamfer2 = The chamfer size for the top of the vertical-ish edges of the prismoid. If given as a list of four numbers, gives individual chamfers for each corner, in the order [X+Y+,X-Y+,X-Y-,X+Y-].
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `BOTTOM`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
//
@ -816,7 +816,7 @@ function octahedron(size=1, anchor=CENTER, spin=0, orient=UP) =
// Module: rect_tube()
// Synopsis: Creates a rectangular tube.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Shapes (3D), Attachable, VNF Generators
// See Also: tube()
// Usage: Typical Rectangular Tubes
@ -1286,6 +1286,8 @@ function cylinder(h, r1, r2, center, r, d, d1, d2, anchor, spin=0, orient=UP) =
// cyl(l|h|length|height, r1=, r2=, texture=, [tex_size=]|[tex_counts=], [tex_scale=], [tex_rot=], [tex_samples=], [tex_style=], [tex_taper=], [tex_inset=], ...);
// cyl(l|h|length|height, d1=, d2=, texture=, [tex_size=]|[tex_counts=], [tex_scale=], [tex_rot=], [tex_samples=], [tex_style=], [tex_taper=], [tex_inset=], ...);
//
// Usage: Caled as a function to get a VNF
// vnf = cyl(...);
//
// Description:
// Creates cylinders in various anchorings and orientations, with optional rounding, chamfers, or textures.
@ -1348,6 +1350,7 @@ function cylinder(h, r1, r2, center, r, d, d1, d2, anchor, spin=0, orient=UP) =
// rounding1 = The radius of the rounding on the bottom end of the cylinder.
// rounding2 = The radius of the rounding on the top end of the cylinder.
// realign = If true, rotate the cylinder by half the angle of one face.
// teardrop = If given as a number, rounding around the bottom edge of the cylinder won't exceed this many degrees from vertical. If true, the limit angle is 45 degrees. Default: `false`
// texture = A texture name string, or a rectangular array of scalar height values (0.0 to 1.0), or a VNF tile that defines the texture to apply to vertical surfaces. See {{texture()}} for what named textures are supported.
// tex_size = An optional 2D target size for the textures. Actual texture sizes will be scaled somewhat to evenly fit the available surface. Default: `[5,5]`
// tex_counts = If given instead of tex_size, gives the tile repetition counts for textures over the surface length and height.
@ -1385,6 +1388,9 @@ function cylinder(h, r1, r2, center, r, d, d1, d2, anchor, spin=0, orient=UP) =
// Example: Rounding
// cyl(l=40, d=40, rounding=10);
//
// Example(VPD=175;VPR=[90,0,0]): Teardrop Bottom Rounding
// cyl(l=40, d=40, rounding=10, teardrop=true);
//
// Example: Heterogenous Chamfers and Rounding
// ydistribute(80) {
// // Shown Front to Back.
@ -1490,6 +1496,7 @@ function cyl(
chamfang, chamfang1, chamfang2,
rounding, rounding1, rounding2,
circum=false, realign=false, shift=[0,0],
teardrop=false,
from_end, from_end1, from_end2,
texture, tex_size=[5,5], tex_counts,
tex_inset=false, tex_rot=false,
@ -1559,6 +1566,12 @@ function cyl(
dy1 = abs(_chamf1 ? chamf1l : round1 ? roundlen1 : 0),
dy2 = abs(_chamf2 ? chamf2l : round2 ? roundlen2 : 0),
td_ang = teardrop == true? 45 :
teardrop == false? 90 :
assert(is_finite(teardrop))
assert(teardrop>=0 && teardrop<=90)
teardrop,
checks2 =
assert(is_finite(round1), "rounding1 must be a number if given.")
assert(is_finite(round2), "rounding2 must be a number if given.")
@ -1570,14 +1583,18 @@ function cyl(
undef,
path = [
if (texture==undef) [0,-l/2],
if (!approx(chamf1r,0))
each [
[r1, -l/2] + polar_to_xy(chamf1r,180),
[r1, -l/2] + polar_to_xy(chamf1l,90+vang),
]
else if (!approx(round1,0))
else if (!approx(round1,0) && td_ang < 90)
each _teardrop_corner(r=abs(round1), corner=[[max(0,r1-2*roundlen1),-l/2],[r1,-l/2],[r2,l/2]], ang=td_ang)
else if (!approx(round1,0) && td_ang >= 90)
each arc(r=abs(round1), corner=[[max(0,r1-2*roundlen1),-l/2],[r1,-l/2],[r2,l/2]])
else [r1,-l/2],
if (is_finite(chamf2r) && !approx(chamf2r,0))
each [
[r2, l/2] + polar_to_xy(chamf2l,270+vang),
@ -1586,6 +1603,7 @@ function cyl(
else if (is_finite(round2) && !approx(round2,0))
each arc(r=abs(round2), corner=[[r1,-l/2],[r2,l/2],[max(0,r2-2*roundlen2),l/2]])
else [r2,l/2],
if (texture==undef) [0,l/2],
]
) rotate_sweep(path,
@ -1603,6 +1621,23 @@ function cyl(
reorient(anchor,spin,orient, r1=r1, r2=r2, l=l, shift=shift, p=ovnf);
function _teardrop_corner(r, corner, ang=45) =
let(
check = assert(len(corner)==3) assert(is_finite(r)) assert(is_finite(ang)),
cp = circle_2tangents(r, corner)[0],
path1 = arc(r=r, corner=corner),
path2 = [
for (p = select(path1,0,-2))
if (v_theta(p-cp) >= -ang) p,
last(path1)
],
path = [
line_intersection([corner[0],corner[1]],[path2[0],path2[0]+polar_to_xy(1,-90-ang)]),
each path2
]
) path;
module cyl(
h, r, center,
l, r1, r2,
@ -1611,6 +1646,7 @@ module cyl(
chamfang, chamfang1, chamfang2,
rounding, rounding1, rounding2,
circum=false, realign=false, shift=[0,0],
teardrop=false,
from_end, from_end1, from_end2,
texture, tex_size=[5,5], tex_counts,
tex_inset=false, tex_rot=false,
@ -1640,6 +1676,7 @@ module cyl(
chamfang=chamfang, chamfang1=chamfang1, chamfang2=chamfang2,
rounding=rounding, rounding1=rounding1, rounding2=rounding2,
from_end=from_end, from_end1=from_end1, from_end2=from_end2,
teardrop=teardrop,
texture=texture, tex_size=tex_size,
tex_counts=tex_counts, tex_scale=tex_scale,
tex_inset=tex_inset, tex_rot=tex_rot,
@ -1657,7 +1694,7 @@ module cyl(
// Module: xcyl()
// Synopsis: creates a cylinder oriented along the X axis.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Cylinders, Textures, Rounding, Chamfers
// See Also: texture(), rotate_sweep(), cyl()
// Description:
@ -1740,7 +1777,7 @@ module xcyl(
// Module: ycyl()
// Synopsis: Creates a cylinder oriented along the y axis.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Cylinders, Textures, Rounding, Chamfers
// See Also: texture(), rotate_sweep(), cyl()
// Description:
@ -1825,7 +1862,7 @@ module ycyl(
// Module: zcyl()
// Synopsis: Creates a cylinder oriented along the Z axis.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Cylinders, Textures, Rounding, Chamfers
// See Also: texture(), rotate_sweep(), cyl()
// Description:
@ -1909,7 +1946,7 @@ module zcyl(
// Module: tube()
// Synopsis: Creates a cylindrical or conical tube.
// SynTags: Geom, VNF
// SynTags: Geom
// Topics: Shapes (3D), Attachable, VNF Generators
// See Also: rect_tube()
// Description:
@ -3211,10 +3248,10 @@ module path_text(path, text, font, size, thickness, lettersize, offset=0, revers
// Topics: Shapes (3D), Attachable
// Module: fillet()
// Synopsis: Creates a smooth fillet between two faces.
// SynTags: Geom, VNF
// Topics: Shapes (3D), Attachable
// See Also: mask2d_roundover()
// Description:
// Creates a shape that can be unioned into a concave joint between two faces, to fillet them.

3
skin.scad
View File

@ -2799,7 +2799,7 @@ function associate_vertices(polygons, split, curpoly=0) =
// Topics: Textures, Knurling
// Synopsis: Produce a standard texture.
// Topics: Extrusion, Textures
// See Also: linear_sweep(), rotate_sweep()
// See Also: linear_sweep(), rotate_sweep(), heightfield(), cylindrical_heightfield()
// Usage:
// tx = texture(tex, [n=], [inset=], [gap=], [roughness=]);
// Description:
@ -2817,7 +2817,6 @@ function associate_vertices(polygons, split, curpoly=0) =
// inset = The amount to inset part of a VNF tile texture. Generally between 0 and 0.5.
// gap = The gap between logically distinct parts of a VNF tile. (ie: gap between bricks, gap between truncated ribs, etc.)
// roughness = The amount of roughness used on the surface of some heightfield textures. Generally between 0 and 0.5.
// See Also: heightfield(), cylindrical_heightfield(), texture()
// Example(3D): **"bricks"** (Heightfield) = A brick-wall pattern. Giving `n=` sets the number of heightfield samples to `n x n`. Default: 24. Giving `roughness=` adds a level of height randomization to add roughness to the texture. Default: 0.05. Use `style="convex"`.
// tex = texture("bricks");
// linear_sweep(

2
sliders.scad
View File

@ -14,6 +14,7 @@
// Module: slider()
// Synopsis: Creates a V-groove slider.
// SynTags: Geom
// Topics: Parts, Sliders
// See Also: rail()
// Usage:
@ -67,6 +68,7 @@ module slider(l=30, w=10, h=10, base=10, wall=5, ang=30, anchor=BOTTOM, spin=0,
// Module: rail()
// Synopsis: Creates a V-groove rail.
// SynTags: Geom
// Topics: Parts, Sliders
// See Also: slider()
// Usage:

54
threading.scad
View File

@ -451,7 +451,6 @@ module threaded_nut(
// right(14)back(19)text("flank",size=4,halign="center");
// right(14)back(14)text("angle",size=4,halign="center");
// }
// Arguments:
// d = Outer diameter of threaded rod.
// l / length / h / height = Length of threaded rod.
@ -1248,7 +1247,6 @@ module buttress_threaded_nut(
// bevel1 = if true bevel the bottom end.
// bevel2 = if true bevel the top end.
// internal = If true, this is a mask for making internal threads.
// blunt_start = If true apply truncated blunt start threads at both ends. Default: true
// blunt_start1 = If true apply truncated blunt start threads bottom end.
// blunt_start2 = If true apply truncated blunt start threads top end.
@ -2039,32 +2037,6 @@ module _nutshape(nutwidth, h, shape, bevel1, bevel2)
// The taper options specify tapering at of the threads at each end, and is given as the linear distance
// over which to taper. If taper is positive the threads are lengthened by the specified distance; if taper
// is negative, the taper is included in the thread length specified by `turns`. Tapering works on both internal and external threads.
// Arguments:
// d = Inside base diameter of threads. Default: 10
// pitch = Distance between threads. Default: 2
// ---
// thread_depth = Depth of threads from top to bottom.
// flank_angle = Angle of thread faces to plane perpendicular to screw. Default: 15 degrees.
// turns = Number of revolutions to rotate thread around.
// thread_angle = Angle between two thread faces.
// profile = If an asymmetrical thread profile is needed, it can be specified here.
// starts = The number of thread starts. Default: 1
// left_handed = If true, thread has a left-handed winding.
// internal = if true make internal threads. The only effect this has is to change how the threads taper if tapering is selected. When true, threads taper towards the outside; when false, they taper towards the inside. Default: false
// d1 = Bottom inside base diameter of threads.
// d2 = Top inside base diameter of threads.
// thread_angle = Angle between
// lead_in = Specify linear length of the lead in section of the threading with blunt start threads
// lead_in1 = Specify linear length of the lead in section of the threading at the bottom with blunt start threads
// lead_in2 = Specify linear length of the lead in section of the threading at the top with blunt start threads
// lead_in_ang = Specify angular length in degrees of the lead in section of the threading with blunt start threads
// lead_in_ang1 = Specify angular length in degrees of the lead in section of the threading at the bottom with blunt start threads
// lead_in_ang2 = Specify angular length in degrees of the lead in section of the threading at the top with blunt start threads
// lead_in_shape = Specify the shape of the thread lead in by giving a text string or function. Default: "default"
// lead_in_sample = Factor to increase sample rate in the lead-in section. Default: 10
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Figure(2D,Med,NoAxes):
// pa_delta = tan(15)/4;
// rr1 = -1/2;
@ -2113,6 +2085,32 @@ module _nutshape(nutwidth, h, shape, bevel1, bevel2)
// back(10)text("thread",size=4,halign="center");
// back(3)text("angle",size=4,halign="center");
// }
// Arguments:
// d = Inside base diameter of threads. Default: 10
// pitch = Distance between threads. Default: 2
// ---
// thread_depth = Depth of threads from top to bottom.
// flank_angle = Angle of thread faces to plane perpendicular to screw. Default: 15 degrees.
// turns = Number of revolutions to rotate thread around.
// thread_angle = Angle between two thread faces.
// profile = If an asymmetrical thread profile is needed, it can be specified here.
// starts = The number of thread starts. Default: 1
// left_handed = If true, thread has a left-handed winding.
// internal = if true make internal threads. The only effect this has is to change how the threads taper if tapering is selected. When true, threads taper towards the outside; when false, they taper towards the inside. Default: false
// d1 = Bottom inside base diameter of threads.
// d2 = Top inside base diameter of threads.
// thread_angle = Angle between
// lead_in = Specify linear length of the lead in section of the threading with blunt start threads
// lead_in1 = Specify linear length of the lead in section of the threading at the bottom with blunt start threads
// lead_in2 = Specify linear length of the lead in section of the threading at the top with blunt start threads
// lead_in_ang = Specify angular length in degrees of the lead in section of the threading with blunt start threads
// lead_in_ang1 = Specify angular length in degrees of the lead in section of the threading at the bottom with blunt start threads
// lead_in_ang2 = Specify angular length in degrees of the lead in section of the threading at the top with blunt start threads
// lead_in_shape = Specify the shape of the thread lead in by giving a text string or function. Default: "default"
// lead_in_sample = Factor to increase sample rate in the lead-in section. Default: 10
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Example(2DMed): Typical Tooth Profile
// pitch = 2;
// depth = pitch * cos(30) * 5/8;

243
transforms.scad
View File

@ -74,6 +74,11 @@ _NO_ARG = [true,[123232345],false];
// Function&Module: move()
// Aliases: translate()
//
// Synopsis: Translates children in an arbitrary direction.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: left(), right(), fwd(), back(), down(), up(), spherical_to_xyz(), altaz_to_xyz(), cylindrical_to_xyz(), polar_to_xy()
//
// Usage: As Module
// move(v) CHILDREN;
// Usage: As a function to translate points, VNF, or Bezier patches
@ -82,11 +87,6 @@ _NO_ARG = [true,[123232345],false];
// Usage: Get Translation Matrix
// mat = move(v);
//
// Synopsis: Translates children in an arbitrary direction.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: left(), right(), fwd(), back(), down(), up(), spherical_to_xyz(), altaz_to_xyz(), cylindrical_to_xyz(), polar_to_xy()
//
// Description:
// Translates position by the given amount.
// * Called as a module, moves/translates all children.
@ -160,6 +160,11 @@ function translate(v=[0,0,0], p=_NO_ARG) = move(v=v, p=p);
// Function&Module: left()
//
// Synopsis: Translates children leftwards (X-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), right(), fwd(), back(), down(), up()
//
// Usage: As Module
// left(x) CHILDREN;
// Usage: Translate Points
@ -167,11 +172,6 @@ function translate(v=[0,0,0], p=_NO_ARG) = move(v=v, p=p);
// Usage: Get Translation Matrix
// mat = left(x);
//
// Synopsis: Translates children leftwards (X-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), right(), fwd(), back(), down(), up()
//
// Description:
// If called as a module, moves/translates all children left (in the X- direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF, point or list of points.
@ -205,6 +205,11 @@ function left(x=0, p=_NO_ARG) =
// Function&Module: right()
// Aliases: xmove()
//
// Synopsis: Translates children rightwards (X+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), fwd(), back(), down(), up()
//
// Usage: As Module
// right(x) CHILDREN;
// Usage: Translate Points
@ -212,11 +217,6 @@ function left(x=0, p=_NO_ARG) =
// Usage: Get Translation Matrix
// mat = right(x);
//
// Synopsis: Translates children rightwards (X+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), fwd(), back(), down(), up()
//
// Description:
// If called as a module, moves/translates all children right (in the X+ direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF point or list of points.
@ -260,6 +260,11 @@ function xmove(x=0, p=_NO_ARG) =
// Function&Module: fwd()
//
// Synopsis: Translates children forwards (Y-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), back(), down(), up()
//
// Usage: As Module
// fwd(y) CHILDREN;
// Usage: Translate Points
@ -267,11 +272,6 @@ function xmove(x=0, p=_NO_ARG) =
// Usage: Get Translation Matrix
// mat = fwd(y);
//
// Synopsis: Translates children forwards (Y-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), back(), down(), up()
//
// Description:
// If called as a module, moves/translates all children forward (in the Y- direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF, point or list of points.
@ -305,6 +305,11 @@ function fwd(y=0, p=_NO_ARG) =
// Function&Module: back()
// Aliases: ymove()
//
// Synopsis: Translates children backwards (Y+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), down(), up()
//
// Usage: As Module
// back(y) CHILDREN;
// Usage: Translate Points
@ -312,11 +317,6 @@ function fwd(y=0, p=_NO_ARG) =
// Usage: Get Translation Matrix
// mat = back(y);
//
// Synopsis: Translates children backwards (Y+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), down(), up()
//
// Description:
// If called as a module, moves/translates all children back (in the Y+ direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF, point or list of points.
@ -360,6 +360,11 @@ function ymove(y=0,p=_NO_ARG) =
// Function&Module: down()
//
// Synopsis: Translates children downwards (Z-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), back(), up()
//
// Usage: As Module
// down(z) CHILDREN;
// Usage: Translate Points
@ -367,11 +372,6 @@ function ymove(y=0,p=_NO_ARG) =
// Usage: Get Translation Matrix
// mat = down(z);
//
// Synopsis: Translates children downwards (Z-).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), back(), up()
//
// Description:
// If called as a module, moves/translates all children down (in the Z- direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF, point or list of points.
@ -403,6 +403,11 @@ function down(z=0, p=_NO_ARG) =
// Function&Module: up()
// Aliases: zmove()
//
// Synopsis: Translates children upwards (Z+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), back(), down()
//
// Usage: As Module
// up(z) CHILDREN;
// Usage: Translate Points
@ -410,11 +415,6 @@ function down(z=0, p=_NO_ARG) =
// Usage: Get Translation Matrix
// mat = up(z);
//
// Synopsis: Translates children upwards (Z+).
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Translation
// See Also: move(), left(), right(), fwd(), back(), down()
//
// Description:
// If called as a module, moves/translates all children up (in the Z+ direction) by the given amount.
// If called as a function with the `p` argument, returns the translated VNF, point or list of points.
@ -463,6 +463,11 @@ function zmove(z=0, p=_NO_ARG) =
// Function&Module: rot()
//
// Synopsis: Rotates children in various ways.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: xrot(), yrot(), zrot()
//
// Usage: As a Module
// rot(a, [cp=], [reverse=]) CHILDREN;
// rot([X,Y,Z], [cp=], [reverse=]) CHILDREN;
@ -479,11 +484,6 @@ function zmove(z=0, p=_NO_ARG) =
// M = rot(a, v, [cp=], [reverse=]);
// M = rot(from=, to=, [a=], [reverse=]);
//
// Synopsis: Rotates children in various ways.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: xrot(), yrot(), zrot()
//
// Description:
// This is a shorthand version of the built-in `rotate()`, and operates similarly, with a few additional capabilities.
// You can specify the rotation to perform in one of several ways:
@ -569,6 +569,11 @@ function rot(a=0, v, cp, from, to, reverse=false, p=_NO_ARG, _m) =
// Function&Module: xrot()
//
// Synopsis: Rotates children around the X axis using the right-hand rule.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), yrot(), zrot()
//
// Usage: As Module
// xrot(a, [cp=]) CHILDREN;
// Usage: As a function to rotate points
@ -576,11 +581,6 @@ function rot(a=0, v, cp, from, to, reverse=false, p=_NO_ARG, _m) =
// Usage: As a function to return rotation matrix
// mat = xrot(a, [cp=]);
//
// Synopsis: Rotates children around the X axis using the right-hand rule.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), yrot(), zrot()
//
// Description:
// Rotates around the X axis by the given number of degrees. If `cp` is given, rotations are performed around that centerpoint.
// * Called as a module, rotates all children.
@ -617,6 +617,11 @@ function xrot(a=0, p=_NO_ARG, cp) = rot([a,0,0], cp=cp, p=p);
// Function&Module: yrot()
//
// Synopsis: Rotates children around the Y axis using the right-hand rule.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), xrot(), zrot()
//
// Usage: As Module
// yrot(a, [cp=]) CHILDREN;
// Usage: Rotate Points
@ -624,11 +629,6 @@ function xrot(a=0, p=_NO_ARG, cp) = rot([a,0,0], cp=cp, p=p);
// Usage: Get Rotation Matrix
// mat = yrot(a, [cp=]);
//
// Synopsis: Rotates children around the Y axis using the right-hand rule.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), xrot(), zrot()
//
// Description:
// Rotates around the Y axis by the given number of degrees. If `cp` is given, rotations are performed around that centerpoint.
// * Called as a module, rotates all children.
@ -665,6 +665,11 @@ function yrot(a=0, p=_NO_ARG, cp) = rot([0,a,0], cp=cp, p=p);
// Function&Module: zrot()
//
// Synopsis: Rotates children around the Z axis using the right-hand rule.
// Topics: Affine, Matrices, Transforms, Rotation
// SynTags: Trans, Path, VNF, Mat
// See Also: rot(), xrot(), yrot()
//
// Usage: As Module
// zrot(a, [cp=]) CHILDREN;
// Usage: As Function to rotate points
@ -672,11 +677,6 @@ function yrot(a=0, p=_NO_ARG, cp) = rot([0,a,0], cp=cp, p=p);
// Usage: As Function to return rotation matrix
// mat = zrot(a, [cp=]);
//
// Synopsis: Rotates children around the Z axis using the right-hand rule.
// Topics: Affine, Matrices, Transforms, Rotation
// SynTags: Trans, Path, VNF, Mat
// See Also: rot(), xrot(), yrot()
//
// Description:
// Rotates around the Z axis by the given number of degrees. If `cp` is given, rotations are performed around that centerpoint.
// * Called as a module, rotates all children.
@ -718,6 +718,12 @@ function zrot(a=0, p=_NO_ARG, cp) = rot(a, cp=cp, p=p);
// Function&Module: scale()
//
// Synopsis: Scales children arbitrarily.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: xscale(), yscale(), zscale()
//
// Usage: As Module
// scale(SCALAR) CHILDREN;
// scale([X,Y,Z]) CHILDREN;
@ -725,10 +731,7 @@ function zrot(a=0, p=_NO_ARG, cp) = rot(a, cp=cp, p=p);
// pts = scale(v, p, [cp=]);
// Usage: Get Scaling Matrix
// mat = scale(v, [cp=]);
// Synopsis: Scales children arbitrarily.
// Topics: Affine, Matrices, Transforms, Scaling
// SynTags: Trans, Path, VNF, Mat
// See Also: xscale(), yscale(), zscale()
//
// Description:
// Scales by the [X,Y,Z] scaling factors given in `v`. If `v` is given as a scalar number, all axes are scaled uniformly by that amount.
// * Called as the built-in module, scales all children.
@ -738,17 +741,20 @@ function zrot(a=0, p=_NO_ARG, cp) = rot(a, cp=cp, p=p);
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the scaled VNF.
// * Called as a function without a `p` argument, and a 2D list of scaling factors in `v`, returns an affine2d scaling matrix.
// * Called as a function without a `p` argument, and a 3D list of scaling factors in `v`, returns an affine3d scaling matrix.
//
// Arguments:
// v = Either a numeric uniform scaling factor, or a list of [X,Y,Z] scaling factors. Default: 1
// p = If called as a function, the point or list of points to scale.
// ---
// cp = If given, centers the scaling on the point `cp`.
//
// Example(NORENDER):
// pt1 = scale(3, p=[3,1,4]); // Returns: [9,3,12]
// pt2 = scale([2,3,4], p=[3,1,4]); // Returns: [6,3,16]
// pt3 = scale([2,3,4], p=[[1,2,3],[4,5,6]]); // Returns: [[2,6,12], [8,15,24]]
// mat2d = scale([2,3]); // Returns: [[2,0,0],[0,3,0],[0,0,1]]
// mat3d = scale([2,3,4]); // Returns: [[2,0,0,0],[0,3,0,0],[0,0,4,0],[0,0,0,1]]
//
// Example(2D):
// path = circle(d=50,$fn=12);
// #stroke(path,closed=true);
@ -770,6 +776,11 @@ function scale(v=1, p=_NO_ARG, cp=[0,0,0]) =
// Function&Module: xscale()
//
// Synopsis: Scales children along the X axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), yscale(), zscale()
//
// Usage: As Module
// xscale(x, [cp=]) CHILDREN;
// Usage: Scale Points
@ -777,11 +788,6 @@ function scale(v=1, p=_NO_ARG, cp=[0,0,0]) =
// Usage: Get Affine Matrix
// mat = xscale(x, [cp=]);
//
// Synopsis: Scales children along the X axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), yscale(), zscale()
//
// Description:
// Scales along the X axis by the scaling factor `x`.
// * Called as the built-in module, scales all children.
@ -826,6 +832,11 @@ function xscale(x=1, p=_NO_ARG, cp=0) =
// Function&Module: yscale()
//
// Synopsis: Scales children along the Y axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), xscale(), zscale()
//
// Usage: As Module
// yscale(y, [cp=]) CHILDREN;
// Usage: Scale Points
@ -833,11 +844,6 @@ function xscale(x=1, p=_NO_ARG, cp=0) =
// Usage: Get Affine Matrix
// mat = yscale(y, [cp=]);
//
// Synopsis: Scales children along the Y axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), xscale(), zscale()
//
// Description:
// Scales along the Y axis by the scaling factor `y`.
// * Called as the built-in module, scales all children.
@ -882,6 +888,11 @@ function yscale(y=1, p=_NO_ARG, cp=0) =
// Function&Module: zscale()
//
// Synopsis: Scales children along the Z axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), xscale(), yscale()
//
// Usage: As Module
// zscale(z, [cp=]) CHILDREN;
// Usage: Scale Points
@ -889,11 +900,6 @@ function yscale(y=1, p=_NO_ARG, cp=0) =
// Usage: Get Affine Matrix
// mat = zscale(z, [cp=]);
//
// Synopsis: Scales children along the Z axis.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Scaling
// See Also: scale(), xscale(), yscale()
//
// Description:
// Scales along the Z axis by the scaling factor `z`.
// * Called as the built-in module, scales all children.
@ -941,16 +947,19 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
//////////////////////////////////////////////////////////////////////
// Function&Module: mirror()
//
// Synopsis: Reflects children across an arbitrary plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: xflip(), yflip(), zflip()
//
// Usage: As Module
// mirror(v) CHILDREN;
// Usage: As Function
// pt = mirror(v, p);
// Usage: Get Reflection/Mirror Matrix
// mat = mirror(v);
// Synopsis: Reflects children across an arbitrary plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: xflip(), yflip(), zflip()
//
// Description:
// Mirrors/reflects across the plane or line whose normal vector is given in `v`.
// * Called as the built-in module, mirrors all children across the line/plane.
@ -960,9 +969,11 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// * Called as a function with a [VNF structure](vnf.scad) in the `p` argument, returns the mirrored VNF.
// * Called as a function without a `p` argument, and with a 2D normal vector `v`, returns the affine2d 3x3 mirror matrix.
// * Called as a function without a `p` argument, and with a 3D normal vector `v`, returns the affine3d 4x4 mirror matrix.
//
// Arguments:
// v = The normal vector of the line or plane to mirror across.
// p = If called as a function, the point or list of points to scale.
//
// Example:
// n = [1,0,0];
// module obj() right(20) rotate([0,15,-15]) cube([40,30,20]);
@ -972,6 +983,7 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// color("red") anchor_arrow(s=20, flag=false);
// color("#7777") cube([75,75,0.1], center=true);
// }
//
// Example:
// n = [1,1,0];
// module obj() right(20) rotate([0,15,-15]) cube([40,30,20]);
@ -981,6 +993,7 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// color("red") anchor_arrow(s=20, flag=false);
// color("#7777") cube([75,75,0.1], center=true);
// }
//
// Example:
// n = [1,1,1];
// module obj() right(20) rotate([0,15,-15]) cube([40,30,20]);
@ -990,6 +1003,7 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// color("red") anchor_arrow(s=20, flag=false);
// color("#7777") cube([75,75,0.1], center=true);
// }
//
// Example(2D):
// n = [0,1];
// path = rot(30, p=square([50,30]));
@ -997,6 +1011,7 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// color("red") stroke([[0,0],10*n],endcap2="arrow2");
// #stroke(path,closed=true);
// stroke(mirror(n, p=path),closed=true);
//
// Example(2D):
// n = [1,1];
// path = rot(30, p=square([50,30]));
@ -1004,6 +1019,7 @@ function zscale(z=1, p=_NO_ARG, cp=0) =
// color("red") stroke([[0,0],10*n],endcap2="arrow2");
// #stroke(path,closed=true);
// stroke(mirror(n, p=path),closed=true);
//
function mirror(v, p=_NO_ARG) =
assert(is_vector(v))
assert(p==_NO_ARG || is_list(p),"Invalid pointlist")
@ -1013,6 +1029,11 @@ function mirror(v, p=_NO_ARG) =
// Function&Module: xflip()
//
// Synopsis: Reflects children across the YZ plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), yflip(), zflip()
//
// Usage: As Module
// xflip([x=]) CHILDREN;
// Usage: As Function
@ -1020,11 +1041,6 @@ function mirror(v, p=_NO_ARG) =
// Usage: Get Affine Matrix
// mat = xflip([x=]);
//
// Synopsis: Reflects children across the YZ plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), yflip(), zflip()
//
// Description:
// Mirrors/reflects across the origin [0,0,0], along the X axis. If `x` is given, reflects across [x,0,0] instead.
// * Called as the built-in module, mirrors all children across the line/plane.
@ -1069,6 +1085,11 @@ function xflip(p=_NO_ARG, x=0) =
// Function&Module: yflip()
//
// Synopsis: Reflects children across the XZ plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), xflip(), zflip()
//
// Usage: As Module
// yflip([y=]) CHILDREN;
// Usage: As Function
@ -1076,11 +1097,6 @@ function xflip(p=_NO_ARG, x=0) =
// Usage: Get Affine Matrix
// mat = yflip([y=]);
//
// Synopsis: Reflects children across the XZ plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), xflip(), zflip()
//
// Description:
// Mirrors/reflects across the origin [0,0,0], along the Y axis. If `y` is given, reflects across [0,y,0] instead.
// * Called as the built-in module, mirrors all children across the line/plane.
@ -1125,6 +1141,11 @@ function yflip(p=_NO_ARG, y=0) =
// Function&Module: zflip()
//
// Synopsis: Reflects children across the XY plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), xflip(), yflip()
//
// Usage: As Module
// zflip([z=]) CHILDREN;
// Usage: As Function
@ -1132,11 +1153,6 @@ function yflip(p=_NO_ARG, y=0) =
// Usage: Get Affine Matrix
// mat = zflip([z=]);
//
// Synopsis: Reflects children across the XY plane.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Reflection, Mirroring
// See Also: mirror(), xflip(), yflip()
//
// Description:
// Mirrors/reflects across the origin [0,0,0], along the Z axis. If `z` is given, reflects across [0,0,z] instead.
// * Called as the built-in module, mirrors all children across the line/plane.
@ -1180,6 +1196,12 @@ function zflip(p=_NO_ARG, z=0) =
//////////////////////////////////////////////////////////////////////
// Function&Module: frame_map()
//
// Synopsis: Rotates and possibly skews children from one frame of reference to another.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), xrot(), yrot(), zrot()
//
// Usage: As module
// frame_map(v1, v2, v3, [reverse=]) CHILDREN;
// Usage: As function to remap points
@ -1189,10 +1211,7 @@ function zflip(p=_NO_ARG, z=0) =
// map = frame_map(x=VECTOR1, y=VECTOR2, [reverse=]);
// map = frame_map(x=VECTOR1, z=VECTOR2, [reverse=]);
// map = frame_map(y=VECTOR1, z=VECTOR2, [reverse=]);
// Synopsis: Rotates and possibly skews children from one frame of reference to another.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Rotation
// See Also: rot(), xrot(), yrot(), zrot()
//
// Description:
// Maps one coordinate frame to another. You must specify two or
// three of `x`, `y`, and `z`. The specified axes are mapped to the vectors you supplied, so if you
@ -1204,19 +1223,24 @@ function zflip(p=_NO_ARG, z=0) =
// You cannot use the `reverse` option with non-orthogonal inputs. Note that only the direction
// of the specified vectors matters: the transformation will not apply scaling, though it can
// skew if your provide non-orthogonal axes.
//
// Arguments:
// x = Destination 3D vector for x axis.
// y = Destination 3D vector for y axis.
// z = Destination 3D vector for z axis.
// p = If given, the point, path, patch, or VNF to operate on. Function use only.
// reverse = reverse direction of the map for orthogonal inputs. Default: false
//
// Example: Remap axes after linear extrusion
// frame_map(x=[0,1,0], y=[0,0,1]) linear_extrude(height=10) square(3);
//
// Example: This map is just a rotation around the z axis
// mat = frame_map(x=[1,1,0], y=[-1,1,0]);
// multmatrix(mat) frame_ref();
//
// Example: This map is not a rotation because x and y aren't orthogonal
// frame_map(x=[1,0,0], y=[1,1,0]) cube(10);
//
// Example: This sends [1,1,0] to [0,1,1] and [-1,1,0] to [0,-1,1]. (Original directions shown in light shade, final directions shown dark.)
// mat = frame_map(x=[0,1,1], y=[0,-1,1]) * frame_map(x=[1,1,0], y=[-1,1,0],reverse=true);
// color("purple",alpha=.2) stroke([[0,0,0],10*[1,1,0]]);
@ -1225,6 +1249,7 @@ function zflip(p=_NO_ARG, z=0) =
// color("purple") stroke([[0,0,0],10*[1,1,0]]);
// color("green") stroke([[0,0,0],10*[-1,1,0]]);
// }
//
function frame_map(x,y,z, p=_NO_ARG, reverse=false) =
p != _NO_ARG
? apply(frame_map(x,y,z,reverse=reverse), p)
@ -1270,15 +1295,18 @@ module frame_map(x,y,z,p,reverse=false)
// Function&Module: skew()
//
// Synopsis: Skews children along various axes.
// SynTags: Trans, Path, VNF, Mat
// Topics: Affine, Matrices, Transforms, Skewing
// See Also: move(), rot(), scale()
//
// Usage: As Module
// skew([sxy=]|[axy=], [sxz=]|[axz=], [syx=]|[ayx=], [syz=]|[ayz=], [szx=]|[azx=], [szy=]|[azy=]) CHILDREN;
// Usage: As Function
// pts = skew(p, [sxy=]|[axy=], [sxz=]|[axz=], [syx=]|[ayx=], [syz=]|[ayz=], [szx=]|[azx=], [szy=]|[azy=]);
// Usage: Get Affine Matrix
// mat = skew([sxy=]|[axy=], [sxz=]|[axz=], [syx=]|[ayx=], [syz=]|[ayz=], [szx=]|[azx=], [szy=]|[azy=]);
// Topics: Affine, Matrices, Transforms, Skewing
// Synopsis: Skews children along various axes.
// SynTags: Trans, Path, VNF, Mat
//
// Description:
// Skews geometry by the given skew factors.
@ -1399,11 +1427,15 @@ function is_2d_transform(t) = // z-parameters are zero, except we allow t[2][
// Function: apply()
//
// Synopsis: Applies a transformation matrix to a point, list of points, array of points, or a VNF.
// SynTags: Path, VNF, Mat
// Topics: Affine, Matrices, Transforms
// See Also: move(), rot(), scale(), skew()
//
// Usage:
// pts = apply(transform, points);
// Topics: Affine, Matrices, Transforms
// Synopsis: Applies a transformation matrix to a point, list of points, array of points, or VNF.
// SynTags: Path, VNF, Mat
//
// Description:
// Applies the specified transformation matrix `transform` to a point, point list, bezier patch or VNF.
// When `points` contains 2D or 3D points the transform matrix may be a 4x4 affine matrix or a 3x4
@ -1418,27 +1450,32 @@ function is_2d_transform(t) = // z-parameters are zero, except we allow t[2][
// If the transform matrix is square then apply() checks the determinant and if it is negative, apply() reverses the face order so that
// the transformed VNF has faces with the same winding direction as the original VNF. This adjustment applies
// only to VNFs, not to beziers or point lists.
//
// Arguments:
// transform = The 2D (3x3 or 2x3) or 3D (4x4 or 3x4) transformation matrix to apply.
// points = The point, point list, bezier patch, or VNF to apply the transformation to.
//
// Example(3D):
// path1 = path3d(circle(r=40));
// tmat = xrot(45);
// path2 = apply(tmat, path1);
// #stroke(path1,closed=true);
// stroke(path2,closed=true);
//
// Example(2D):
// path1 = circle(r=40);
// tmat = translate([10,5]);
// path2 = apply(tmat, path1);
// #stroke(path1,closed=true);
// stroke(path2,closed=true);
//
// Example(2D):
// path1 = circle(r=40);
// tmat = rot(30) * back(15) * scale([1.5,0.5,1]);
// path2 = apply(tmat, path1);
// #stroke(path1,closed=true);
// stroke(path2,closed=true);
//
function apply(transform,points) =
points==[] ? []
: is_vector(points) ? _apply(transform, [points])[0] // point

2
tripod_mounts.scad
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@ -11,7 +11,9 @@
// Module: manfrotto_rc2_plate()
// Synopsis: Creates a Manfrotto RC2 tripod quick release mount plate.
// SynTags: Geom
// Topics: Parts
// See Also: threaded_rod()
// Usage:
// manfrotto_rc2_plate([chamfer],[anchor],[orient],[spin]) [ATTACHMENTS];
// Description:

5
turtle3d.scad
View File

@ -21,10 +21,13 @@ function _rotpart(T) = [for(i=[0:3]) [for(j=[0:3]) j<3 || i==3 ? T[i][j] : 0]];
// Function: turtle3d()
// Synopsis: Extends [turtle graphics](https://en.wikipedia.org/wiki/Turtle_graphics) to 3d. Generates a 3D path or returns a list of transforms.
// SynTags: MatList, Path
// Topics: Shapes (3D), Path Generators (3D), Mini-Language
// See Also: turtle()
// Usage:
// turtle3d(commands, [state], [transforms], [full_state], [repeat])
// path = turtle3d(commands, [state=], [repeat=]);
// mats = turtle3d(commands, transforms=true, [state=], [repeat=]);
// state = turtle3d(commands, full_state=true, [state=], [repeat=]);
// Description:
// Like the classic two dimensional turtle, the 3d turtle flies through space following a sequence
// of turtle graphics commands to generate either a sequence of transformations (suitable for input

18
utility.scad
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@ -73,10 +73,11 @@ function is_type(x,types) =
// Function: is_def()
// Usage:
// bool = is_def(x);
// Synopsis: Returns true if `x` is not `undef`.
// Topics: Type Checking
// See Also: typeof(), is_type(), is_str()
// Usage:
// bool = is_def(x);
// Description:
// Returns true if `x` is not `undef`. False if `x==undef`.
// Arguments:
@ -108,8 +109,8 @@ function is_str(x) = is_string(x);
// Function: is_int()
// Synopsis: Returns true if the argument is an integer.
// Alias: is_integer()
// Synopsis: Returns true if the argument is an integer.
// Topics: Type Checking
// See Also: typeof(), is_type(), is_str(), is_def()
// Usage:
@ -197,10 +198,10 @@ function is_finite(x) = is_num(x) && !is_nan(0*x);
// Function: is_range()
// Synopsis: Returns true if the argument is a range.
// Usage:
// bool = is_range(x);
// Topics: Type Checking
// See Also: typeof(), is_type(), is_str(), is_def(), is_int()
// Usage:
// bool = is_range(x);
// Description:
// Returns true if its argument is a range
// Arguments:
@ -768,6 +769,7 @@ function scalar_vec3(v, dflt) =
// Function: segs()
// Synopsis: Returns the number of sides for a circle given `$fn`, `$fa`, and `$fs`.
// Topics: Geometry
// See Also: circle(), cyl()
// Usage:
// sides = segs(r);
// Description:
@ -831,10 +833,10 @@ module req_children(count) {
// Function: no_function()
// Synopsis: Assert that the argument exists only as a module and not as a function.
// Usage:
// dummy = no_function(name)
// Topics: Error Checking
// See Also: no_children(), no_module()
// Usage:
// dummy = no_function(name)
// Description:
// Asserts that the function, "name", only exists as a module.
// Example:
@ -860,6 +862,8 @@ module no_module() {
// Module: deprecate()
// Synopsis: Display a console note that a module is deprecated and suggest a replacement.
// Topics: Error Checking
// See Also: no_function(), no_module()
// Usage:
// deprecate(new_name);
// Description:

2
vectors.scad
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@ -339,7 +339,7 @@ function vector_bisect(v1,v2) =
let(
axis = vector_axis(v1,v2),
ang = vector_angle(v1,v2),
v3 = rot(ang/2, v=axis, p=v1)
v3 = unit(rot(ang/2, v=axis, p=v1))
) v3;

22
vnf.scad
View File

@ -29,6 +29,7 @@ EMPTY_VNF = [[],[]]; // The standard empty VNF with no vertices or faces.
// Function: vnf_vertex_array()
// Synopsis: Returns a VNF structure from a rectangular vertex list.
// SynTags: VNF
// Topics: VNF Generators, Lists
// See Also: vnf_tri_array(), vnf_join(), vnf_from_polygons(), vnf_from_region()
// Usage:
@ -232,6 +233,7 @@ function vnf_vertex_array(
// Function: vnf_tri_array()
// Synopsis: Returns a VNF from an array of points.
// SynTags: VNF
// Topics: VNF Generators, Lists
// See Also: vnf_vertex_array(), vnf_join(), vnf_from_polygons(), vnf_from_region()
// Usage:
@ -327,6 +329,7 @@ function vnf_tri_array(points, row_wrap=false, reverse=false) =
// Function: vnf_join()
// Synopsis: Returns a single VNF structure from a list of VNF structures.
// SynTags: VNF
// Topics: VNF Generators, Lists
// See Also: vnf_tri_array(), vnf_vertex_array(), vnf_from_polygons(), vnf_from_region()
// Usage:
@ -413,6 +416,7 @@ function vnf_join(vnfs) =
// Function: vnf_from_polygons()
// Synopsis: Returns a VNF from a list of 3D polygons.
// SynTags: VNF
// Topics: VNF Generators, Lists
// See Also: vnf_tri_array(), vnf_join(), vnf_vertex_array(), vnf_from_region()
// Usage:
@ -579,8 +583,9 @@ function _bridge(pt, outer,eps) =
// Function: vnf_from_region()
// Topics: VNF Generators, Lists
// Synopsis: Returns a 3D VNF given a 2D region.
// SynTags: VNF
// Topics: VNF Generators, Lists
// See Also: vnf_vertex_array(), vnf_tri_array(), vnf_join(), vnf_from_polygons()
// Usage:
// vnf = vnf_from_region(region, [transform], [reverse]);
@ -672,6 +677,7 @@ function vnf_faces(vnf) = vnf[1];
// Function: vnf_reverse_faces()
// Synopsis: Reverses the faces of a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_quantize(), vnf_merge_points(), vnf_drop_unused_points(), vnf_triangulate(), vnf_slice()
// Usage:
@ -684,6 +690,7 @@ function vnf_reverse_faces(vnf) =
// Function: vnf_quantize()
// Synopsis: Quantizes the vertex coordinates of a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_reverse_faces(), vnf_merge_points(), vnf_drop_unused_points(), vnf_triangulate(), vnf_slice()
// Usage:
@ -699,7 +706,8 @@ function vnf_quantize(vnf,q=pow(2,-12)) =
// Function: vnf_merge_points()
// Synopsis: COnsolidates duplicate vertices of a VNF.
// Synopsis: Consolidates duplicate vertices of a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_reverse_faces(), vnf_quantize(), vnf_drop_unused_points(), vnf_triangulate(), vnf_slice()
// Usage:
@ -735,6 +743,7 @@ function vnf_merge_points(vnf,eps=EPSILON) =
// Function: vnf_drop_unused_points()
// Synopsis: Removes unreferenced vertices from a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_reverse_faces(), vnf_quantize(), vnf_merge_points(), vnf_triangulate(), vnf_slice()
// Usage:
@ -766,6 +775,7 @@ function _link_indicator(l,imin,imax) =
// Function: vnf_triangulate()
// Synopsis: Triangulates the faces of a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_reverse_faces(), vnf_quantize(), vnf_merge_points(), vnf_drop_unused_points(), vnf_slice()
// Usage:
@ -809,6 +819,7 @@ function _vnf_sort_vertices(vnf, idx=[2,1,0]) =
// Function: vnf_slice()
// Synopsis: Slice the faces of a VNF along an axis.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_reverse_faces(), vnf_quantize(), vnf_merge_points(), vnf_drop_unused_points(), vnf_triangulate()
// Usage:
@ -937,6 +948,7 @@ function _slice_3dpolygons(polys, dir, cuts) =
// Module: vnf_polyhedron()
// Synopsis: Returns a polyhedron from a VNF or list of VNFs.
// SynTags: Geom
// Topics: VNF Manipulation
// See Also: vnf_wireframe()
// Usage:
@ -970,6 +982,7 @@ module vnf_polyhedron(vnf, convexity=2, extent=true, cp="centroid", anchor="orig
// Module: vnf_wireframe()
// Synopsis: Creates a wireframe model from a VNF.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_polyhedron()
// Usage:
@ -1082,9 +1095,9 @@ function _vnf_centroid(vnf,eps=EPSILON) =
// Function: vnf_halfspace()
// Synopsis: Returns the intersection of the vnf with a half space.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_volume(), vnf_area(), vnf_bend()
// Usage:
// newvnf = vnf_halfspace(plane, vnf, [closed], [boundary]);
// Description:
@ -1286,6 +1299,7 @@ function _triangulate_planar_convex_polygons(polys) =
// Function: vnf_bend()
// Synopsis: Bends a VNF around an axis.
// SynTags: VNF
// Topics: VNF Manipulation
// See Also: vnf_volume(), vnf_area(), vnf_halfspace()
// Usage:
@ -1495,6 +1509,7 @@ module _show_faces(vertices, faces, size=1, filter) {
// Module: debug_vnf()
// Synopsis: A replacement for `vnf_polyhedron()` to help with debugging.
// SynTags: VNF
// Topics: VNF Manipulation, Debugging
// See Also: vnf_validate()
// Usage:
@ -1538,6 +1553,7 @@ module debug_vnf(vnf, faces=true, vertices=true, opacity=0.5, size=1, convexity=
// Module: vnf_validate()
// Synopsis: Echos non-manifold VNF errors to the console.
// SynTags: VNF
// Topics: VNF Manipulation, Debugging
// See Also: debug_vnf()
//

5
walls.scad
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@ -14,6 +14,7 @@
// Module: sparse_wall()
// Synopsis: Makes an open cross-braced rectangular wall.
// SynTags: Geom
// Topics: FDM Optimized, Walls
// See Also: sparse_wall(), corrugated_wall(), thinning_wall(), thinning_triangle(), narrowing_strut()
//
@ -88,6 +89,7 @@ module sparse_wall(h=50, l=100, thick=4, maxang=30, strut=5, max_bridge=20, anch
// Module: corrugated_wall()
// Synopsis: Makes a corrugated rectangular wall.
// SynTags: Geom
// Topics: FDM Optimized, Walls
// See Also: sparse_wall(), corrugated_wall(), thinning_wall(), thinning_triangle(), narrowing_strut()
//
@ -147,6 +149,7 @@ module corrugated_wall(h=50, l=100, thick=5, strut=5, wall=2, anchor=CENTER, spi
// Module: thinning_wall()
// Synopsis: Makes a rectangular wall with a thin middle.
// SynTags: Geom
// Topics: FDM Optimized, Walls
// See Also: sparse_wall(), corrugated_wall(), thinning_wall(), thinning_triangle(), narrowing_strut()
//
@ -331,6 +334,7 @@ module thinning_wall(h=50, l=100, thick=5, ang=30, braces=false, strut, wall, an
// Module: thinning_triangle()
// Synopsis: Makes a triangular wall with a thin middle.
// SynTags: Geom
// Topics: FDM Optimized, Walls
// See Also: sparse_wall(), corrugated_wall(), thinning_wall(), thinning_triangle(), narrowing_strut()
//
@ -399,6 +403,7 @@ module thinning_triangle(h=50, l=100, thick=5, ang=30, strut=5, wall=3, diagonly
// Module: narrowing_strut()
// Synopsis: Makes a strut like an extruded baseball home plate.
// SynTags: Geom
// Topics: FDM Optimized
// See Also: sparse_wall(), corrugated_wall(), thinning_wall(), thinning_triangle(), narrowing_strut()
//

1
wiring.scad
View File

@ -55,6 +55,7 @@ function _hex_offsets(n, d, lev=0, arr=[]) =
// Module: wire_bundle()
// Synopsis: Creates a wire bundle for a given number of wires.
// SynTags: Geom
// Topics: Wiring
// See Also: path_sweep(), path_sweep2d()
// Usage: