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add region centroid capability and consolidate into one centroid

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function for polygons, regions and VNFs.
Fix bug with anchors for linear_sweep (due to centerpoint issues)
Fix intersection anchors for vnfs when anchor vector intersects
in a path instead of a single point.
This commit is contained in:
Adrian Mariano 2021-10-20 22:44:55 -04:00
parent a7ca1b1b64
commit 76272d9d9a
10 changed files with 158 additions and 101 deletions
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67
attachments.scad
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@ -1269,7 +1269,7 @@ function _attach_geom(
axis=UP
) =
assert(is_bool(extent))
assert(is_vector(cp))
assert(is_vector(cp) || is_string(cp))
assert(is_vector(offset))
assert(is_list(anchors))
assert(is_bool(two_d))
@ -1496,6 +1496,21 @@ function _attach_transform(anchor, spin, orient, geom, p) =
apply(m, p);
function _get_cp(geom) =
let(cp=select(geom,-3))
is_vector(cp) ? cp
: let(
type = in_list(geom[0],["vnf_extent","vnf_isect"]) ? "vnf"
: in_list(geom[0],["path_extent","path_isect"]) ? "path"
: "other"
)
assert(type!="other", "Invalid cp value")
cp=="centroid" ? centroid(geom[1])
: let(points = type=="vnf"?geom[1][0]:geom[1])
cp=="mean" ? mean(points)
: cp=="box" ? mean(pointlist_bounds(points))
: assert(false,"Invalid cp specification");
/// Internal Function: _find_anchor()
// Usage:
@ -1512,15 +1527,15 @@ function _attach_transform(anchor, spin, orient, geom, p) =
// geom = The geometry description of the shape.
function _find_anchor(anchor, geom) =
let(
cp = select(geom,-3),
cp = _get_cp(geom),
offset_raw = select(geom,-2),
offset = [for (i=[0:2]) anchor[i]==0? 0 : offset_raw[i]], // prevents bad centering.
anchors = last(geom),
type = geom[0]
)
is_string(anchor)? (
anchor=="origin"? [anchor, CENTER, UP, 0] :
let(found = search([anchor], anchors, num_returns_per_match=1)[0])
anchor=="origin"? [anchor, CENTER, UP, 0]
: let(found = search([anchor], anchors, num_returns_per_match=1)[0])
assert(found!=[], str("Unknown anchor: ",anchor))
anchors[found]
) :
@ -1590,27 +1605,25 @@ function _find_anchor(anchor, geom) =
eps = 1/2048,
points = vnf[0],
faces = vnf[1],
rpts = apply(rot(from=anchor, to=RIGHT) * move(point3d(-cp)), points),
rpts = apply(rot(from=anchor, to=RIGHT) * move(-cp), points),
hits = [
for (face = faces) let(
for (face = faces)
let(
verts = select(rpts, face),
xs = columns(verts,0),
ys = columns(verts,1),
zs = columns(verts,2)
) if (
max(xs) >= -eps &&
max(ys) >= -eps &&
max(zs) >= -eps &&
min(ys) <= eps &&
min(zs) <= eps
) let(
poly = select(points, face),
pt = polygon_line_intersection(poly, [cp,cp+anchor], bounded=[true,false], eps=eps)
) if (!is_undef(pt)) let(
plane = plane_from_polygon(poly),
n = unit(plane_normal(plane))
)
[norm(pt-cp), n, pt]
if (max(ys) >= -eps && max(zs) >= -eps &&
min(ys) <= eps && min(zs) <= eps)
let(
poly = select(points, face),
isect = polygon_line_intersection(poly, [cp,cp+anchor], eps=eps),
ptlist = is_undef(isect) ? [] :
is_vector(isect) ? [isect]
: flatten(isect), // parallel to a face
n = len(ptlist)>0 ? polygon_normal(poly) : undef
)
for(pt=ptlist) [anchor * (pt-cp), n, pt]
]
)
assert(len(hits)>0, "Anchor vector does not intersect with the shape. Attachment failed.")
@ -1619,16 +1632,16 @@ function _find_anchor(anchor, geom) =
dist = hits[furthest][0],
pos = hits[furthest][2],
hitnorms = [for (hit = hits) if (approx(hit[0],dist,eps=eps)) hit[1]],
unorms = len(hitnorms) > 7
? unique([for (nn = hitnorms) quant(nn,1e-9)])
: [
for (i = idx(hitnorms)) let(
nn = hitnorms[i],
unorms = [
for (i = idx(hitnorms))
let(
thisnorm = hitnorms[i],
isdup = [
for (j = [i+1:1:len(hitnorms)-1])
if (approx(nn, hitnorms[j])) 1
if (approx(thisnorm, hitnorms[j])) 1
] != []
) if (!isdup) nn
)
if (!isdup) thisnorm
],
n = unit(sum(unorms)),
oang = approx(point2d(n), [0,0])? 0 : atan2(n.y, n.x) + 90

59
geometry.scad
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@ -546,7 +546,7 @@ function plane_from_points(points, fast=false, eps=EPSILON) =
// xyzpath = rot(45, v=[0,1,0], p=path3d(star(n=5,step=2,d=100), 70));
// plane = plane_from_polygon(xyzpath);
// #stroke(xyzpath,closed=true,width=3);
// cp = polygon_centroid(xyzpath);
// cp = centroid(xyzpath);
// move(cp) rot(from=UP,to=plane_normal(plane)) anchor_arrow(45);
function plane_from_polygon(poly, fast=false, eps=EPSILON) =
assert( is_path(poly,dim=3), "Invalid polygon." )
@ -897,7 +897,7 @@ function plane_line_angle(plane, line) =
// proj = plane_closest_point(plane,points);
// color("red") move_copies(points) sphere(d=4,$fn=12);
// color("blue") move_copies(proj) sphere(d=4,$fn=12);
// move(polygon_centroid(proj)) {
// move(centroid(proj)) {
// rot(from=UP,to=plane_normal(plane)) {
// anchor_arrow(50);
// %cube([120,150,0.1],center=true);
@ -1403,21 +1403,56 @@ function polygon_area(poly, signed=false) =
signed ? total : abs(total);
// Function: polygon_centroid()
// Function: centroid()
// Usage:
// cpt = polygon_centroid(poly);
// c = centroid(object);
// Topics: Geometry, Polygons, Centroid
// 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.
// Collinear points produce an error. The results are meaningless for self-intersecting
// polygons or an error is produced.
// Arguments:
// poly = Points of the polygon from which the centroid is calculated.
// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
function polygon_centroid(poly, eps=EPSILON) =
// If you provide a non-planar or collinear polygon you will get an error. For self-intersecting
// polygons you may get an error or you may get meaningless results.
// .
// If object is a manifold VNF then returns the 3d centroid of the polyhedron. The VNF must
// describe a valid polyhedron with consistent face direction and no holes in the mesh; otherwise
// the results are undefined.
function centroid(object,eps=EPSILON) =
assert(is_finite(eps) && (eps>=0), "The tolerance should a non-negative value." )
is_vnf(object) ? _vnf_centroid(object,eps)
: is_path(object,[2,3]) ? _polygon_centroid(object,eps)
: is_region(object) ? (len(object)==1 ? _polygon_centroid(object[0],eps) : _region_centroid(object,eps))
: assert(false, "Input must be a VNF, a region, or a 2D or 3D polygon");
// Internal Function: _region_centroid()
// Compute centroid of region
function _region_centroid(region,eps=EPSILON) =
let(
region=force_region(region),
parts = region_parts(region),
// Rely on region_parts returning all outside polygons clockwise
// and inside (hole) polygons counterclockwise, so areas have reversed sign
cent_area = [for(R=parts, p=R)
let(A=polygon_area(p,signed=true))
[A*_polygon_centroid(p),A]],
total = sum(cent_area)
)
total[0]/total[1];
/// Function: _polygon_centroid()
/// Usage:
/// cpt = _polygon_centroid(poly);
/// Topics: Geometry, Polygons, Centroid
/// 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.
/// Collinear points produce an error. The results are meaningless for self-intersecting
/// polygons or an error is produced.
/// Arguments:
/// poly = Points of the polygon from which the centroid is calculated.
/// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
function _polygon_centroid(poly, eps=EPSILON) =
assert( is_path(poly,dim=[2,3]), "The input must be a 2D or 3D polygon." )
assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
let(
n = len(poly[0])==2 ? 1 :
let( plane = plane_from_points(poly, fast=false))

6
math.scad
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@ -958,7 +958,7 @@ function linear_solve(A,b,pivot=true) =
// 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.
// Instead use [[`linear_solve()`|linear_solve]], or use [[`qr_factor()`|qr_factor]]. The computation
// Instead use {{linear_solve()}}, or use {{qr_factor}}. The computation
// will be faster and more accurate.
function matrix_inverse(A) =
assert(is_matrix(A) && len(A)==len(A[0]),"Input to matrix_inverse() must be a square matrix")
@ -1007,7 +1007,7 @@ function null_space(A,eps=1e-12) =
// qr = qr_factor(A,[pivot]);
// 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)
// used to solve linear systems of equations. The factorization is `A = Q*R*transpose(P)`. If pivot is false (the default)
// then P is the identity matrix and A = Q*R. If pivot is true then column pivoting results in an R matrix where the diagonal
// is non-decreasing. The use of pivoting is supposed to increase accuracy for poorly conditioned problems, and is necessary
// for rank estimation or computation of the null space, but it may be slower.
@ -1088,7 +1088,7 @@ function _back_substitute(R, b, x=[]) =
// L = cholesky(A);
// 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
// The matrix L is lower triangular and `L * transpose(L) = A`. If the A is
// not symmetric then an error is displayed. If the matrix is symmetric but
// not positive definite then undef is returned.
function cholesky(A) =

16
regions.scad
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@ -390,7 +390,9 @@ function region_parts(region) =
// If called as a module, creates a polyhedron that is the linear extrusion of the given 2D region or path.
// If called as a function, returns a VNF that can be used to generate a polyhedron of the linear extrusion
// of the given 2D region or path. The benefit of using this, over using `linear_extrude region(rgn)` is
// that you can use `anchor`, `spin`, `orient` and attachments with it. Also, you can make more refined
// that you can use `anchor`, `spin`, `orient` and attachments with it. You can set `cp` to "mean", "centroid"
// or "box" to get different centerpoint computations, or you can give a custom vector centerpoint.
// Also, you can make more refined
// twisted extrusions by using `maxseg` to subsample flat faces.
// Arguments:
// region = The 2D [Region](regions.scad) or path that is to be extruded.
@ -402,8 +404,9 @@ function region_parts(region) =
// scale = The amount to scale the shape, from bottom to top. Default: 1
// style = The style to use when triangulating the surface of the object. Valid values are `"default"`, `"alt"`, or `"quincunx"`.
// convexity = Max number of surfaces any single ray could pass through. Module use only.
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `"origin"`
// anchor_isect = If true, anchoring it performed by finding where the anchor vector intersects the swept shape. Default: false
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER`
// cp = Centerpoint for determining intersection anchors or centering the shape. Determintes the base of the anchor vector. Default: "centroid"
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
// Example: Extruding a Compound Region.
@ -427,10 +430,9 @@ function region_parts(region) =
// mrgn = union(rgn1,rgn2);
// orgn = difference(mrgn,rgn3);
// linear_sweep(orgn,height=20,convexity=16) show_anchors();
module linear_sweep(region, height=1, center, twist=0, scale=1, slices, maxseg, style="default", convexity, anchor_isect=false, anchor, spin=0, orient=UP) {
module linear_sweep(region, height=1, center, twist=0, scale=1, slices, maxseg, style="default", convexity, anchor_isect=false, anchor, spin=0, orient=UP, cp="centroid") {
region = force_region(region);
dummy=assert(is_region(region),"Input is not a region");
cp = mean(pointlist_bounds(flatten(region)));
anchor = get_anchor(anchor, center, "origin", "origin");
vnf = linear_sweep(
region, height=height,
@ -446,15 +448,15 @@ module linear_sweep(region, height=1, center, twist=0, scale=1, slices, maxseg,
function linear_sweep(region, height=1, center, twist=0, scale=1, slices,
maxseg, style="default", anchor_isect=false, anchor, spin=0, orient=UP) =
maxseg, style="default", cp="centroid", anchor_isect=false, anchor, spin=0, orient=UP) =
let(
region = force_region(region)
)
assert(is_region(region), "Input is not a region")
let(
anchor = get_anchor(anchor,center,BOT,BOT),
anchor = get_anchor(anchor,center,"origin","origin"),
regions = region_parts(region),
cp = mean(pointlist_bounds(flatten(region))),
// cp = mean(pointlist_bounds(flatten(region))),
slices = default(slices, floor(twist/5+1)),
step = twist/slices,
hstep = height/slices,

4
rounding.scad
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@ -1041,7 +1041,7 @@ module offset_sweep(path, height,
quality=quality, check_valid=true, extra=extra, cut=cut, chamfer_width=chamfer_width,
chamfer_height=chamfer_height, joint=joint, k=k, angle=angle);
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
vnf_polyhedron(vnf,convexity=convexity);
children();
@ -1818,7 +1818,7 @@ module rounded_prism(bottom, top, joint_bot=0, joint_top=0, joint_sides=0, k_bot
result = rounded_prism(bottom=bottom, top=top, joint_bot=joint_bot, joint_top=joint_top, joint_sides=joint_sides,
k_bot=k_bot, k_top=k_top, k_sides=k_sides, k=k, splinesteps=splinesteps, h=h, length=length, height=height, l=l,debug=debug);
vnf = debug ? result[1] : result;
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
if (debug){
vnf_polyhedron(vnf, convexity=convexity);

14
skin.scad
View File

@ -278,12 +278,12 @@
// Example(FlatSpin,VPD=32,VPT=[1.2,4.3,2]): Another "distance" example:
// off = [0,2];
// shape = turtle(["right",45,"move", "left",45,"move", "left",45, "move", "jump", [.5+sqrt(2)/2,8]]);
// rshape = rot(180,cp=polygon_centroid(shape)+off, p=shape);
// rshape = rot(180,cp=centroid(shape)+off, p=shape);
// skin([shape,rshape],z=[0,4], method="distance",slices=10,refine=15);
// Example(FlatSpin,VPD=32,VPT=[1.2,4.3,2]): Slightly shifting the profile changes the optimal linkage
// off = [0,1];
// shape = turtle(["right",45,"move", "left",45,"move", "left",45, "move", "jump", [.5+sqrt(2)/2,8]]);
// rshape = rot(180,cp=polygon_centroid(shape)+off, p=shape);
// rshape = rot(180,cp=centroid(shape)+off, p=shape);
// skin([shape,rshape],z=[0,4], method="distance",slices=10,refine=15);
// Example(FlatSpin,VPD=444,VPT=[0,0,50]): This optimal solution doesn't look terrible:
// prof1 = path3d([[-50,-50], [-50,50], [50,50], [25,25], [50,0], [25,-25], [50,-50]]);
@ -386,7 +386,7 @@ module skin(profiles, slices, refine=1, method="direct", sampling, caps, closed=
anchor="origin",cp,spin=0, orient=UP, extent=false)
{
vnf = skin(profiles, slices, refine, method, sampling, caps, closed, z, style=style);
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
vnf_polyhedron(vnf,convexity=convexity);
children();
@ -816,7 +816,7 @@ module path_sweep(shape, path, method="incremental", normal, closed=false, twist
{
vnf = path_sweep(shape, path, method, normal, closed, twist, twist_by_length,
symmetry, last_normal, tangent, relaxed, caps, style);
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
vnf_polyhedron(vnf,convexity=convexity);
children();
@ -1001,7 +1001,7 @@ module path_sweep2d(profile, path, closed=false, caps, quality=1, style="min_edg
anchor="origin", cp, spin=0, orient=UP, extent=false)
{
vnf = path_sweep2d(profile, path, closed, caps, quality, style);
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
vnf_polyhedron(vnf,convexity=convexity);
children();
@ -1128,7 +1128,7 @@ module sweep(shape, transforms, closed=false, caps, style="min_edge", convexity=
anchor="origin",cp,spin=0, orient=UP, extent=false)
{
vnf = sweep(shape, transforms, closed, caps, style);
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : vnf_centroid(vnf))
attachable(anchor=anchor, spin=spin, orient=orient, vnf=vnf, extent=extent, cp=is_def(cp) ? cp : centroid(vnf))
{
vnf_polyhedron(vnf,convexity=convexity);
children();
@ -1591,7 +1591,7 @@ function _skin_tangent_match(poly1, poly2) =
swap = len(poly1)>len(poly2),
big = swap ? poly1 : poly2,
small = swap ? poly2 : poly1,
curve_offset = polygon_centroid(small)-polygon_centroid(big),
curve_offset = centroid(small)-centroid(big),
cutpts = [for(i=[0:len(small)-1]) _find_one_tangent(big, select(small,i,i+1),curve_offset=curve_offset)],
shift = last(cutpts)+1,
newbig = polygon_shift(big, shift),

30
tests/test_geometry.scad
View File

@ -46,7 +46,7 @@ test_is_polygon_convex();
test_polygon_shift();
test_reindex_polygon();
test_align_polygon();
test_polygon_centroid();
test_centroid();
test_point_in_polygon();
test_is_polygon_clockwise();
test_clockwise_polygon();
@ -819,15 +819,31 @@ module test_noncollinear_triple() {
*test_noncollinear_triple();
module test_polygon_centroid() {
module test_centroid() {
// polygons
$fn = 24;
assert_approx(polygon_centroid(circle(d=100)), [0,0]);
assert_approx(polygon_centroid(rect([40,60],rounding=10,anchor=LEFT)), [20,0]);
assert_approx(polygon_centroid(rect([40,60],rounding=10,anchor=FWD)), [0,30]);
assert_approx(centroid(circle(d=100)), [0,0]);
assert_approx(centroid(rect([40,60],rounding=10,anchor=LEFT)), [20,0]);
assert_approx(centroid(rect([40,60],rounding=10,anchor=FWD)), [0,30]);
poly = move([1,2.5,3.1],p=rot([12,49,24], p=path3d(circle(10,$fn=33))));
assert_approx(polygon_centroid(poly), [1,2.5,3.1]);
assert_approx(centroid(poly), [1,2.5,3.1]);
// regions
R = [square(10), move([5,4],circle(r=3,$fn=32)), right(15,square(7)), move([18,3],circle(r=2,$fn=5))];
assert_approx(centroid(R), [9.82836532809, 4.76313546433]);
// VNFs
assert_approx(centroid(cube(100, center=false)), [50,50,50]);
assert_approx(centroid(cube(100, center=true)), [0,0,0]);
assert_approx(centroid(cube(100, anchor=ALLPOS)), [-50,-50,-50]);
assert_approx(centroid(cube(100, anchor=BOT)), [0,0,50]);
assert_approx(centroid(cube(100, anchor=TOP)), [0,0,-50]);
assert_approx(centroid(sphere(d=100, anchor=CENTER, $fn=36)), [0,0,0]);
assert_approx(centroid(sphere(d=100, anchor=BOT, $fn=36)), [0,0,50]);
ellipse = xscale(2, p=circle($fn=24, r=3));
assert_approx(centroid(path_sweep(pentagon(r=1), path3d(ellipse), closed=true)),[0,0,0]);
}
*test_polygon_centroid();
*test_centroid();

2
tests/test_regions.scad
View File

@ -78,7 +78,7 @@ module test_exclusive_or() {
assert(are_regions_equal(exclusive_or(R9,R8),[[[-5, -5], [-13, -5], [-13, 5], [-5, 5], [-5, 3], [-3, 3], [-3, -3], [-5, -3]], [[-3, -5], [-5, -5], [-5, -13], [5, -13], [5, -5], [3, -5], [3, -3], [-3, -3]], [[-5, 5], [-3, 5], [-3, 3], [3, 3], [3, 5], [5, 5], [5, 13], [-5, 13]], [[3, -3], [3, 3], [5, 3], [5, 5], [13, 5], [13, -5], [5, -5], [5, -3]]],either_winding=true));
p = turtle(["move",100,"left",144], repeat=4);
p2 = move(-polygon_centroid(p),p);
p2 = move(-centroid(p),p);
p3 = polygon_parts(p2);
p4 = exclusive_or(p3,square(51,center=true));

12
tests/test_vnf.scad
View File

@ -43,18 +43,6 @@ module test_vnf_from_polygons() {
test_vnf_from_polygons();
module test_vnf_centroid() {
assert_approx(vnf_centroid(cube(100, center=false)), [50,50,50]);
assert_approx(vnf_centroid(cube(100, center=true)), [0,0,0]);
assert_approx(vnf_centroid(cube(100, anchor=ALLPOS)), [-50,-50,-50]);
assert_approx(vnf_centroid(cube(100, anchor=BOT)), [0,0,50]);
assert_approx(vnf_centroid(cube(100, anchor=TOP)), [0,0,-50]);
assert_approx(vnf_centroid(sphere(d=100, anchor=CENTER, $fn=36)), [0,0,0]);
assert_approx(vnf_centroid(sphere(d=100, anchor=BOT, $fn=36)), [0,0,50]);
ellipse = xscale(2, p=circle($fn=24, r=3));
assert_approx(vnf_centroid(path_sweep(pentagon(r=1), path3d(ellipse), closed=true)),[0,0,0]);}
test_vnf_centroid();
module test_vnf_volume() {
assert_approx(vnf_volume(cube(100, center=false)), 1000000);

29
vnf.scad
View File

@ -457,12 +457,15 @@ function vnf_from_region(region, transform, reverse=false) =
// bool = is_vnf(x);
// Description:
// Returns true if the given value looks like a VNF structure.
function is_vnf(x) = is_list(x) && len(x)==2 && is_list(x[0]) && is_list(x[1])
&& is_vector(x[0][0],3) && is_vector(x[1][0]);
function is_vnf(x) =
is_list(x) &&
len(x)==2 &&
is_list(x[0]) &&
is_list(x[1]) &&
(x[0]==[] || (len(x[0])>=3 && is_vector(x[0][0]))) &&
(x[0]==[] || (len(x[0])>=3 && is_vector(x[0][0],3))) &&
(x[1]==[] || is_vector(x[1][0]));
@ -684,7 +687,7 @@ function _slice_3dpolygons(polys, dir, cuts) =
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
module vnf_polyhedron(vnf, convexity=2, extent=true, cp=[0,0,0], anchor="origin", spin=0, orient=UP) {
vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
cp = is_def(cp) ? cp : vnf_centroid(vnf);
cp = is_def(cp) ? cp : centroid(vnf);
attachable(anchor,spin,orient, vnf=vnf, extent=extent, cp=cp) {
polyhedron(vnf[0], vnf[1], convexity=convexity);
children();
@ -760,17 +763,17 @@ function vnf_area(vnf) =
sum([for(face=vnf[1]) polygon_area(select(verts,face))]);
// Function: vnf_centroid()
// Usage:
// vol = vnf_centroid(vnf);
// Description:
// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined.
/// Function: _vnf_centroid()
/// Usage:
/// vol = _vnf_centroid(vnf);
/// Description:
/// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
/// no holes; otherwise the results are undefined.
// Divide the solid up into tetrahedra with the origin as one vertex.
// The centroid of a tetrahedron is the average of its vertices.
// The centroid of the total is the volume weighted average.
function vnf_centroid(vnf) =
/// Divide the solid up into tetrahedra with the origin as one vertex.
/// The centroid of a tetrahedron is the average of its vertices.
/// The centroid of the total is the volume weighted average.
function _vnf_centroid(vnf,eps=EPSILON) =
assert(is_vnf(vnf) && len(vnf[0])!=0 )
let(
verts = vnf[0],
@ -784,7 +787,7 @@ function vnf_centroid(vnf) =
[ vol, (v0+v1+v2)*vol ]
])
)
assert(!approx(pos[0],0, EPSILON), "The vnf has self-intersections.")
assert(!approx(pos[0],0, eps), "The vnf has self-intersections.")
pos[1]/pos[0]/4;