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Fixed clip face edge cases, added debug view to metaballs

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This commit is contained in:
Alex Matulich
2025-03-04 11:26:24 -08:00
parent dffa8a656c
commit 9a848b3925
1 changed files with 324 additions and 200 deletions
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524
isosurface.scad
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@@ -625,7 +625,6 @@ _MCTriangleTable_reverse = [
[]
];
/// _cubindex() - private function, called by _isosurface_cubes()
/// Return the index ID of a voxel depending on the field strength at each corner exceeding isoval.
function _cubeindex(f, isoval) =
@@ -668,50 +667,118 @@ The clip face uses different indexing. After vertex coordinates and function val
/// four indices for each face of the cube, counterclockwise looking from inside out
_MCFaceVertexIndices = [
[],
[0,2,3,1], // left, x=0 plane
[0,1,5,4], // front, y=0 plane
[0,4,6,2], // bottom, z=0 plane
[4,5,7,6], // right, x=voxsize plane
[2,6,7,3], // back, y=voxsize plane
[1,3,7,5], // top, z=voxsize plane
[],
[0,2,3,1], // left, x=0 plane
[0,1,5,4], // front, y=0 plane
[0,4,6,2], // bottom, z=0 plane
[4,5,7,6], // right, x=voxsize plane
[2,6,7,3], // back, y=voxsize plane
[1,3,7,5], // top, z=voxsize plane
];
/*
/// Pair of vertex indices for each edge on the clip face (using clip face indexing)
_MCClipEdgeVertexIndices = [
[0,1], [1,2], [2,3], [3,0]
[0,1], [1,2], [2,3], [3,0]
];
/// For each of the 16 configurations of a clip face, define a list of triangles, specified as pairs of corner ID and edge ID arrays, with a total of 3 points in each pair. Each pair has the form [corner],[edge1,edge2] or [corner1,corner2],[edge].
/// In keeping with the convention for triangulating an isosurface through a voxel, analogous to the case in which two surfaces separate two diagonally opposite greater-than-isovalue corners of one face, in 2D contour terms it is assumed there is a valley separating two diagonally-opposite high corners, not a ridge connecting them. The two triangulation cases for opposing corners are set up accordingly.
/// In keeping with the convention for triangulating an isosurface through a voxel, analogous to the case in which two surfaces separate two diagonally opposite high-value corners of one face, in 2D contour terms it is assumed there is a valley separating two high corners, not a ridge connecting them. The 8 ambiguous triangulation cases for opposing corners are set up accordingly. These are the rotational groups of indices {10,30}, {11,19,33,57}, {20,60} in the array below.
/// For each of the 81 possible configurations of a clip face intersected by a minimum and/or maximum isovalue, define a list of triangles, specified as pairs of corner ID and edge ID arrays, with a total of 3 points in each pair. Each pair has the form [corner],[edge1,edge2] or [corner1,corner2],[edge], or [corner1,corner2,corner3],[] or [],[edge1,edge2,edge3].
_MCClipTriangleTable = [
[], // 0 - 0000 - ignored
[[0],[0,3]], // 1 - 0001
[[1],[1,0]], // 2 - 0010
[[0,1],[1], [0],[1,3]], // 3 - 0011
[[2],[2,1]], // 4 - 0100
[[0],[0,3], [2],[2,1]], // 5 - 0101 - opposing corners
[[1,2],[0], [2],[2,0]], // 6 - 0110
[[0,1],[3], [1],[2,3], [1,2],[2]], // 7 - 0111
[[3],[3,2]], // 8 - 1000
[[3,0],[0], [3],[0,2]], // 9 - 1001
[[1],[1,0], [3],[3,2]], //10 - 1010 - opposing corners
[[0,1],[1], [0],[1,2], [3,0],[2]], //11 - 1011
[[2,3],[3], [2],[3,1]], //12 - 1100
[[3,0],[0], [3],[0,1], [2,3],[1]], //13 - 1101
[[2,3],[3], [2],[3,0], [1,2],[0]], //14 - 1110
[[0,1,2],[], [0,2,3],[]], //15 - 1111
// Explanation of inline comments:
// "base-3 index = decimal index", followed by
// "(xRotations)" for number of rotation versions, or
// "(Rotation n from decimal index)" indicating which decimal index this was rotated from, where n=the number of 90° clockwise rotations from the original.
[], // 0000 = 0 (×1)
[[0],[0,3]], // 0001 = 1 (×4)
[[],[7,4,3,3,4,0]], // 0002 = 2 (×4)
[[1],[1,0]], // 0010 = 3 (r1 from 1)
[[0,1],[1],[0],[1,3]], // 0011 = 4 (×4)
[[1],[1,4],[],[4,3,7],[],[4,1,3]], // 0012 = 5 (×4)
[[],[4,5,0,0,5,1]], // 0020 = 6 (r1 from 2)
[[0],[4,3],[],[4,5,1],[],[4,1,3]], // 0021 = 7 (×4)
[[],[7,5,1,1,3,7]], // 0022 = 8 (×4)
[[2],[2,1]], // 0100 = 9 (r2 from 1)
[[0],[0,3],[2],[2,1]], // 0101 = 10 (×2)
[[],[7,4,3,3,4,0],[2],[2,1]], // 0102 = 11 (×4)
[[1,2],[2],[1],[2,0]], // 0110 = 12 (r1 from 4)
[[0,1],[3],[1],[2,3],[1,2],[2]], // 0111 = 13 (×4)
[[1,2],[4],[2],[2,4],[],[2,3,7],[],[2,7,4]], // 0112 = 14 (×4)
[[2],[2,5],[],[5,0,4],[],[5,2,0]], // 0120 = 15 (r1 from 5)
[[0],[4,3],[2],[2,5],[],[4,5,2],[],[2,3,4]], // 0121 = 16 (×4)
[[2],[2,5],[],[2,3,7],[],[5,2,7]], // 0122 = 17 (×4)
[[],[5,6,1,1,6,2]], // 0200 = 18 (r2 from 2)
[[],[5,6,1,1,6,2],[0],[0,3]], // 0201 = 19 (r2 from 11)
[[],[7,4,0],[],[0,3,7],[],[1,5,6],[],[6,2,1]], // 0202 = 20 (×2)
[[1],[5,0],[],[5,6,2],[],[5,2,0]], // 0210 = 21 (r1 from 7)
[[0,1],[3],[1],[5,3],[],[3,5,2],[],[5,6,2]], // 0211 = 22 (×4)
[[1],[5,4],[],[5,6,7],[],[6,2,3],[],[6,3,7],[],[7,4,5]], // 0212 = 23 (×4)
[[],[4,6,2,2,0,4]], // 0220 = 24 (r1 from 8)
[[0],[4,3],[],[3,4,6],[],[6,2,3]], // 0221 = 25 (×4)
[[],[2,3,7,2,7,6]], // 0222 = 26 (×4)
[[3],[3,2]], // 1000 = 27 (r3 from 1)
[[3,0],[0],[3],[0,2]], // 1001 = 28 (r3 from 4)
[[3],[7,2],[],[7,4,0],[],[7,0,2]], // 1002 = 29 (r3 from 7)
[[1],[1,0],[3],[3,2]], // 1010 = 30 (r1 from 10)
[[3,0],[2],[0],[1,2],[0,1],[1]], // 1011 = 31 (r3 from 13)
[[3],[7,2],[1],[1,4],[],[7,4,1],[],[1,2,7]], // 1012 = 32 (r3 from 16)
[[],[4,5,0,0,5,1],[3],[3,2]], // 1020 = 33 (r1 from 11)
[[3,0],[2],[0],[4,2],[],[2,4,1],[],[4,5,1]], // 1021 = 34 (r3 from 22)
[[3],[7,2],[],[2,7,5],[],[5,1,2]], // 1022 = 35 (r3 from 25)
[[2,3],[3],[2],[3,1]], // 1100 = 36 (r2 from 4)
[[2,3],[1],[3],[0,1],[3,0],[0]], // 1101 = 37 (r2 from 13)
[[2,3],[1],[3],[7,1],[],[1,7,0],[],[7,4,0]], // 1102 = 38 (r2 from 22)
[[1,2],[0],[2],[3,0],[2,3],[3]], // 1110 = 39 (r1 from 13)
[[0,1,2],[],[0,2,3],[]], // 1111 = 40 (×1)
[[1,2],[4],[2],[7,4],[2,3],[7]], // 1112 = 41 (×4)
[[2,3],[5],[3],[3,5],[],[3,0,4],[],[3,4,5]], // 1120 = 42 (r1 from 14)
[[2,3],[5],[3],[4,5],[3,0],[4]], // 1121 = 43 (r1 from 41)
[[2],[7,5],[2,3],[7]], // 1122 = 44 (×4)
[[3],[3,6],[],[6,1,5],[],[6,3,1]], // 1200 = 45 (r2 from 5)
[[3,0],[6],[0],[0,6],[],[0,1,5],[],[0,5,6]], // 1201 = 46 (r2 from 14)
[[3],[7,6],[],[7,4,5],[],[4,0,1],[],[4,1,5],[],[5,6,7]], // 1202 = 47 (r2 from 23)
[[1],[5,0],[3],[3,6],[],[5,6,3],[],[3,0,5]], // 1210 = 48 (r1 from 16)
[[3,0],[6],[0],[5,6],[0,1],[5]], // 1211 = 49 (r2 from 41)
[[1],[5,4],[3],[7,6],[],[4,5,6],[],[4,6,7]], // 1212 = 50 (×2)
[[3],[3,6],[],[3,0,4],[],[6,3,4]], // 1220 = 51 (r1 from 17)
[[3],[4,6],[3,0],[4]], // 1221 = 52 (r1 from 44)
[[3],[7,6]], // 1222 = 53 (×4)
[[],[6,7,2,2,7,3]], // 2000 = 54 (r3 from 2)
[[0],[0,7],[],[7,2,6],[],[7,0,2]], // 2001 = 55 (r3 from 5)
[[],[6,4,0,0,2,6]], // 2002 = 56 (r3 from 8)
[[],[6,7,2,2,7,3],[1],[1,0]], // 2010 = 57 (r3 from 11)
[[0,1],[7],[1],[1,7],[],[1,2,6],[],[1,6,7]], // 2011 = 58 (r3 from 14)
[[1],[1,4],[],[1,2,6],[],[4,1,6]], // 2012 = 59 (r3 from 17)
[[],[4,5,1],[],[1,0,4],[],[2,6,7],[],[7,3,2]], // 2020 = 60 (r1 from 20)
[[0],[4,7],[],[4,5,6],[],[5,1,2],[],[5,2,6],[],[6,7,4]], // 2021 = 61 (r3 from 23)
[[],[1,2,6,1,6,5]], // 2022 = 62 (r3 from 26)
[[2],[6,1],[],[6,7,3],[],[6,3,1]], // 2100 = 63 (r2 from 7)
[[2],[6,1],[0],[0,7],[],[6,7,0],[],[0,1,6]], // 2101 = 64 (r2 from 16)
[[2],[6,1],[],[1,6,4],[],[4,0,1]], // 2102 = 65 (r2 from 25)
[[1,2],[0],[2],[6,0],[],[0,6,3],[],[6,7,3]], // 2110 = 66 (r1 from 22)
[[0,1],[7],[1],[6,7],[1,2],[6]], // 2111 = 67 (r3 from 41)
[[1],[6,4],[1,2],[6]], // 2112 = 68 (r3 from 44)
[[2],[6,5],[],[6,7,4],[],[7,3,0],[],[7,0,4],[],[4,5,6]], // 2120 = 69 (r1 from 23)
[[2],[6,5],[0],[4,7],[],[5,6,7],[],[5,7,4]], // 2121 = 70 (r1 from 50)
[[2],[6,5]], // 2122 = 71 (r3 from 53)
[[],[5,7,3,3,1,5]], // 2200 = 72 (r2 from 8)
[[0],[0,7],[],[0,1,5],[],[7,0,5]], // 2201 = 73 (r2 from 17)
[[],[0,1,5,0,5,4]], // 2202 = 74 (r2 from 26)
[[1],[5,0],[],[0,5,7],[],[7,3,0]], // 2210 = 75 (r1 from 25)
[[0],[5,7],[0,1],[5]], // 2211 = 76 (r2 from 44)
[[1],[5,4]], // 2212 = 77 (r2 from 53)
[[],[3,0,4,3,4,7]], // 2220 = 78 (r1 from 26)
[[0],[4,7]], // 2221 = 79 (r1 from 53)
[] // 2222 = 80 (×1)
];
/// _clipfacindex() - private function, called by _clipfacevertices()
/// Return the index ID of a voxel face depending on the field strength at each corner exceeding isoval.
function _clipfacindex(f, isoval) =
(f[0] > isoval ? 1 : 0) +
(f[1] > isoval ? 2 : 0) +
(f[2] > isoval ? 4 : 0) +
(f[3] > isoval ? 8 : 0);
*/
/// Return the index ID of a voxel face depending on the field strength at each corner in relation to isovalmin and isovalmax.
// Returns a decimal version of a 4-digit base-3 index.
function _clipfacindex(f, isovalmin, isovalmax) =
(f[0] >= isovalmax ? 2 : f[0] >= isovalmin ? 1 : 0) +
(f[1] >= isovalmax ? 6 : f[1] >= isovalmin ? 3 : 0) +
(f[2] >= isovalmax ? 18 : f[2] >= isovalmin ? 9 : 0) +
(f[3] >= isovalmax ? 54 : f[3] >= isovalmin ? 27 : 0);
/// return an array of face indices in _MCFaceVertexIndices if the voxel at coordinate v0 corresponds to the bounding box. voxsize is a 3-vector.
function _bbox_faces(v0, voxsize, bbox) = let(
@@ -833,91 +900,36 @@ function _isosurface_triangles(cubelist, voxsize, isovalmin, isovalmax, tritable
)
vcube[vi0] + u*(vcube[vi1]-vcube[vi0]),
if(len(bbfaces)>0) for(bf = bbfaces)
each _bbfacevertices(vcube, f, bf, isovalmax, isovalmin)
each _clipfacevertices(vcube, f, bf, isovalmin, isovalmax)
]
];
/*
/// Generate triangles for the special case of voxel faces clipped by the bounding box
/// (more efficient than _bbfacevertices below but doesn't work with isovalue ranges)
function _clipfacevertices(vcube, f, bbface, isovalmax, isovalmin) =
function _clipfacevertices(vcube, fld, bbface, isovalmin, isovalmax) =
let(
vi = _MCFaceVertexIndices[bbface], // four voxel face vertex indices
vfc = [ for(i=vi) vcube[i] ], // four voxel face vertex coordinates
fld = [ for(i=vi) f[i] ], // four corner field values
minidx = _clipfacindex(fld, isovalmin),
maxidx = _clipfacindex(fld, isovalmax)
vface = [ for(i=vi) vcube[i] ], // four voxel face vertex coordinates
f = [ for(i=vi) fld[i] ], // four corner field values
idx = _clipfacindex(f, isovalmin, isovalmax)
) [
if(minidx>0)
let(tabl = _MCClipTriangleTable[minidx])
for(i=[0:2:len(tabl)-1]) each [
for(c=tabl[i]) vfc[c],
for(ei=tabl[i+1]) let(
edge = _MCClipEdgeVertexIndices[ei],
vi0 = edge[0],
vi1 = edge[1],
denom = fld[vi1] - fld[vi0],
u = abs(denom)<0.00001 ? 0.5 : (isovalmin-fld[vi0]) / denom
) vfc[vi0] + u*(vfc[vi1]-vfc[vi0])
],
if(false && maxidx>0)
let(tabl = _MCClipTriangleTable[maxidx])
for(i=[0:2:len(tabl)-1]) each [
for(c=tabl[i]) vfc[c],
for(ei=tabl[i+1]) let(
edge = _MCClipEdgeVertexIndices[ei],
vi0 = edge[0],
vi1 = edge[1],
denom = fld[vi1] - fld[vi0],
u = abs(denom)<0.00001 ? 0.5 : (isovalmin-fld[vi0]) / denom
) vfc[vi0] + u*(vfc[vi1]-vfc[vi0])
if(idx>0 && idx<80)
let(tri = _MCClipTriangleTable[idx])
for(i=[0:2:len(tri)-1]) let(
cpath = tri[i],
epath = tri[i+1]
) each [
for(corner=cpath) vface[corner],
for(edge=epath) let(
iso = edge>3 ? isovalmax : isovalmin,
e = edge>3 ? edge-4 : edge,
v0 = e,
v1 = (e+1)%4,
denom = f[v1]-f[v0],
u = abs(denom)<0.00001 ? 0.5 : (iso-f[v0]) / denom
) vface[v0] + u*(vface[v1]-vface[v0])
]
];
*/
/// Generate triangles for the special case of voxel faces clipped by the bounding box
/// TODO: Address isolated manifold error in edge case where two different isosurfaces intersect the same voxel AND that voxel is on a box boundary. This can be contrived but hasn't yet come up in actual testing.
function _bbfacevertices(vcube, f, bbface, isovalmax, isovalmin) = let(
vi = _MCFaceVertexIndices[bbface], // four voxel face vertex indices
//vfc = [ for(i=vi) vcube[i] ], // four voxel face vertex coordinates
//fld = [ for(i=vi) f[i] ], // four corner field values
pgon = flatten([
for(i=[0:3]) let( // for each line segment...
vi0=vi[i], // voxel corner 0 index
vi1=vi[(i+1)%4], // voxel corner 1 index
f0 = f[vi0], // field value at corner 0
f1 = f[vi1], // field value at corner 1
fmin = min(f0, f1), // min field of the corners
fmax = max(f0, f1), // max field of the corners
ilowbetween = (fmin < isovalmin && isovalmin < fmax),
ihighbetween = (fmin < isovalmax && isovalmax < fmax),
denom = f1-f0
) [ // traverse the edge, output vertices as they are found
if(isovalmin <= f0 && f0 <= isovalmax)// && abs(f1-f0)>0.001)
// vertex 0 is on or between min and max isovalues
//echo(vfc, fld)
vcube[vi0],
// for f0<f1, find isovalmin, then isovalmax intersections
if(ilowbetween && f0<f1)
let(u = abs(denom)<0.00001 ? 0.5 : (isovalmin-f0)/denom)
vcube[vi0] + u*(vcube[vi1]-vcube[vi0]),
if(ihighbetween && f0<f1)
let(u = abs(denom)<0.00001 ? 0.5 : (isovalmax-f0)/denom)
vcube[vi0] + u*(vcube[vi1]-vcube[vi0]),
// for f1<f0, find isovalmax, then isovalmin intersections
if(ihighbetween && f0>f1)
let(u = abs(denom)<0.00001 ? 0.5 : (isovalmax-f0)/denom)
vcube[vi0] + u*(vcube[vi1]-vcube[vi0]),
if(ilowbetween && f0>f1)
let(u = abs(denom)<0.00001 ? 0.5 : (isovalmin-f0)/denom)
vcube[vi0] + u*(vcube[vi1]-vcube[vi0])
]
]),
npgon = len(pgon),
triangles = npgon<3 ? [] : [
for(i=[1:len(pgon)-2]) [pgon[0], pgon[i], pgon[i+1]]
]) flatten(triangles);
@@ -927,6 +939,7 @@ function _bbfacevertices(vcube, f, bbface, isovalmax, isovalmin) = let(
/// Built-in metaball functions corresponding to each MB_ index.
/// For speed, they are split into four functions, each handling a different combination of influence != 1 or influence == 1, and cutoff < INF or cutoff == INF.
/// Each function returns a list: [function literal [sign, vnf]]
/// public metaball cutoff function if anyone wants it (demonstrated in example)
@@ -942,18 +955,19 @@ function _mb_sphere_cutoff(point, r, cutoff, neg) = let(dist=norm(point))
function _mb_sphere_full(point, r, cutoff, ex, neg) = let(dist=norm(point))
neg * mb_cutoff(dist, cutoff) * (r/dist)^ex;
function mb_sphere(r, cutoff=INF, influence=1, negative=false, d) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
r = get_radius(r=r,d=d),
dummy=assert(is_finite(r) && r>0, "\ninvalid radius or diameter."),
neg = negative ? -1 : 1
)
!is_finite(cutoff) && influence==1 ? function(point) _mb_sphere_basic(point,r,neg)
: !is_finite(cutoff) ? function (point) _mb_sphere_influence(point,r,1/influence, neg)
: influence==1 ? function (point) _mb_sphere_cutoff(point,r,cutoff,neg)
: function (point) _mb_sphere_full(point,r,cutoff,1/influence,neg);
function mb_sphere(r, cutoff=INF, influence=1, negative=false, nodebug=false, d) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
r = get_radius(r=r,d=d),
dummy=assert(is_finite(r) && r>0, "\ninvalid radius or diameter."),
neg = negative ? -1 : 1,
vnf = [neg, nodebug ? cube(0.02,true) : sphere(r=r, $fn=20)]
)
!is_finite(cutoff) && influence==1 ? [function(point) _mb_sphere_basic(point,r,neg), vnf]
: !is_finite(cutoff) ? [function (point) _mb_sphere_influence(point,r,1/influence, neg), vnf]
: influence==1 ? [function (point) _mb_sphere_cutoff(point,r,cutoff,neg), vnf]
: [function (point) _mb_sphere_full(point,r,cutoff,1/influence,neg), vnf];
/// metaball rounded cube
@@ -980,7 +994,7 @@ function _mb_cuboid_full(point, inv_size, xp, ex, cutoff, neg) = let(
:(abs(point.x)^xp + abs(point.y)^xp + abs(point.z)^xp) ^ (1/xp)
) neg * mb_cutoff(dist, cutoff) / dist^ex;
function mb_cuboid(size, squareness=0.5, cutoff=INF, influence=1, negative=false) =
function mb_cuboid(size, squareness=0.5, cutoff=INF, influence=1, negative=false, nodebug=false) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
assert(squareness>=0 && squareness<=1, "\nsquareness must be inside the range [0,1].")
@@ -989,12 +1003,13 @@ function mb_cuboid(size, squareness=0.5, cutoff=INF, influence=1, negative=false
xp = _squircle_se_exponent(squareness),
neg = negative ? -1 : 1,
inv_size = is_num(size) ? 2/size
: [[2/size.x,0,0],[0,2/size.y,0],[0,0,2/size.z]]
: [[2/size.x,0,0],[0,2/size.y,0],[0,0,2/size.z]],
vnf=[neg, nodebug ? cube(0.02,true) : _debug_cube(size,squareness)]
)
!is_finite(cutoff) && influence==1 ? function(point) _mb_cuboid_basic(point, inv_size, xp, neg)
: !is_finite(cutoff) ? function(point) _mb_cuboid_influence(point, inv_size, xp, 1/influence, neg)
: influence==1 ? function(point) _mb_cuboid_cutoff(point, inv_size, xp, cutoff, neg)
: function (point) _mb_cuboid_full(point, inv_size, xp, 1/influence, cutoff, neg);
!is_finite(cutoff) && influence==1 ? [function(point) _mb_cuboid_basic(point, inv_size, xp, neg), vnf]
: !is_finite(cutoff) ? [function(point) _mb_cuboid_influence(point, inv_size, xp, 1/influence, neg), vnf]
: influence==1 ? [function(point) _mb_cuboid_cutoff(point, inv_size, xp, cutoff, neg), vnf]
: [function (point) _mb_cuboid_full(point, inv_size, xp, 1/influence, cutoff, neg), vnf];
/// metaball rounded cylinder / cone
@@ -1077,7 +1092,7 @@ function _revsurf_full(point, path, coef, cutoff, exp, neg, maxdist) =
)
neg * mb_cutoff(d, cutoff) * (coef/d)^exp;
function mb_cyl(h,r,rounding=0,r1,r2,l,height,length,d1,d2,d, cutoff=INF, influence=1, negative=false) =
function mb_cyl(h,r,rounding=0,r1,r2,l,height,length,d1,d2,d, cutoff=INF, influence=1, negative=false, nodebug=false) =
let(
r1 = get_radius(r1=r1,r=r, d1=d1, d=d),
r2 = get_radius(r1=r2,r=r, d1=d2, d=d),
@@ -1108,12 +1123,13 @@ function mb_cyl(h,r,rounding=0,r1,r2,l,height,length,d1,d2,d, cutoff=INF, influe
bot_isect = line_intersection(bisect2,[[0,0],[0,1]]),
maxdist = side_isect.x>0 ?point_line_distance(side_isect, select(shifted,1,2))
: max(point_line_distance(top_isect, select(shifted,1,2)),
point_line_distance(bot_isect, select(shifted,1,2)))
point_line_distance(bot_isect, select(shifted,1,2))),
vnf = [neg, nodebug ? cube(0.02,true) : cyl(h,r1=r1,r2=r2,rounding=rounding,$fn=20)]
)
!is_finite(cutoff) && influence==1 ? function(point) _revsurf_basic(point, shifted, maxdist+rounding, neg, maxdist)
: !is_finite(cutoff) ? function(point) _revsurf_influence(point, shifted, maxdist+rounding, 1/influence, neg, maxdist)
: influence==1 ? function(point) _revsurf_cutoff(point, shifted, maxdist+rounding, cutoff, neg, maxdist)
: function (point) _revsurf_full(point, shifted, maxdist+rounding, cutoff, 1/influence, neg, maxdist);
!is_finite(cutoff) && influence==1 ? [function(point) _revsurf_basic(point, shifted, maxdist+rounding, neg, maxdist), vnf]
: !is_finite(cutoff) ? [function(point) _revsurf_influence(point, shifted, maxdist+rounding, 1/influence, neg, maxdist), vnf]
: influence==1 ? [function(point) _revsurf_cutoff(point, shifted, maxdist+rounding, cutoff, neg, maxdist), vnf]
: [function (point) _revsurf_full(point, shifted, maxdist+rounding, cutoff, 1/influence, neg, maxdist), vnf];
/// metaball disk with rounded edge
@@ -1137,9 +1153,9 @@ function _mb_disk_full(point, hl, r, cutoff, ex, neg) =
let(
rdist=norm([point.x,point.y]),
dist = rdist<r ? abs(point.z) : norm([rdist-r,point.z])
) neg* mb_cutoff(dist, cutoff) * (hl/dist)^ex;
) neg*mb_cutoff(dist, cutoff) * (hl/dist)^ex;
function mb_disk(h, r, cutoff=INF, influence=1, negative=false, d,l,height,length) =
function mb_disk(h, r, cutoff=INF, influence=1, negative=false, nodebug=false, d,l,height,length) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
@@ -1150,12 +1166,13 @@ function mb_disk(h, r, cutoff=INF, influence=1, negative=false, d,l,height,lengt
dum2 = assert(is_finite(r) && or>0, "\ninvalid radius or diameter."),
r = or - h2,
dum3 = assert(r>0, "\nDiameter must be greater than height."),
neg = negative ? -1 : 1
neg = negative ? -1 : 1,
vnf = [neg, nodebug ? cube(0.02,true) : cyl(h,r,rounding=min(0.499*h,0.999*r), $fn=20)]
)
!is_finite(cutoff) && influence==1 ? function(point) _mb_disk_basic(point,h2,r,neg)
: !is_finite(cutoff) ? function(point) _mb_disk_influence(point,h2,r,1/influence, neg)
: influence==1 ? function(point) _mb_disk_cutoff(point,h2,r,cutoff,neg)
: function (point) _mb_disk_full(point, h2, r, cutoff, 1/influence, neg);
!is_finite(cutoff) && influence==1 ? [function(point) _mb_disk_basic(point,h2,r,neg), vnf]
: !is_finite(cutoff) ? [function(point) _mb_disk_influence(point,h2,r,1/influence, neg), vnf]
: influence==1 ? [function(point) _mb_disk_cutoff(point,h2,r,cutoff,neg), vnf]
: [function (point) _mb_disk_full(point, h2, r, cutoff, 1/influence, neg), vnf];
/// metaball capsule (round-ended cylinder)
@@ -1177,7 +1194,7 @@ function _mb_capsule_full(dv, hl, r, cutoff, ex, neg) = let(
: dv.z<hl ? norm([dv.x,dv.y]) : norm(dv-[0,0,hl])
) neg * mb_cutoff(dist, cutoff) * (r/dist)^ex;
function mb_capsule(h, r, cutoff=INF, influence=1, negative=false, d,l,height,length) =
function mb_capsule(h, r, cutoff=INF, influence=1, negative=false, nodebug=false, d,l,height,length) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
@@ -1187,17 +1204,18 @@ function mb_capsule(h, r, cutoff=INF, influence=1, negative=false, d,l,height,le
dum2 = assert(is_finite(r) && r>0, "\ninvalid radius or diameter."),
sh = h-2*r, // straight side length
dum3 = assert(sh>0, "\nTotal length must accommodate rounded ends of cylinder."),
neg = negative ? -1 : 1
neg = negative ? -1 : 1,
vnf = [neg, nodebug ? cube(0.02,true) : cyl(h, r, rounding=0.999*r, $fn=20)]
)
!is_finite(cutoff) && influence==1 ? function(dv) _mb_capsule_basic(dv,sh/2,r,neg)
: !is_finite(cutoff) ? function(dv) _mb_capsule_influence(dv,sh/2,r,1/influence, neg)
: influence==1 ? function(dv) _mb_capsule_cutoff(dv,sh/2,r,cutoff,neg)
: function (dv) _mb_capsule_full(dv, sh/2, r, cutoff, 1/influence, neg);
!is_finite(cutoff) && influence==1 ? [function(dv) _mb_capsule_basic(dv,sh/2,r,neg), vnf]
: !is_finite(cutoff) ? [function(dv) _mb_capsule_influence(dv,sh/2,r,1/influence,neg), vnf]
: influence==1 ? [function(dv) _mb_capsule_cutoff(dv,sh/2,r,cutoff,neg), vnf]
: [function (dv) _mb_capsule_full(dv, sh/2, r, cutoff, 1/influence, neg), vnf];
/// metaball connector cylinder - calls mb_capsule* functions after transform
function mb_connector(p1, p2, r, cutoff=INF, influence=1, negative=false, d) =
function mb_connector(p1, p2, r, cutoff=INF, influence=1, negative=false, nodebug=false, d) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
@@ -1210,20 +1228,21 @@ function mb_connector(p1, p2, r, cutoff=INF, influence=1, negative=false, d) =
dc = p2-p1, // center-to-center distance
midpt = reverse(-0.5*(p1+p2)),
h = norm(dc)/2, // center-to-center length (cylinder height)
transform = submatrix(down(h)*rot(from=dc,to=UP)*move(-p1) ,[0:2], [0:3])
transform = submatrix(down(h)*rot(from=dc,to=UP)*move(-p1) ,[0:2], [0:3]),
vnf=[neg, move(p1, rot(from=UP,to=dc,p=up(h, nodebug ? cube(0.02,true) : cyl(2*(r+h),r,rounding=0.999*r,$fn=20))))]
)
!is_finite(cutoff) && influence==1 ? function(dv)
!is_finite(cutoff) && influence==1 ? [function(dv)
let(newdv = transform * [each dv,1])
_mb_capsule_basic(newdv,h,r,neg)
: !is_finite(cutoff) ? function(dv)
_mb_capsule_basic(newdv,h,r,neg), vnf]
: !is_finite(cutoff) ? [function(dv)
let(newdv = transform * [each dv,1])
_mb_capsule_influence(newdv,h,r,1/influence, neg)
: influence==1 ? function(dv)
_mb_capsule_influence(newdv,h,r,1/influence, neg), vnf]
: influence==1 ? [function(dv)
let(newdv = transform * [each dv,1])
_mb_capsule_cutoff(newdv,h,r,cutoff,neg)
: function (dv)
_mb_capsule_cutoff(newdv,h,r,cutoff,neg), vnf]
: [function (dv)
let(newdv = transform * [each dv,1])
_mb_capsule_full(newdv, h, r, cutoff, 1/influence, neg);
_mb_capsule_full(newdv, h, r, cutoff, 1/influence, neg), vnf];
/// metaball torus
@@ -1239,7 +1258,7 @@ function _mb_torus_full(point, rmaj, rmin, cutoff, ex, neg) =
let(dist = norm([norm([point.x,point.y])-rmaj, point.z]))
neg * mb_cutoff(dist, cutoff) * (rmin/dist)^ex;
function mb_torus(r_maj, r_min, cutoff=INF, influence=1, negative=false, d_maj, d_min, or,od,ir,id) =
function mb_torus(r_maj, r_min, cutoff=INF, influence=1, negative=false, nodebug=false, d_maj, d_min, or,od,ir,id) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
let(
@@ -1256,12 +1275,13 @@ function mb_torus(r_maj, r_min, cutoff=INF, influence=1, negative=false, d_maj,
is_finite(_ir)? (maj_rad - _ir) :
is_finite(_or)? (_or - maj_rad) :
assert(false, "\nBad minor size parameter."),
neg = negative ? -1 : 1
)
!is_finite(cutoff) && influence==1 ? function(point) _mb_torus_basic(point, r_maj, r_min, neg)
: !is_finite(cutoff) ? function(point) _mb_torus_influence(point, r_maj, r_min, 1/influence, neg)
: influence==1 ? function(point) _mb_torus_cutoff(point, r_maj, r_min, cutoff, neg)
: function(point) _mb_torus_full(point, r_maj, r_min, cutoff, 1/influence, neg);
neg = negative ? -1 : 1,
vnf = [neg, nodebug ? cube(0.02,true) : torus(r_maj,r_min,$fn=20)]
)
!is_finite(cutoff) && influence==1 ? [function(point) _mb_torus_basic(point, r_maj, r_min, neg), vnf]
: !is_finite(cutoff) ? [function(point) _mb_torus_influence(point, r_maj, r_min, 1/influence, neg), vnf]
: influence==1 ? [function(point) _mb_torus_cutoff(point, r_maj, r_min, cutoff, neg), vnf]
: [function(point) _mb_torus_full(point, r_maj, r_min, cutoff, 1/influence, neg), vnf];
/// metaball octahedron
@@ -1287,7 +1307,7 @@ function _mb_octahedron_full(point, invr, xp, cutoff, ex, neg) =
: (abs(p.x+p.y+p.z)^xp + abs(-p.x-p.y+p.z)^xp + abs(-p.x+p.y-p.z)^xp + abs(p.x-p.y-p.z)^xp) ^ (1/xp)
) neg * mb_cutoff(dist, cutoff) / dist^ex;
function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=false) =
function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=false, nodebug=false) =
assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
assert(squareness>=0 && squareness<=1, "\nsquareness must be inside the range [0,1].")
assert(is_finite(influence) && is_num(influence) && influence>0, "\ninfluence must be a positive number.")
@@ -1296,14 +1316,71 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
xp = _squircle_se_exponent(squareness),
invr = _mb_octahedron_basic([1/3,1/3,1/3],1,xp,1) * // correction factor
(is_num(size) ? 2/size : [[2/size.x,0,0],[0,2/size.y,0],[0,0,2/size.z]]),
neg = negative ? -1 : 1
neg = negative ? -1 : 1,
vnf = [neg, nodebug ? cube(0.02,true) : _debug_octahedron(size,squareness)]
)
!is_finite(cutoff) && influence==1 ? function(point) _mb_octahedron_basic(point,invr,xp,neg)
: !is_finite(cutoff) ? function(point) _mb_octahedron_influence(point,invr,xp,1/influence, neg)
: influence==1 ? function(point) _mb_octahedron_cutoff(point,invr,xp,cutoff,neg)
: function(point) _mb_octahedron_full(point,invr,xp,cutoff,1/influence,neg);
!is_finite(cutoff) && influence==1 ? [function(point) _mb_octahedron_basic(point,invr,xp,neg), vnf]
: !is_finite(cutoff) ? [function(point) _mb_octahedron_influence(point,invr,xp,1/influence, neg), vnf]
: influence==1 ? [function(point) _mb_octahedron_cutoff(point,invr,xp,cutoff,neg), vnf]
: [function(point) _mb_octahedron_full(point,invr,xp,cutoff,1/influence,neg), vnf];
/// debug shape approximations
/// beveled cube with squareness argument to approximate mb_cuboid() for debug view
function _debug_cube(size, squareness) =
squareness > 0.998 ? cube(size, true)
: let(
hw = is_num(size) ? [size,size,size]*0.5 : 0.5*size,
sq2 = sqrt(2),
cut = (2-sq2)*squareness + sq2 - 1,
xo = hw.x, yo = hw.y, zo = hw.z,
xi = xo*cut, yi = yo*cut, zi = zo*cut,
pts = [
[-xi,-yi,-zo], [xi,-yi,-zo], [xi,yi,-zo], [-xi,yi,-zo], // 0,1,2,3
[-xi,-yo,-zi], [xi,-yo,-zi], [xo,-yi,-zi], [xo,yi,-zi], // 4,5,6,7
[xi,yo,-zi], [-xi,yo,-zi], [-xo,yi,-zi], [-xo,-yi,-zi], // 8,9,10,11
[-xi,-yo,zi], [xi,-yo,zi], [xo,-yi,zi], [xo,yi,zi], // 12,13,14,15
[xi,yo,zi], [-xi,yo,zi], [-xo,yi,zi], [-xo,-yi,zi], // 16,17,18,19
[-xi,-yi,zo], [xi,-yi,zo], [xi,yi,zo], [-xi,yi,zo] // 20,21,22,23
],
faces = [
[0,1,2,3], // bottom
[4,5,1,0], [6,7,2,1], [8,9,3,2], [10,11,0,3], // bottom bevel
[1,5,6], [2,7,8], [3,9,10], [0,11,4], // bottom corners
[4,12,13,5], [5,13,14,6], [6,14,15,7], [7,15,16,8], [8,16,17,9], [9,17,18,10], [10,18,19,11], [11,19,12,4], // vertical sides
[21,14,13], [22,16,15], [23,18,17], [20,12,19], // top corners
[20,21,13,12], [21,22,15,14], [22,23,17,16], [23,20,19,18], // top bevels
[23,22,21,20] // top
]
) [pts, faces]; // vnf structure
/// beveled octahedron with squareness argument to approximate mb_octahedron for debug view
function _debug_octahedron(size, squareness) =
squareness > 0.998 ? octahedron(size)
: let(
hw = is_num(size) ? [size,size,size]*0.5 : 0.5*size,
isq3 = 1/sqrt(3),
r = hw*(isq3+squareness*(1-isq3)), // 3-vector radius to tips
ra = hw - r, // distance from axis tip face corner
rx = r.x, ry=r.y, rz=r.z, ax=ra.x, ay=ra.y, az=ra.z,
pts = [
[ax,0,-rz], [0,ay,-rz], [-ax,0,-rz], [0,-ay,-rz], // 0,1,2,3 botttom
[rx,0,-az], [0,ry,-az], [-rx,0,-az], [0,-ry,-az], // 4,5,6,7 below waist
[rx,ay,0], [ax,ry,0], [-ax,ry,0], [-rx,ay,0], // 8,9,10,11 waist
[-rx,-ay,0], [-ax,-ry,0], [ax,-ry,0], [rx,-ay,0], // 12,13,14,15 waist
[rx,0,az], [0,ry,az], [-rx,0,az], [0,-ry,az], // 16,17,18,19 above waist
[ax,0,rz], [0,ay,rz], [-ax,0,rz], [0,-ay,rz] // 20,21,22,23 botttom
],
faces = [
[0,1,2,3], // bottom
[1,0,4,8,9,5], [2,1,5,10,11,6], [3,2,6,12,13,7], [0,3,7,14,15,4], // bottom angle faces
[4,15,16,8], [5,9,17,10], [6,11,18,12], [7,13,19,14], // corner faces
[9,8,16,20,21,17], [11,10,17,21,22,18], [13,12,18,22,23,19], [15,14,19,23,20,16], // top angle faces
[23,22,21,20] // top
]
) [pts, faces]; // vnf structure
// Function&Module: metaballs()
// Synopsis: Creates a group of 3D metaballs (smoothly connected blobs).
@@ -1415,19 +1492,20 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// The built-in metaball functions are listed below. As usual, arguments without a trailing `=` can be used positionally; arguments with a trailing `=` must be used as named arguments.
// .
// * `mb_sphere(r|d=)` &mdash; spherical metaball, with radius r or diameter d. You can create an ellipsoid using `scale()` as the last transformation entry of the metaball `spec` array.
// * `mb_cuboid(size, [squareness=])` &mdash; cuboid metaball with rounded edges and corners. The corner sharpness is controlled by the `squareness` parameter ranging from 0 (spherical) to 1 (cubical), and defaults to 0.5. The `size` parameter specifies the dimensions of the cuboid that circumscribes the rounded shape, which is tangent to the center of each cube face. `size` may be a scalar or a vector, as in {{cuboid()}}. Except when `squareness=1`, the faces are always a little bit curved.
// * `mb_cuboid(size, [squareness=])` &mdash; cuboid metaball with rounded edges and corners. The corner sharpness is controlled by the `squareness` parameter ranging from 0 (spherical) to 1 (cubical), and defaults to 0.5. The `size` parameter specifies the dimensions of the cuboid that circumscribes the rounded shape, which is tangent to the center of each cube face. The `size` parameter may be a scalar or a vector, as in {{cuboid()}}. Except when `squareness=1`, the faces are always a little bit curved.
// * `mb_cyl(h|l|height|length, [r|d=], [r1=|d1=], [r2=|d2=], [rounding=])` &mdash; vertical cylinder or cone metaball with the same dimensional arguments as {{cyl()}}. At least one of the radius or diameter arguments is required. The `rounding` argument defaults to 0 (sharp edge) if not specified. Only one rounding value is allowed: the rounding is the same at both ends. For a fully rounded cylindrical shape, consider using `mb_capsule()` or `mb_disk()`, which are less flexible but have faster execution times.
// * `mb_disk(h|l|height|length, r|d=)` &mdash; rounded disk with flat ends. The diameter specifies the total diameter of the shape including the rounded sides, and must be greater than its height.
// * `mb_capsule(h|l|height|length, [r|d=]` &mdash; vertical cylinder or cone with rounded caps, using the same dimensional arguments as {{cyl()}}. The object resembles a convex hull of two spheres. The height or length specifies the distance between the spherical centers of the ends.
// * `mb_connector(p1, p2, [r|d=])` &mdash; a connecting rod of radius `r` or diameter `d` with hemispherical caps (like `mb_capsule()`), but specified to connect point `p1` to point `p2` (where `p1` and `p2` must be different 3D coordinates). As with `mb_capsule()`, the object resembles a convex hull of two spheres. The points `p1` and `p2` are at the centers of the two round caps. The connectors themselves are still influenced by other metaballs, but it may be undesirable to have them influence others, or each other. If two connectors are connected, the joint may appear swollen unless `influence` or `cutoff` is reduced. Reducing `cutoff` is preferable if feasible, because reducing `influence` can produce interpolation artifacts.
// * `mb_torus([r_maj|d_maj=], [r_min|d_min=], [or=|od=], [ir=|id=])` &mdash; torus metaball oriented perpendicular to the z axis. You can specify the torus dimensions using the same arguments as {{torus()}}; that is, major radius (or diameter) with `r_maj` or `d_maj`, and minor radius and diameter using `r_min` or `d_min`. Alternatively you can give the inner radius or diameter with `ir` or `id` and the outer radius or diameter with `or` or `od`. You must provide a combination of inputs that completely specifies the torus. If `cutoff` is applied, it is measured from the circle represented by `r_min=0`.
// * `mb_octahedron(size, [squareness=])` &mdash; octahedron metaball with rounded edges and corners. The corner sharpness is controlled by the `squareness` parameter ranging from 0 (spherical) to 1 (sharp), and defaults to 0.5. The `size` parameter specifies the tip-to-tip distance of the octahedron that circumscribes the rounded shape, which is tangent to the center of each octahedron face. `size` may be a scalar or a vector, as in {{octahedron()}}. At `squareness=0`, the shape reduces to a sphere curcumscribed by the octahedron. Except when `squareness=1`, the faces are always curved.
// * `mb_octahedron(size, [squareness=])` &mdash; octahedron metaball with rounded edges and corners. The corner sharpness is controlled by the `squareness` parameter ranging from 0 (spherical) to 1 (sharp), and defaults to 0.5. The `size` parameter specifies the tip-to-tip distance of the octahedron that circumscribes the rounded shape, which is tangent to the center of each octahedron face. The `size` parameter may be a scalar or a vector, as in {{octahedron()}}. At `squareness=0`, the shape reduces to a sphere curcumscribed by the octahedron. Except when `squareness=1`, the faces are always curved.
// .
// In addition to the dimensional arguments described above, all of the built-in functions accept the
// following named arguments:
// * `cutoff` &mdash; positive value giving the distance beyond which the metaball does not interact with other balls. Cutoff is measured from the object's center. Default: INF
// * `influence` &mdash; a positive number specifying the strength of interaction this ball has with other balls. Default: 1
// * `negative` &mdash; when true, creates a negative metaball. Default: false
// * `nodebug` &mdash; when true, suppresses the display of the underlying metaball shape when `debug=true` is set in the `metaballs()` module. This is useful to hide shapes that may be overlapping others in the debug view. Default: false
// .
// ***Metaball functions and user defined functions***
// .
@@ -1493,7 +1571,8 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// exact_bounds = When true, shrinks voxels as needed to fit whole voxels inside the requested bounding box. When false, enlarges `bounding_box` as needed to fit whole voxels of `voxel_size`, and centers the new bounding box over the requested box. Default: false
// show_stats = If true, display statistics about the metaball isosurface in the console window. Besides the number of voxels that the surface passes through, and the number of triangles making up the surface, this is useful for getting information about a possibly smaller bounding box to improve speed for subsequent renders. Enabling this parameter has a small speed penalty. Default: false
// convexity = (Module only) Maximum number of times a line could intersect a wall of the shape. Affects preview only. Default: 6
// show_box = (Module only) display the requested bounding box as transparent. This box may appear slightly inside the bounds of the figure if the actual bounding box had to be expanded to accommodate whole voxels. Default: false
// show_box = (Module only) Display the requested bounding box as transparent. This box may appear slightly inside the bounds of the figure if the actual bounding box had to be expanded to accommodate whole voxels. Default: false
// debug = (Module only) Display the underlying primitive metaball shapes, overlaid with the transparent metaball scene. Positive metaballs appear blue, negative appears orange, and custom functions with no debug VNF defined appear as gray diameter-10 spheres.
// cp = (Module only) Center point for determining intersection anchors or centering the shape. Determines the base of the anchor vector. Can be "centroid", "mean", "box" or a 3D point. Default: "centroid"
// anchor = (Module only) Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `"origin"`
// spin = (Module only) Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
@@ -1689,27 +1768,32 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// ],
// bounding_box = [[-16,-13,-5],[18,13,6]],
// voxel_size=0.4);
// Example(3D): Next we show how to create a function that works like the built-ins. **This is a full-fledged implementation** that allows you to specify the function directly by name in the `spec` argument without needing the function literal syntax, and without needing the `point` argument in `spec`, as in the prior examples. You must define a calculation function that accepts the `point` position argument and then whatever other parameters your metaball uses (here `r` and `noise_level`). Then there is a "master" function that does some error checking and returns a function literal expression that sets all of your parameters. The call to `mb_cutoff()` at the end handles the cutoff function for the noisy ball consistent with the other internal metaball functions; it requires `dist` and `cutoff` as arguments. You are not required to use this implementation in your own custom functions; in fact it's easier simply to declare the function literal in your `spec` argument, but this example shows how to do it all.
// Example(3D): Next we show how to create a function that works like the built-ins. **This is a full-fledged implementation** that allows you to specify the function directly by name in the `spec` argument without needing the function literal syntax, and without needing the `point` argument in `spec`, as in the prior examples. Here, `noisy_sphere_calcs() is the calculation function that accepts the `point` position argument and any other parameters needed (here `r` and `noise_level`), and returns a single value. Then there is a "master" function `noisy_sphere() that does some error checking and returns an array consisting of (a) a function literal expression that sets all of your parameters, and (b) another array containing the metaball sign and a simple "debug" VNF representation of the metaball for viewing when `debug=true` is passed to `metaballs()`. The call to `mb_cutoff()` at the end handles the cutoff function for the noisy ball consistent with the other internal metaball functions; it requires `dist` and `cutoff` as arguments. You are not required to use this implementation in your own custom functions; in fact it's easier simply to declare the function literal in your `spec` argument, but this example shows how to do it all.
// //
// // noisy sphere internal calculation function
//
// function noisy_sphere_calcs(point, r, noise_level, cutoff, exponent, neg) =
// let(
// noise = rands(0, noise_level, 1)[0],
// dist = norm(point) + noise
// dist = norm(point) + noise // distance to point from metaball center
// ) neg * mb_cutoff(dist,cutoff) * (r/dist)^exponent;
//
// // noisy sphere "master" entry function to use in spec argument
//
// function noisy_sphere(r, noise_level, cutoff=INF, influence=1, negative=false, d) =
// function noisy_sphere(r, noise_level, cutoff=INF, influence=1, negative=false, nodebug=false, d) =
// assert(is_num(cutoff) && cutoff>0, "\ncutoff must be a positive number.")
// assert(is_finite(influence) && influence>0, "\ninfluence must be a positive number.")
// let(
// r = get_radius(r=r,d=d),
// dummy=assert(is_finite(r) && r>0, "\ninvalid radius or diameter."),
// neg = negative ? -1 : 1
// ) // pass control as a function literal to the calc function
// function (point) noisy_sphere_calcs(point, r, noise_level, cutoff, 1/influence, neg);
// neg = negative ? -1 : 1,
// // create [sign, vnf] for debug view; display tiny cube if nodebug=true
// debug_vnf = [neg, nodebug ? cube(0.02,true) : sphere(r, $fn=16)]
// ) [
// // pass control as a function literal to the calc function
// function (point) noisy_sphere_calcs(point, r, noise_level, cutoff, 1/influence, neg),
// debug_vnf
// ];
//
// // define the scene and render it
//
@@ -1720,7 +1804,7 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// voxel_size = 0.5;
// boundingbox = [[-16,-8,-8], [16,8,8]];
// metaballs(spec, boundingbox, voxel_size);
// Example(3D,Med,NoAxes,VPR=[55,0,0],VPD=200,VPT=[7,2,2]): A more complex example using ellipsoids, a capsule, spheres, and a torus to make a tetrahedral object with rounded feet and a ring on top. The bottoms of the feet are flattened by clipping with the bottom of the bounding box. The center of the object is thick due to the contributions of three ellipsoids and a capsule converging. Designing an object like this using metaballs requires trial and error with low-resolution renders.
// Example(3D,Med,NoAxes,VPR=[55,0,0],VPD=200,VPT=[7,2,2]): Demonstration of `debug=true` with a more complex example using ellipsoids, a capsule, spheres, and a torus to make a tetrahedral object with rounded feet and a ring on top. The bottoms of the feet are flattened by clipping with the bottom of the bounding box. The center of the object is thick due to the contributions of three ellipsoids and a capsule converging. Designing an object like this using metaballs requires trial and error with low-resolution renders.
// include <BOSL2/polyhedra.scad>
// tetpts = zrot(15, p = 22 * regular_polyhedron_info("vertices", "tetrahedron"));
// tettransform = [ for(pt = tetpts) move(pt)*rot(from=RIGHT, to=pt)*scale([7,1.5,1.5]) ];
@@ -1737,9 +1821,7 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// ];
// voxel_size = 1;
// boundingbox = [[-22,-32,-13], [36,32,46]];
// // useful to save as VNF for copies and manipulations
// vnf = metaballs(spec, boundingbox, voxel_size, isovalue=1);
// vnf_polyhedron(vnf);
// metaballs(spec, boundingbox, voxel_size, isovalue=1, debug=true);
// Example(3D,Med,NoAxes,VPR=[70,0,30],VPD=520,VPT=[0,0,80]): This example demonstrates grouping metaballs together and nesting them in lists of other metaballs, to make a crude model of a hand. Here, just one finger is defined, and a thumb is defined from one less joint in the finger. Individual fingers are grouped together with different positions and scaling, along with the thumb. Finally, this group of all fingers is used to combine with a rounded cuboid, with a slight ellipsoid dent subtracted to hollow out the palm, to make the hand.
// joints = [[0,0,1], [0,0,85], [0,-5,125], [0,-16,157], [0,-30,178]];
// finger = [
@@ -1797,22 +1879,23 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// stance = [12,6]; // leg position offsets
//
// spec = [
// // Legs
// move([-stance.x,-stance.y]), mb_connector([-4,0,0],[-6,0,tibia],legD, influence = 0.2),
// // Lower legs
// move([-stance.x,-stance.y]), mb_connector([-4,0,0.25],[-6,0,tibia],legD, influence = 0.2),
// move([-stance.x,stance.y]), mb_connector([0,0,0],[0,0,tibia],legD, influence = 0.2),
// move([stance.x,-stance.y]), mb_connector([-2,0,0],[-3,0,tibia],legD, influence = 0.2),
// move([stance.x,stance.y]), mb_connector([0,0,0],[0,0,tibia],legD, influence = 0.2),
//
// Upper legs
// move([-stance.x,-stance.y,tibia]), mb_connector([-6,0,0],[-2,0,femur],legD),
// move([-stance.x,stance.y,tibia]), mb_connector([0,0,0],[0,0,femur],legD),
// move([stance.x,-stance.y,tibia]), mb_connector([-3,0,0],[-1,0,femur],legD),
// move([stance.x,stance.y,tibia]), mb_connector([0,0,0],[0,0,femur],legD),
//
// // Hooves
// move([-stance.x-6,-stance.y,1]), mb_capsule(d= 2, h = 3, cutoff = 2),
// move([-stance.x-1,stance.y,1]), mb_capsule(d= 2, h = 3, cutoff = 2),
// move([stance.x-3.5,-stance.y,1]), mb_capsule(d= 2, h = 3, cutoff = 2),
// move([stance.x-1,stance.y,1]), mb_capsule(d= 2, h = 3, cutoff = 2),
// move([-stance.x-5.5,-stance.y,1.25])*yrot(-5), mb_capsule(d=2, h=3, cutoff=2),
// move([-stance.x-4.5,-stance.y,-1.4])*yrot(-5), mb_cuboid(size=4, squareness=1, cutoff=1, influence=20, negative=true), // truncate bottom of raised hoof
// move([-stance.x-1,stance.y,1]), mb_capsule(d=2, h=3, cutoff=2),
// move([stance.x-3.5,-stance.y,1]), mb_capsule(d=2, h=3, cutoff=2),
// move([stance.x-1,stance.y,1]), mb_capsule(d=2, h=3, cutoff=2),
//
// // Body
// up(tibia+femur+10) * yrot(10), mb_cuboid([16,7,7]),
@@ -1885,11 +1968,49 @@ function mb_octahedron(size, squareness=0.5, cutoff=INF, influence=1, negative=f
// xflip_copy() move([5,-8,54]) color("skyblue") sphere(2, $fn = 32);
// // add teeth
// xflip_copy() move([1.1,-10,44]) color("white") cuboid([2,0.5,4], rounding = 0.15);
// Example(3D,Med,NoAxes,VPD=120,VPT=[2,0,6],VPR=[60,0,320]): A model of a duck made from spheres, disks, a capsule, and a cone for the tail. In the head sphere, `nodebug=true` is set because when using the debug view (passing `debug=true` into `metaballs()`), this head sphere overlaps the other structural components.
// b_box = [[-31,-18,-10], [29,18,31]];
// headZ = 21;
// headX = 11;
// spec =[
// scale([1.5,1,1]), mb_disk(17,15), //body
// left(headX)*up(14), mb_disk(3,5, influence=0.5), //neck shim
// left(headX)*up(headZ)*scale([1,0.9,1]), mb_sphere(10,cutoff=11,nodebug=true), //head
// left(headX+5)*up(headZ-1)*fwd(5), mb_disk(1,2, cutoff=4), //cheek bulge
// left(headX+5)*up(headZ-1)*back(5), mb_disk(1,2, cutoff=4), //cheek bulge
// // eye indentations
// move([-headX,0,headZ+3])*zrot(70)*left(9)*yrot(25)*scale([1,3,1.3]), mb_sphere(1, negative=true, influence=1, cutoff=10),
// move([-headX,0,headZ+3])*zrot(-70)*left(9)*yrot(25)*scale([1,3,1.3]), mb_sphere(1, negative=true, influence=1, cutoff=10),
// //beak
// left(headX+13)*up(headZ)*zscale(0.4)*yrot(90), mb_capsule(12,3, cutoff=5),
// left(headX+8)*up(headZ), mb_disk(2,4),
// left(headX+16)*up(30), mb_sphere(5, negative=true, cutoff=8),
// left(headX+12)*up(headZ+1)*scale([1.2,1,0.75]), mb_sphere(2, cutoff = 3),
// //tail
// right(20)*up(8)*yscale(1.7)*yrot(35), mb_cyl(h=15, r1=4, r2=0.5),
// ];
// metaballs(spec, b_box, voxel_size=0.75);
// // add eyeballs
// move([-headX,0,headZ+2.5])zrot(53)left(4.9) color("#223300") sphere(3, $fn=64);
// move([-headX,0,headZ+2.5])zrot(-53)left(4.9) color("#223300") sphere(3, $fn=64);
module metaballs(spec, bounding_box, voxel_size, voxel_count, isovalue=1, closed=true, exact_bounds=false, convexity=6, cp="centroid", anchor="origin", spin=0, orient=UP, atype="hull", show_stats=false, show_box=false) {
vnf = metaballs(spec, bounding_box, voxel_size, voxel_count, isovalue, closed, exact_bounds, show_stats);
module metaballs(spec, bounding_box, voxel_size, voxel_count, isovalue=1, closed=true, exact_bounds=false, convexity=6, cp="centroid", anchor="origin", spin=0, orient=UP, atype="hull", show_stats=false, show_box=false, debug=false) {
vnf = metaballs(spec, bounding_box, voxel_size, voxel_count, isovalue, closed, exact_bounds, show_stats);
if(debug) {
funclist = _mb_unwind_list(spec);
for(i=[0:2:len(funclist)-1]) {
if(is_vnf(funclist[i+1][1][1])) {
color(funclist[i+1][1][0]>0 ? "#3399FF" : "#FF9933")
vnf_polyhedron(apply(funclist[i], funclist[i+1][1][1]));
} else
color("silver") vnf_polyhedron(apply(funclist[i], sphere(5, $fn=20)));
}
%vnf_polyhedron(vnf, convexity=convexity, cp=cp, anchor=anchor, spin=spin, orient=orient, atype=atype)
children();
} else {
vnf_polyhedron(vnf, convexity=convexity, cp=cp, anchor=anchor, spin=spin, orient=orient, atype=atype)
children();
}
if(show_box)
let(bbox = _getbbox(voxel_size, bounding_box, exact_bounds, undef))
%translate(bbox[0]) cube(bbox[1]-bbox[0]);
@@ -1935,14 +2056,15 @@ function metaballs(spec, bounding_box, voxel_size, voxel_count, isovalue=1, clos
zset = list([bot.z:voxsize.z:top.z+halfvox.z]),
allpts = [for(x=xset, y=yset, z=zset) [x,y,z,1]],
trans_pts = [for(i=[0:nballs-1]) allpts*transmatrix[i]],
allvals = [for(i=[0:nballs-1]) [for(pt=trans_pts[i]) funclist[2*i+1](pt)]],
allvals = [for(i=[0:nballs-1]) [for(pt=trans_pts[i]) funclist[2*i+1][0](pt)]],
//total = _sum(allvals,allvals[0]*EPSILON),
total = _sum(slice(allvals,1,-1), allvals[0]),
fieldarray = list_to_matrix(list_to_matrix(total,len(zset)),len(yset))
) isosurface(fieldarray, isoval, newbbox, voxsize, closed=closed, exact_bounds=true, show_stats=show_stats, _mball=true);
/// internal function: unwrap nested metaball specs in to a single list
function _mb_unwind_list(list, parent_trans=[IDENT]) =
function _mb_unwind_list(list, parent_trans=[IDENT], depth=0) =
let(
dum1 = assert(is_list(list), "\nDid not find valid list of metaballs."),
n=len(list),
@@ -1950,15 +2072,17 @@ function _mb_unwind_list(list, parent_trans=[IDENT]) =
) [
for(i=[0:2:n-1])
let(
dum = assert(is_matrix(list[i],4,4), str("\nInvalid 4×4 transformation matrix found at position ",i,".")),
dum = assert(is_matrix(list[i],4,4), str("\nInvalid 4×4 transformation matrix found at position ",i,", depth ",depth,": ", list[i])),
trans = parent_trans[0] * list[i],
j=i+1
) if(is_function(list[j]))
) if (is_function(list[j])) // for custom function without brackets...
each [trans, [list[j], []]] // ...add brackets and empty vnf
else if(is_function(list[j][0]))
each [trans, list[j]]
else if (is_list(list[j]))
each _mb_unwind_list(list[j], [trans])
else if (is_list(list[j][0])) // likely a nested spec if not a function
each _mb_unwind_list(list[j], [trans], depth+1)
else
assert(false, str("\nExpected function literal or list at position ",j,"."))
assert(false, str("\nExpected function literal or list at position ",j,", depth ",depth,"."))
];