//////////////////////////////////////////////////////////////////////
// LibFile: vnf.scad
// The Vertices'N'Faces structure (VNF) holds the data used by polyhedron() to construct objects: a vertex
// list and a list of faces. This library makes it easier to construct polyhedra by providing
// functions to construct, merge, and modify VNF data, while avoiding common pitfalls such as
// reversed faces.
// Includes:
// include <BOSL2/std.scad>
// FileGroup: Advanced Modeling
// FileSummary: Vertices 'n' Faces structure. Makes polyhedron() easier to use.
// FileFootnotes: STD=Included in std.scad
//////////////////////////////////////////////////////////////////////
// Section: Creating Polyhedrons with VNF Structures
// VNF stands for "Vertices'N'Faces". VNF structures are 2-item lists, `[VERTICES,FACES]` where the
// first item is a list of vertex points, and the second is a list of face indices into the vertex
// list. Each VNF is self contained, with face indices referring only to its own vertex list.
// You can construct a `polyhedron()` in parts by describing each part in a self-contained VNF, then
// merge the various VNFs to get the completed polyhedron vertex list and faces.
/// Constant: EMPTY_VNF
/// Description:
/// The empty VNF data structure. Equal to `[[],[]]`.
EMPTY_VNF = [[],[]]; // The standard empty VNF with no vertices or faces.
// Function: vnf_vertex_array()
// Usage:
// vnf = vnf_vertex_array(points, [caps], [cap1], [cap2], [style], [reverse], [col_wrap], [row_wrap]);
// Description:
// Creates a VNF structure from a rectangular vertex list, by dividing the vertices into columns and rows,
// adding faces to tile the surface. You can optionally have faces added to wrap the last column
// back to the first column, or wrap the last row to the first. Endcaps can be added to either
// the first and/or last rows. The style parameter determines how the quadrilaterals are divided into
// triangles. The default style is an arbitrary, systematic subdivision in the same direction. The "alt" style
// is the uniform subdivision in the other (alternate) direction. The "min_edge" style picks the shorter edge to
// subdivide for each quadrilateral, so the division may not be uniform across the shape. The "quincunx" style
// adds a vertex in the center of each quadrilateral and creates four triangles, and the "convex" and "concave" styles
// chooses the locally convex/concave subdivision. Degenerate faces
// are not included in the output, but if this results in unused vertices they will still appear in the output.
// Arguments:
// points = A list of vertices to divide into columns and rows.
// ---
// caps = If true, add endcap faces to the first AND last rows.
// cap1 = If true, add an endcap face to the first row.
// cap2 = If true, add an endcap face to the last row.
// col_wrap = If true, add faces to connect the last column to the first.
// row_wrap = If true, add faces to connect the last row to the first.
// reverse = If true, reverse all face normals.
// style = The style of subdividing the quads into faces. Valid options are "default", "alt", "min_edge", "quincunx", "convex" and "concave".
// Example(3D):
// vnf = vnf_vertex_array(
// points=[
// for (h = [0:5:180-EPSILON]) [
// for (t = [0:5:360-EPSILON])
// cylindrical_to_xyz(100 + 12 * cos((h/2 + t)*6), t, h)
// ]
// ],
// col_wrap=true, caps=true, reverse=true, style="alt"
// );
// vnf_polyhedron(vnf);
// Example(3D): Both `col_wrap` and `row_wrap` are true to make a torus.
// vnf = vnf_vertex_array(
// points=[
// for (a=[0:5:360-EPSILON])
// apply(
// zrot(a) * right(30) * xrot(90),
// path3d(circle(d=20))
// )
// ],
// col_wrap=true, row_wrap=true, reverse=true
// );
// vnf_polyhedron(vnf);
// Example(3D): Möbius Strip. Note that `row_wrap` is not used, and the first and last profile copies are the same.
// vnf = vnf_vertex_array(
// points=[
// for (a=[0:5:360]) apply(
// zrot(a) * right(30) * xrot(90) * zrot(a/2+60),
// path3d(square([1,10], center=true))
// )
// ],
// col_wrap=true, reverse=true
// );
// vnf_polyhedron(vnf);
// Example(3D): Assembling a Polyhedron from Multiple Parts
// wall_points = [
// for (a = [-90:2:90]) apply(
// up(a) * scale([1-0.1*cos(a*6),1-0.1*cos((a+90)*6),1]),
// path3d(circle(d=100))
// )
// ];
// cap = [
// for (a = [0:0.01:1+EPSILON]) apply(
// up(90-5*sin(a*360*2)) * scale([a,a,1]),
// wall_points[0]
// )
// ];
// cap1 = [for (p=cap) down(90, p=zscale(-1, p=p))];
// cap2 = [for (p=cap) up(90, p=p)];
// vnf1 = vnf_vertex_array(points=wall_points, col_wrap=true);
// vnf2 = vnf_vertex_array(points=cap1, col_wrap=true);
// vnf3 = vnf_vertex_array(points=cap2, col_wrap=true, reverse=true);
// vnf_polyhedron([vnf1, vnf2, vnf3]);
function vnf_vertex_array(
points,
caps, cap1, cap2,
col_wrap=false,
row_wrap=false,
reverse=false,
style="default"
) =
assert(!(any([caps,cap1,cap2]) && !col_wrap), "col_wrap must be true if caps are requested")
assert(!(any([caps,cap1,cap2]) && row_wrap), "Cannot combine caps with row_wrap")
assert(in_list(style,["default","alt","quincunx", "convex","concave", "min_edge"]))
assert(is_matrix(points[0], n=3),"Point array has the wrong shape or points are not 3d")
assert(is_consistent(points), "Non-rectangular or invalid point array")
let(
pts = flatten(points),
pcnt = len(pts),
rows = len(points),
cols = len(points[0])
)
rows<=1 || cols<=1 ? EMPTY_VNF :
let(
cap1 = first_defined([cap1,caps,false]),
cap2 = first_defined([cap2,caps,false]),
colcnt = cols - (col_wrap?0:1),
rowcnt = rows - (row_wrap?0:1),
verts = [
each pts,
if (style=="quincunx")
for (r = [0:1:rowcnt-1], c = [0:1:colcnt-1])
let(
i1 = ((r+0)%rows)*cols + ((c+0)%cols),
i2 = ((r+1)%rows)*cols + ((c+0)%cols),
i3 = ((r+1)%rows)*cols + ((c+1)%cols),
i4 = ((r+0)%rows)*cols + ((c+1)%cols)
)
mean([pts[i1], pts[i2], pts[i3], pts[i4]])
],
allfaces = [
if (cap1) count(cols,reverse=!reverse),
if (cap2) count(cols,(rows-1)*cols, reverse=reverse),
for (r = [0:1:rowcnt-1], c=[0:1:colcnt-1])
each
let(
i1 = ((r+0)%rows)*cols + ((c+0)%cols),
i2 = ((r+1)%rows)*cols + ((c+0)%cols),
i3 = ((r+1)%rows)*cols + ((c+1)%cols),
i4 = ((r+0)%rows)*cols + ((c+1)%cols),
faces =
style=="quincunx"?
let(i5 = pcnt + r*colcnt + c)
[[i1,i5,i2],[i2,i5,i3],[i3,i5,i4],[i4,i5,i1]]
: style=="alt"?
[[i1,i4,i2],[i2,i4,i3]]
: style=="min_edge"?
let(
d42=norm(pts[i4]-pts[i2]),
d13=norm(pts[i1]-pts[i3]),
shortedge = d42<=d13 ? [[i1,i4,i2],[i2,i4,i3]]
: [[i1,i3,i2],[i1,i4,i3]]
)
shortedge
: style=="convex"?
let( // Find normal for 3 of the points. Is the other point above or below?
n = (reverse?-1:1)*cross(pts[i2]-pts[i1],pts[i3]-pts[i1]),
convexfaces = n==0 ? [[i1,i4,i3]]
: n*pts[i4] > n*pts[i1] ? [[i1,i4,i2],[i2,i4,i3]]
: [[i1,i3,i2],[i1,i4,i3]]
)
convexfaces
: style=="concave"?
let( // Find normal for 3 of the points. Is the other point above or below?
n = (reverse?-1:1)*cross(pts[i2]-pts[i1],pts[i3]-pts[i1]),
concavefaces = n==0 ? [[i1,i4,i3]]
: n*pts[i4] <= n*pts[i1] ? [[i1,i4,i2],[i2,i4,i3]]
: [[i1,i3,i2],[i1,i4,i3]]
)
concavefaces
: [[i1,i3,i2],[i1,i4,i3]],
// remove degenerate faces
culled_faces= [for(face=faces)
if (norm(verts[face[0]]-verts[face[1]])>EPSILON &&
norm(verts[face[1]]-verts[face[2]])>EPSILON &&
norm(verts[face[2]]-verts[face[0]])>EPSILON)
face
],
rfaces = reverse? [for (face=culled_faces) reverse(face)] : culled_faces
)
rfaces,
]
)
[verts,allfaces];
// Function: vnf_tri_array()
// Usage:
// vnf = vnf_tri_array(points, [row_wrap], [reverse])
// Description:
// Produces a vnf from an array of points where each row length can differ from the adjacent rows by up to 2 in length. This enables
// the construction of triangular VNF patches. The resulting VNF can be wrapped along the rows by setting `row_wrap` to true.
// You cannot wrap columns: if you need to do that you'll need to merge two VNF arrays that share edges. Degenerate faces
// are not included in the output, but if this results in unused vertices they will still appear in the output.
// Arguments:
// points = List of point lists for each row
// row_wrap = If true then add faces connecting the first row and last row. These rows must differ by at most 2 in length.
// reverse = Set this to reverse the direction of the faces
// Example(3D,NoAxes): Each row has one more point than the preceeding one.
// pts = [for(y=[1:1:10]) [for(x=[0:y-1]) [x,y,y]]];
// vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
// Example(3D,NoAxes): Each row has two more points than the preceeding one.
// pts = [for(y=[0:2:10]) [for(x=[-y/2:y/2]) [x,y,y]]];
// vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
// Example(3D): Merging two VNFs to construct a cone with one point length change between rows.
// pts1 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[0,180]),10-z)];
// pts2 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[180,360]),10-z)];
// vnf = vnf_join([vnf_tri_array(pts1),
// vnf_tri_array(pts2)]);
// color("green")vnf_wireframe(vnf,width=0.1);
// vnf_polyhedron(vnf);
// Example(3D): Cone with length change two between rows
// pts1 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[0,180]),10-z)];
// pts2 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[180,360]),10-z)];
// vnf = vnf_join([vnf_tri_array(pts1),
// vnf_tri_array(pts2)]);
// color("green")vnf_wireframe(vnf,width=0.1);
// vnf_polyhedron(vnf);
// Example(3D,NoAxes): Point count can change irregularly
// lens = [10,9,7,5,6,8,8,10];
// pts = [for(y=idx(lens)) lerpn([-lens[y],y,y],[lens[y],y,y],lens[y])];
// vnf = vnf_tri_array(pts);
// vnf_wireframe(vnf,width=0.1);
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
function vnf_tri_array(points, row_wrap=false, reverse=false) =
let(
lens = [for(row=points) len(row)],
rowstarts = [0,each cumsum(lens)],
faces =
[for(i=[0:1:len(points) - 1 - (row_wrap ? 0 : 1)]) each
let(
rowstart = rowstarts[i],
nextrow = select(rowstarts,i+1),
delta = select(lens,i+1)-lens[i]
)
delta == 0 ?
[for(j=[0:1:lens[i]-2]) reverse ? [j+rowstart+1, j+rowstart, j+nextrow] : [j+rowstart, j+rowstart+1, j+nextrow],
for(j=[0:1:lens[i]-2]) reverse ? [j+rowstart+1, j+nextrow, j+nextrow+1] : [j+rowstart+1, j+nextrow+1, j+nextrow]] :
delta == 1 ?
[for(j=[0:1:lens[i]-2]) reverse ? [j+rowstart+1, j+rowstart, j+nextrow+1] : [j+rowstart, j+rowstart+1, j+nextrow+1],
for(j=[0:1:lens[i]-1]) reverse ? [j+rowstart, j+nextrow, j+nextrow+1] : [j+rowstart, j+nextrow+1, j+nextrow]] :
delta == -1 ?
[for(j=[0:1:lens[i]-3]) reverse ? [j+rowstart+1, j+nextrow, j+nextrow+1]: [j+rowstart+1, j+nextrow+1, j+nextrow],
for(j=[0:1:lens[i]-2]) reverse ? [j+rowstart+1, j+rowstart, j+nextrow] : [j+rowstart, j+rowstart+1, j+nextrow]] :
let(count = floor((lens[i]-1)/2))
delta == 2 ?
[
for(j=[0:1:count-1]) reverse ? [j+rowstart+1, j+rowstart, j+nextrow+1] : [j+rowstart, j+rowstart+1, j+nextrow+1], // top triangles left
for(j=[count:1:lens[i]-2]) reverse ? [j+rowstart+1, j+rowstart, j+nextrow+2] : [j+rowstart, j+rowstart+1, j+nextrow+2], // top triangles right
for(j=[0:1:count]) reverse ? [j+rowstart, j+nextrow, j+nextrow+1] : [j+rowstart, j+nextrow+1, j+nextrow], // bot triangles left
for(j=[count+1:1:select(lens,i+1)-2]) reverse ? [j+rowstart-1, j+nextrow, j+nextrow+1] : [j+rowstart-1, j+nextrow+1, j+nextrow], // bot triangles right
] :
delta == -2 ?
[
for(j=[0:1:count-2]) reverse ? [j+nextrow, j+nextrow+1, j+rowstart+1] : [j+nextrow, j+rowstart+1, j+nextrow+1],
for(j=[count-1:1:lens[i]-4]) reverse ? [j+nextrow,j+nextrow+1,j+rowstart+2] : [j+nextrow,j+rowstart+2, j+nextrow+1],
for(j=[0:1:count-1]) reverse ? [j+nextrow, j+rowstart+1, j+rowstart] : [j+nextrow, j+rowstart, j+rowstart+1],
for(j=[count:1:select(lens,i+1)]) reverse ? [ j+nextrow-1, j+rowstart+1, j+rowstart]: [ j+nextrow-1, j+rowstart, j+rowstart+1],
] :
assert(false,str("Unsupported row length difference of ",delta, " between row ",i," and ",(i+1)%len(points)))
],
verts = flatten(points),
culled_faces=
[for(face=faces)
if (norm(verts[face[0]]-verts[face[1]])>EPSILON &&
norm(verts[face[1]]-verts[face[2]])>EPSILON &&
norm(verts[face[2]]-verts[face[0]])>EPSILON)
face
]
)
[flatten(points), culled_faces];
// Function: vnf_join()
// Usage:
// vnf = vnf_join([VNF, VNF, VNF, ...]);
// Description:
// Given a list of VNF structures, merges them all into a single VNF structure.
// Combines all the points of the input VNFs and labels the faces appropriately.
// All the points in the input VNFs will appear in the output, even if they are
// duplicates of each other. It is valid to repeat points in a VNF, but if you
// with to remove the duplicates that will occur along joined edges, use {{vnf_merge_points()}}.
// Arguments:
// vnfs = a list of the VNFs to joint into one VNF.
function vnf_join(vnfs) =
assert(is_vnf_list(vnfs) , "Input must be a list of VNFs")
len(vnfs)==1 ? vnfs[0]
:
let (
offs = cumsum([ 0, for (vnf = vnfs) len(vnf[0]) ]),
verts = [for (vnf=vnfs) each vnf[0]],
faces =
[ for (i = idx(vnfs))
let( faces = vnfs[i][1] )
for (face = faces)
if ( len(face) >= 3 )
[ for (j = face)
assert( j>=0 && j<len(vnfs[i][0]),
str("VNF number ", i, " has a face indexing an nonexistent vertex") )
offs[i] + j ]
]
)
[verts,faces];
// Function: vnf_from_polygons()
// Usage:
// vnf = vnf_from_polygons(polygons);
// Description:
// Given a list of 3d polygons, produces a VNF containing those polygons.
// It is up to the caller to make sure that the points are in the correct order to make the face
// normals point outwards. No checking for duplicate vertices is done. If you want to
// remove duplicate vertices use {{vnf_merge_points()}}.
// Arguments:
// polygons = The list of 3d polygons to turn into a VNF
function vnf_from_polygons(polygons) =
assert(is_list(polygons) && is_path(polygons[0]),"Input should be a list of polygons")
let(
offs = cumsum([0, for(p=polygons) len(p)]),
faces = [for(i=idx(polygons))
[for (j=idx(polygons[i])) offs[i]+j]
]
)
[flatten(polygons), faces];
function _path_path_closest_vertices(path1,path2) =
let(
dists = [for (i=idx(path1)) let(j=closest_point(path1[i],path2)) [j,norm(path2[j]-path1[i])]],
i1 = min_index(column(dists,1)),
i2 = dists[i1][0]
) [dists[i1][1], i1, i2];
function _join_paths_at_vertices(path1,path2,v1,v2) =
let(
repeat_start = !approx(path1[v1],path2[v2]),
path1 = clockwise_polygon(list_rotate(path1,v1)),
path2 = ccw_polygon(list_rotate(path2,v2))
)
[
each path1,
if (repeat_start) path1[0],
each path2,
if (repeat_start) path2[0],
];
/// Internal Function: _cleave_connected_region(region, eps)
/// Description:
/// Given a region that is connected and has its outer border in region[0],
/// produces a overlapping connected path to join internal holes to
/// the outer border without adding points. Output is a single non-simple polygon.
/// Requirements:
/// It expects that all region paths be simple closed paths, with region[0] CW and
/// the other paths CCW and encircled by region[0]. The input region paths are also
/// supposed to be disjoint except for common vertices and common edges but with
/// no crossings. It may return `undef` if these conditions are not met.
/// This function implements an extension of the algorithm discussed in:
/// https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
function _cleave_connected_region(region, eps=EPSILON) =
len(region)==1 ? region[0] :
let(
outer = deduplicate(region[0]), //
holes = [for(i=[1:1:len(region)-1]) // deduplication possibly unneeded
deduplicate( region[i] ) ], //
extridx = [for(li=holes) max_index(column(li,0)) ],
// the right extreme vertex for each hole sorted by decreasing x values
extremes = sort( [for(i=idx(holes)) [ i, extridx[i], -holes[i][extridx[i]].x] ], idx=2 )
)
_polyHoles(outer, holes, extremes, eps, 0);
// connect the hole paths one at a time to the outer path.
// 'extremes' is the list of the right extreme vertex of each hole sorted by decreasing abscissas
// see: _cleave_connected_region(region, eps)
function _polyHoles(outer, holes, extremes, eps=EPSILON, n=0) =
let(
extr = extremes[n], //
hole = holes[extr[0]], // hole path to bridge to the outer path
ipt = extr[1], // index of the hole point with maximum abscissa
brdg = _bridge(hole[ipt], outer, eps) // the index of a point in outer to bridge hole[ipt] to
)
brdg == undef ? undef :
let(
l = len(outer),
lh = len(hole),
// the new outer polygon bridging the hole to the old outer
npoly =
approx(outer[brdg], hole[ipt], eps)
? [ for(i=[brdg: 1: brdg+l]) outer[i%l] ,
for(i=[ipt+1: 1: ipt+lh-1]) hole[i%lh] ]
: [ for(i=[brdg: 1: brdg+l]) outer[i%l] ,
for(i=[ipt: 1: ipt+lh]) hole[i%lh] ]
)
n==len(holes)-1 ? npoly :
_polyHoles(npoly, holes, extremes, eps, n+1);
// find a point in outer to be connected to pt in the interior of outer
// by a segment that not cross or touch any non adjacente edge of outer.
// return the index of a vertex in the outer path where the bridge should end
// see _polyHoles(outer, holes, extremes, eps)
function _bridge(pt, outer,eps) =
// find the intersection of a ray from pt to the right
// with the boundary of the outer cycle
let(
l = len(outer),
crxs =
let( edges = pair(outer,wrap=true) )
[for( i = idx(edges) )
let( edge = edges[i] )
// consider just descending outer edges at right of pt crossing ordinate pt.y
if( (edge[0].y > pt.y+eps)
&& (edge[1].y <= pt.y)
&& _is_at_left(pt, [edge[1], edge[0]], eps) )
[ i,
// the point of edge with ordinate pt.y
abs(pt.y-edge[1].y)<eps ? edge[1] :
let( u = (pt-edge[1]).y / (edge[0]-edge[1]).y )
(1-u)*edge[1] + u*edge[0]
]
]
)
crxs == [] ? undef :
let(
// the intersection point of the nearest edge to pt with minimum slope
minX = min([for(p=crxs) p[1].x]),
crxcand = [for(crx=crxs) if(crx[1].x < minX+eps) crx ], // nearest edges
nearest = min_index([for(crx=crxcand)
(outer[crx[0]].x - pt.x) / (outer[crx[0]].y - pt.y) ]), // minimum slope
proj = crxcand[nearest],
vert0 = outer[proj[0]], // the two vertices of the nearest crossing edge
vert1 = outer[(proj[0]+1)%l],
isect = proj[1] // the intersection point
)
norm(pt-vert1) < eps ? (proj[0]+1)%l : // if pt touches an outer vertex, return its index
// as vert0.y > pt.y then pt!=vert0
norm(pt-isect) < eps ? undef : // if pt touches the middle of an outer edge -> error
let(
// the edge [vert0, vert1] necessarily satisfies vert0.y > vert1.y
// indices of candidates to an outer bridge point
cand =
(vert0.x > pt.x)
? [ proj[0],
// select reflex vertices inside of the triangle [pt, vert0, isect]
for(i=idx(outer))
if( _tri_class(select(outer,i-1,i+1),eps) <= 0
&& _pt_in_tri(outer[i], [pt, vert0, isect], eps)>=0 )
i
]
: [ (proj[0]+1)%l,
// select reflex vertices inside of the triangle [pt, isect, vert1]
for(i=idx(outer))
if( _tri_class(select(outer,i-1,i+1),eps) <= 0
&& _pt_in_tri(outer[i], [pt, isect, vert1], eps)>=0 )
i
],
// choose the candidate outer[i] such that the line [pt, outer[i]] has minimum slope
// among those with minimum slope choose the nearest to pt
slopes = [for(i=cand) 1-abs(outer[i].x-pt.x)/norm(outer[i]-pt) ],
min_slp = min(slopes),
cand2 = [for(i=idx(cand)) if(slopes[i]<=min_slp+eps) cand[i] ],
nearest = min_index([for(i=cand2) norm(pt-outer[i]) ])
)
cand2[nearest];
// Function: vnf_from_region()
// Usage:
// vnf = vnf_from_region(region, [transform], [reverse]);
// Description:
// Given a (two-dimensional) region, applies the given transformation matrix to it and makes a (three-dimensional) triangulated VNF of
// faces for that region, reversed if desired.
// Arguments:
// region = The region to conver to a vnf.
// transform = If given, a transformation matrix to apply to the faces generated from the region. Default: No transformation applied.
// reverse = If true, reverse the normals of the faces generated from the region. An untransformed region will have face normals pointing `UP`. Default: false
// Example(3D):
// region = [square([20,10],center=true),
// right(5,square(4,center=true)),
// left(5,square(6,center=true))];
// vnf = vnf_from_region(region);
// color("gray")down(.125)
// linear_extrude(height=.125)region(region);
// vnf_wireframe(vnf,width=.25);
function vnf_from_region(region, transform, reverse=false) =
let (
regions = region_parts(force_region(region)),
vnfs =
[ for (rgn = regions)
let( cleaved = path3d(_cleave_connected_region(rgn)) )
assert( cleaved, "The region is invalid")
let(
face = is_undef(transform)? cleaved : apply(transform,cleaved),
faceidxs = reverse? [for (i=[len(face)-1:-1:0]) i] : [for (i=[0:1:len(face)-1]) i]
) [face, [faceidxs]]
],
outvnf = vnf_join(vnfs)
)
vnf_triangulate(outvnf);
// Section: VNF Testing and Access
// Function: is_vnf()
// Usage:
// 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]) &&
(x[0]==[] || (len(x[0])>=3 && is_vector(x[0][0],3))) &&
(x[1]==[] || is_vector(x[1][0]));
// Function: is_vnf_list()
// Description: Returns true if the given value looks passingly like a list of VNF structures.
function is_vnf_list(x) = is_list(x) && all([for (v=x) is_vnf(v)]);
// Function: vnf_vertices()
// Description: Given a VNF structure, returns the list of vertex points.
function vnf_vertices(vnf) = vnf[0];
// Function: vnf_faces()
// Description: Given a VNF structure, returns the list of faces, where each face is a list of indices into the VNF vertex list.
function vnf_faces(vnf) = vnf[1];
// Section: Altering the VNF Internals
// Function: vnf_reverse_faces()
// Usage:
// rvnf = vnf_reverse_faces(vnf);
// Description:
// Reverses the orientation of all the faces in the given VNF.
function vnf_reverse_faces(vnf) =
[vnf[0], [for (face=vnf[1]) reverse(face)]];
// Function: vnf_quantize()
// Usage:
// vnf2 = vnf_quantize(vnf,[q]);
// Description:
// Quantizes the vertex coordinates of the VNF to the given quanta `q`.
// Arguments:
// vnf = The VNF to quantize.
// q = The quanta to quantize the VNF coordinates to.
function vnf_quantize(vnf,q=pow(2,-12)) =
[[for (pt = vnf[0]) quant(pt,q)], vnf[1]];
// Function: vnf_merge_points()
// Usage:
// new_vnf = vnf_merge_points(vnf, [eps]);
// Description:
// Given a VNF, consolidates all duplicate vertices with a tolerance `eps`, relabeling the faces as necessary,
// and eliminating any face with fewer than 3 vertices. Unreferenced vertices of the input VNF are not dropped.
// To remove such vertices uses {{vnf_drop_unused_points()}}.
// Arguments:
// vnf = a VNF to consolidate
// eps = the tolerance in finding duplicates. Default: EPSILON
function vnf_merge_points(vnf,eps=EPSILON) =
let(
verts = vnf[0],
dedup = vector_search(verts,eps,verts), // collect vertex duplicates
map = [for(i=idx(verts)) min(dedup[i]) ], // remap duplic vertices
offset = cumsum([for(i=idx(verts)) map[i]==i ? 0 : 1 ]), // remaping face vertex offsets
map2 = list(idx(verts))-offset, // map old vertex indices to new indices
nverts = [for(i=idx(verts)) if(map[i]==i) verts[i] ], // this doesn't eliminate unreferenced vertices
nfaces =
[ for(face=vnf[1])
let(
nface = [ for(vi=face) map2[map[vi]] ],
dface = [for (i=idx(nface))
if( nface[i]!=nface[(i+1)%len(nface)])
nface[i] ]
)
if(len(dface) >= 3) dface
]
)
[nverts, nfaces];
// Function: vnf_drop_unused_points()
// Usage:
// clean_vnf=vnf_drop_unused_points(vnf);
// Description:
// Remove all unreferenced vertices from a VNF. Note that in most
// cases unreferenced vertices cause no harm, and this function may
// be slow on large VNFs.
function vnf_drop_unused_points(vnf) =
let(
flat = flatten(vnf[1]),
ind = _link_indicator(flat,0,len(vnf[0])-1),
verts = [for(i=idx(vnf[0])) if(ind[i]==1) vnf[0][i] ],
map = cumsum(ind)
)
[ verts, [for(face=vnf[1]) [for(v=face) map[v]-1 ] ] ];
function _link_indicator(l,imin,imax) =
len(l) == 0 ? repeat(imax-imin+1,0) :
imax-imin<100 || len(l)<400 ? [for(si=search(list([imin:1:imax]),l,1)) si!=[] ? 1: 0 ] :
let(
pivot = floor((imax+imin)/2),
lesser = [ for(li=l) if( li< pivot) li ],
greater = [ for(li=l) if( li> pivot) li ]
)
concat( _link_indicator(lesser ,imin,pivot-1),
search(pivot,l,1) ? 1 : 0 ,
_link_indicator(greater,pivot+1,imax) ) ;
// Function: vnf_triangulate()
// Usage:
// vnf2 = vnf_triangulate(vnf);
// Description:
// Triangulates faces in the VNF that have more than 3 vertices.
// Arguments:
// vnf = vnf to triangulate
// Example(3D):
// include <BOSL2/polyhedra.scad>
// vnf = zrot(33,regular_polyhedron_info("vnf", "dodecahedron", side=12));
// vnf_polyhedron(vnf);
// triangulated = vnf_triangulate(vnf);
// color("red")vnf_wireframe(triangulated,width=.3);
function vnf_triangulate(vnf) =
let(
verts = vnf[0],
faces = [for (face=vnf[1])
each (len(face)==3 ? [face] :
let( tris = polygon_triangulate(verts, face) )
assert( tris!=undef, "Some `vnf` face cannot be triangulated.")
tris ) ]
)
[verts, faces];
// Function: vnf_slice()
// Usage:
// sliced = vnf_slice(vnf, dir, cuts);
// Description:
// Slice the faces of a VNF along a specified axis direction at a given list
// of cut points. The cut points can appear in any order. You can use this to refine the faces of a VNF before applying
// a nonlinear transformation to its vertex set.
// Arguments:
// vnf = vnf to slice
// dir = normal direction to the slices, either "X", "Y" or "Z"
// cuts = X, Y or Z values where cuts occur
// Example(3D):
// include <BOSL2/polyhedra.scad>
// vnf = regular_polyhedron_info("vnf", "dodecahedron", side=12);
// vnf_polyhedron(vnf);
// sliced = vnf_slice(vnf, "X", [-6,-1,10]);
// color("red")vnf_wireframe(sliced,width=.3);
function vnf_slice(vnf,dir,cuts) =
let(
vert = vnf[0],
faces = [for(face=vnf[1]) select(vert,face)],
poly_list = _slice_3dpolygons(faces, dir, cuts)
)
vnf_merge_points(vnf_from_polygons(poly_list));
function _split_polygon_at_x(poly, x) =
let(
xs = column(poly,0)
) (min(xs) >= x || max(xs) <= x)? [poly] :
let(
poly2 = [
for (p = pair(poly,true)) each [
p[0],
if(
(p[0].x < x && p[1].x > x) ||
(p[1].x < x && p[0].x > x)
) let(
u = (x - p[0].x) / (p[1].x - p[0].x)
) [
x, // Important for later exact match tests
u*(p[1].y-p[0].y)+p[0].y
]
]
],
out1 = [for (p = poly2) if(p.x <= x) p],
out2 = [for (p = poly2) if(p.x >= x) p],
out3 = [
if (len(out1)>=3) each split_path_at_self_crossings(out1),
if (len(out2)>=3) each split_path_at_self_crossings(out2),
],
out = [for (p=out3) if (len(p) > 2) cleanup_path(p)]
) out;
function _split_2dpolygons_at_each_x(polys, xs, _i=0) =
_i>=len(xs)? polys :
_split_2dpolygons_at_each_x(
[
for (poly = polys)
each _split_polygon_at_x(poly, xs[_i])
], xs, _i=_i+1
);
/// Internal Function: _slice_3dpolygons()
/// Usage:
/// splitpolys = _slice_3dpolygons(polys, dir, cuts);
/// Topics: Geometry, Polygons, Intersections
/// Description:
/// Given a list of 3D polygons, a choice of X, Y, or Z, and a cut list, `cuts`, splits all of the polygons where they cross
/// X/Y/Z at any value given in cuts.
/// Arguments:
/// polys = A list of 3D polygons to split.
/// dir_ind = slice direction, 0=X, 1=Y, or 2=Z
/// cuts = A list of scalar values for locating the cuts
function _slice_3dpolygons(polys, dir, cuts) =
assert( [for (poly=polys) if (!is_path(poly,3)) 1] == [], "Expects list of 3D paths.")
assert( is_vector(cuts), "The split list must be a vector.")
assert( in_list(dir, ["X", "Y", "Z"]))
let(
I = ident(3),
dir_ind = ord(dir)-ord("X")
)
flatten([for (poly = polys)
let(
plane = plane_from_polygon(poly)
)
assert(plane,"Found non-coplanar face.")
let(
normal = point3d(plane),
pnormal = normal - (normal*I[dir_ind])*I[dir_ind]
)
approx(pnormal,[0,0,0]) ? [poly] :
let (
pind = max_index(v_abs(pnormal)), // project along this direction
otherind = 3-pind-dir_ind, // keep dir_ind and this direction
keep = [I[dir_ind], I[otherind]], // dir ind becomes the x dir
poly2d = poly*transpose(keep), // project to 2d, putting selected direction in the X position
poly_list = [for(p=_split_2dpolygons_at_each_x([poly2d], cuts))
let(
a = p*keep, // unproject, but pind dimension data is missing
ofs = outer_product((repeat(plane[3], len(a))-a*normal)/plane[pind],I[pind])
)
a+ofs] // ofs computes the missing pind dimension data and adds it back in
)
poly_list
]);
// Section: Turning a VNF into geometry
// Module: vnf_polyhedron()
// Usage:
// vnf_polyhedron(vnf);
// vnf_polyhedron([VNF, VNF, VNF, ...]);
// Description:
// Given a VNF structure, or a list of VNF structures, creates a polyhedron from them.
// Arguments:
// vnf = A VNF structure, or list of VNF structures.
// convexity = Max number of times a line could intersect a wall of the shape.
// extent = If true, calculate anchors by extents, rather than intersection. Default: true.
// cp = Centerpoint for determining intersection anchors or centering the shape. Determintes the base of the anchor vector. Can be "centroid", "mean", "box" or a 3D point. Default: "centroid"
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `"origin"`
// 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`
// atype = Select "hull" or "intersect" anchor type. Default: "hull"
module vnf_polyhedron(vnf, convexity=2, extent=true, cp="centroid", anchor="origin", spin=0, orient=UP, atype="hull") {
vnf = is_vnf_list(vnf)? vnf_join(vnf) : vnf;
assert(in_list(atype, _ANCHOR_TYPES), "Anchor type must be \"hull\" or \"intersect\"");
attachable(anchor,spin,orient, vnf=vnf, extent=atype=="hull", cp=cp) {
polyhedron(vnf[0], vnf[1], convexity=convexity);
children();
}
}
// Module: vnf_wireframe()
// Usage:
// vnf_wireframe(vnf, [width]);
// Description:
// Given a VNF, creates a wire frame ball-and-stick model of the polyhedron with a cylinder for
// each edge and a sphere at each vertex. The width parameter specifies the width of the sticks
// that form the wire frame and the diameter of the balls.
// Arguments:
// vnf = A vnf structure
// width = width of the cylinders forming the wire frame. Default: 1
// Example:
// $fn=32;
// ball = sphere(r=20, $fn=6);
// vnf_wireframe(ball,width=1);
// Example:
// include <BOSL2/polyhedra.scad>
// $fn=32;
// cube_oct = regular_polyhedron_info("vnf",
// name="cuboctahedron", or=20);
// vnf_wireframe(cube_oct);
// Example: The spheres at the vertex are imperfect at aligning with the cylinders, so especially at low $fn things look prety ugly. This is normal.
// include <BOSL2/polyhedra.scad>
// $fn=8;
// octahedron = regular_polyhedron_info("vnf",
// name="octahedron", or=20);
// vnf_wireframe(octahedron,width=5);
module vnf_wireframe(vnf, width=1)
{
vertex = vnf[0];
edges = unique([for (face=vnf[1], i=idx(face))
sort([face[i], select(face,i+1)])
]);
for (e=edges) extrude_from_to(vertex[e[0]],vertex[e[1]]) circle(d=width);
// Identify vertices actually used and draw them
vertused = search(count(len(vertex)), flatten(edges), 1);
for(i=idx(vertex)) if(vertused[i]!=[]) move(vertex[i]) sphere(d=width);
}
// Section: Operations on VNFs
// Function: vnf_volume()
// Usage:
// vol = vnf_volume(vnf);
// Description:
// Returns the volume enclosed by the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
// no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume
// if face direction is counter-clockwise.
// Divide the polyhedron into tetrahedra with the origin as one vertex and sum up the signed volume.
function vnf_volume(vnf) =
let(verts = vnf[0])
sum([
for(face=vnf[1], j=[1:1:len(face)-2])
cross(verts[face[j+1]], verts[face[j]]) * verts[face[0]]
])/6;
// Function: vnf_area()
// Usage:
// area = vnf_area(vnf);
// Description:
// Returns the surface area in any VNF by adding up the area of all its faces. The VNF need not be a manifold.
function vnf_area(vnf) =
let(verts=vnf[0])
sum([for(face=vnf[1]) polygon_area(select(verts,face))]);
/// Internal 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,eps=EPSILON) =
assert(is_vnf(vnf) && len(vnf[0])!=0 && len(vnf[1])!=0,"Invalid or empty VNF given to centroid")
let(
verts = vnf[0],
pos = sum([
for(face=vnf[1], j=[1:1:len(face)-2]) let(
v0 = verts[face[0]],
v1 = verts[face[j]],
v2 = verts[face[j+1]],
vol = cross(v2,v1)*v0
)
[ vol, (v0+v1+v2)*vol ]
])
)
assert(!approx(pos[0],0, eps), "The vnf has self-intersections.")
pos[1]/pos[0]/4;
// Function: vnf_halfspace()
// Usage:
// newvnf = vnf_halfspace(plane, vnf, [closed]);
// Description:
// Returns the intersection of the vnf with a half space. The half space is defined by
// plane = [A,B,C,D], taking the side where the normal [A,B,C] points: Ax+By+Cz≥D.
// If closed is set to false then the cut face is not included in the vnf. This could
// allow further extension of the vnf by merging with other vnfs.
// Arguments:
// plane = plane defining the boundary of the half space
// vnf = vnf to cut
// closed = if false do not return include cut face(s). Default: true
// Example(3D):
// vnf = cube(10,center=true);
// cutvnf = vnf_halfspace([-1,1,-1,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut face has 2 components
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([-1,1,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut face is not simply connected
// vnf = path_sweep(circle(r=4, $fn=16),
// circle(r=20, $fn=64),closed=true);
// cutvnf = vnf_halfspace([0,0.7,-4,0], vnf);
// vnf_polyhedron(cutvnf);
// Example(3D): Cut object has multiple components
// function knot(a,b,t) = // rolling knot
// [ a * cos (3 * t) / (1 - b* sin (2 *t)),
// a * sin( 3 * t) / (1 - b* sin (2 *t)),
// 1.8 * b * cos (2 * t) /(1 - b* sin (2 *t))];
// a = 0.8; b = sqrt (1 - a * a);
// ksteps = 400;
// knot_path = [for (i=[0:ksteps-1]) 50 * knot(a,b,(i/ksteps)*360)];
// ushape = [[-10, 0],[-10, 10],[ -7, 10],[ -7, 2],[ 7, 2],[ 7, 7],[ 10, 7],[ 10, 0]];
// knot=path_sweep(ushape, knot_path, closed=true, method="incremental");
// cut_knot = vnf_halfspace([1,0,0,0], knot);
// vnf_polyhedron(cut_knot);
function vnf_halfspace(plane, vnf, closed=true) =
assert(_valid_plane(plane), "Invalid plane")
assert(is_vnf(vnf), "Invalid vnf")
let(
inside = [for(x=vnf[0]) plane*[each x,-1] >= 0 ? 1 : 0],
vertexmap = [0,each cumsum(inside)],
faces_edges_vertices = _vnfcut(plane, vnf[0],vertexmap,inside, vnf[1], last(vertexmap)),
newvert = concat(bselect(vnf[0],inside), faces_edges_vertices[2])
)
closed==false ? [newvert, faces_edges_vertices[0]] :
let(
allpaths = _assemble_paths(newvert, faces_edges_vertices[1]),
newpaths = [for(p=allpaths) if (len(p)>=3) p
else assert(approx(p[0],p[1]),"Orphan edge found when assembling cut edges.")
]
)
len(newpaths)<=1 ? [newvert, concat(faces_edges_vertices[0], newpaths)]
:
let(
M = project_plane(plane),
faceregion = [for(path=newpaths) path2d(apply(M,select(newvert,path)))],
facevnf = vnf_from_region(faceregion,transform=rot_inverse(M),reverse=true)
)
vnf_join([[newvert, faces_edges_vertices[0]], facevnf]);
function _assemble_paths(vertices, edges, paths=[],i=0) =
i==len(edges) ? paths :
norm(vertices[edges[i][0]]-vertices[edges[i][1]])<EPSILON ? _assemble_paths(vertices,edges,paths,i+1) :
let( // Find paths that connects on left side and right side of the edges (if one exists)
left = [for(j=idx(paths)) if (approx(vertices[last(paths[j])],vertices[edges[i][0]])) j],
right = [for(j=idx(paths)) if (approx(vertices[edges[i][1]],vertices[paths[j][0]])) j]
)
assert(len(left)<=1 && len(right)<=1)
let(
keep_path = list_remove(paths,concat(left,right)),
update_path = left==[] && right==[] ? edges[i]
: left==[] ? concat([edges[i][0]],paths[right[0]])
: right==[] ? concat(paths[left[0]],[edges[i][1]])
: left != right ? concat(paths[left[0]], paths[right[0]])
: paths[left[0]]
)
_assemble_paths(vertices, edges, concat(keep_path, [update_path]), i+1);
function _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount, newfaces=[], newedges=[], newvertices=[], i=0) =
i==len(faces) ? [newfaces, newedges, newvertices] :
let(
pts_inside = select(inside,faces[i])
)
all(pts_inside) ? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,
concat(newfaces, [select(vertexmap,faces[i])]), newedges, newvertices, i+1):
!any(pts_inside) ? _vnfcut(plane, vertices, vertexmap,inside, faces, vertcount, newfaces, newedges, newvertices, i+1):
let(
first = search([[1,0]],pair(pts_inside,wrap=true),0)[0],
second = search([[0,1]],pair(pts_inside,wrap=true),0)[0]
)
assert(len(first)==1 && len(second)==1, "Found concave face in VNF. Run vnf_triangulate first to ensure convex faces.")
let(
newface = [each select(vertexmap,select(faces[i],second[0]+1,first[0])),vertcount, vertcount+1],
newvert = [plane_line_intersection(plane, select(vertices,select(faces[i],first[0],first[0]+1)),eps=0),
plane_line_intersection(plane, select(vertices,select(faces[i],second[0],second[0]+1)),eps=0)]
)
true //!approx(newvert[0],newvert[1])
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+2,
concat(newfaces, [newface]), concat(newedges,[[vertcount+1,vertcount]]),concat(newvertices,newvert),i+1)
:len(newface)>3
? _vnfcut(plane, vertices, vertexmap, inside, faces, vertcount+1,
concat(newfaces, [list_head(newface)]), newedges,concat(newvertices,[newvert[0]]),i+1)
:
_vnfcut(plane, vertices, vertexmap, inside, faces, vertcount,newfaces, newedges, newvert, i+1);
function _triangulate_planar_convex_polygons(polys) =
polys==[]? [] :
let(
tris = [for (poly=polys) if (len(poly)==3) poly],
bigs = [for (poly=polys) if (len(poly)>3) poly],
newtris = [for (poly=bigs) select(poly,-2,0)],
newbigs = [for (poly=bigs) select(poly,0,-2)],
newtris2 = _triangulate_planar_convex_polygons(newbigs),
outtris = concat(tris, newtris, newtris2)
) outtris;
//**
// this function may produce degenerate triangles:
// _triangulate_planar_convex_polygons([ [for(i=[0:1]) [i,i],
// [1,-1], [-1,-1],
// for(i=[-1:0]) [i,i] ] ] )
// == [[[-1, -1], [ 0, 0], [0, 0]]
// [[-1, -1], [-1, -1], [0, 0]]
// [[ 1, -1], [-1, -1], [0, 0]]
// [[ 0, 0], [ 1, 1], [1, -1]] ]
//
// Function: vnf_bend()
// Usage:
// bentvnf = vnf_bend(vnf,r,d,[axis]);
// Description:
// Bend a VNF around the X, Y or Z axis, splitting up faces as necessary. Returns the bent
// VNF. For bending around the Z axis the input VNF must not cross the Y=0 plane. For bending
// around the X or Y axes the VNF must not cross the Z=0 plane. Note that if you wrap a VNF all the way around
// it may intersect itself, which produces an invalid polyhedron. It is your responsibility to
// avoid this situation. The 1:1
// radius is where the curved length of the bent VNF matches the length of the original VNF. If the
// `r` or `d` arguments are given, then they will specify the 1:1 radius or diameter. If they are
// not given, then the 1:1 radius will be defined by the distance of the furthest vertex in the
// original VNF from the Z=0 plane. You can adjust the granularity of the bend using the standard
// `$fa`, `$fs`, and `$fn` variables.
// Arguments:
// vnf = The original VNF to bend.
// r = If given, the radius where the size of the original shape is the same as in the original.
// ---
// d = If given, the diameter where the size of the original shape is the same as in the original.
// axis = The axis to wrap around. "X", "Y", or "Z". Default: "Z"
// Example(3D):
// vnf0 = cube([100,40,10], center=true);
// vnf1 = up(50, p=vnf0);
// vnf2 = down(50, p=vnf0);
// bent1 = vnf_bend(vnf1, axis="Y");
// bent2 = vnf_bend(vnf2, axis="Y");
// vnf_polyhedron([bent1,bent2]);
// Example(3D):
// vnf0 = linear_sweep(star(n=5,step=2,d=100), height=10);
// vnf1 = up(50, p=vnf0);
// vnf2 = down(50, p=vnf0);
// bent1 = vnf_bend(vnf1, axis="Y");
// bent2 = vnf_bend(vnf2, axis="Y");
// vnf_polyhedron([bent1,bent2]);
// Example(3D):
// rgn = union(rect([100,20]),
// rect([20,100]));
// vnf0 = linear_sweep(zrot(45,p=rgn), height=10);
// vnf1 = up(50, p=vnf0);
// vnf2 = down(50, p=vnf0);
// bent1 = vnf_bend(vnf1, axis="Y");
// bent2 = vnf_bend(vnf2, axis="Y");
// vnf_polyhedron([bent1,bent2]);
// Example(3D): Bending Around X Axis.
// rgnr = union(
// rect([20,100]),
// back(50, p=trapezoid(w1=40, w2=0, h=20, anchor=FRONT))
// );
// vnf0 = xrot(00,p=linear_sweep(rgnr, height=10));
// vnf1 = up(50, p=vnf0);
// #vnf_polyhedron(vnf1);
// bent1 = vnf_bend(vnf1, axis="X");
// vnf_polyhedron([bent1]);
// Example(3D): Bending Around Y Axis.
// rgn = union(
// rect([20,100]),
// back(50, p=trapezoid(w1=40, w2=0, h=20, anchor=FRONT))
// );
// rgnr = zrot(-90, p=rgn);
// vnf0 = xrot(00,p=linear_sweep(rgnr, height=10));
// vnf1 = up(50, p=vnf0);
// #vnf_polyhedron(vnf1);
// bent1 = vnf_bend(vnf1, axis="Y");
// vnf_polyhedron([bent1]);
// Example(3D): Bending Around Z Axis.
// rgn = union(
// rect([20,100]),
// back(50, p=trapezoid(w1=40, w2=0, h=20, anchor=FRONT))
// );
// rgnr = zrot(90, p=rgn);
// vnf0 = xrot(90,p=linear_sweep(rgnr, height=10));
// vnf1 = fwd(50, p=vnf0);
// #vnf_polyhedron(vnf1);
// bent1 = vnf_bend(vnf1, axis="Z");
// vnf_polyhedron([bent1]);
// Example(3D): Bending more than once around the cylinder
// $fn=32;
// vnf = apply(fwd(5)*yrot(30),cube([100,2,5],center=true));
// bent = vnf_bend(vnf, axis="Z");
// vnf_polyhedron(bent);
function vnf_bend(vnf,r,d,axis="Z") =
let(
chk_axis = assert(in_list(axis,["X","Y","Z"])),
verts = vnf[0],
bounds = pointlist_bounds(verts),
bmin = bounds[0],
bmax = bounds[1],
dflt = axis=="Z"?
max(abs(bmax.y), abs(bmin.y)) :
max(abs(bmax.z), abs(bmin.z)),
r = get_radius(r=r,d=d,dflt=dflt),
extent = axis=="X" ? [bmin.y, bmax.y] : [bmin.x, bmax.x]
)
let(
span_chk = axis=="Z"?
assert(bmin.y > 0 || bmax.y < 0, "Entire shape MUST be completely in front of or behind y=0.") :
assert(bmin.z > 0 || bmax.z < 0, "Entire shape MUST be completely above or below z=0."),
steps = ceil(segs(r) * (extent[1]-extent[0])/(2*PI*r)),
step = (extent[1]-extent[0]) / steps,
bend_at = [for(i = [1:1:steps-1]) i*step+extent[0]],
slicedir = axis=="X"? "Y" : "X", // slice in y dir for X axis case, and x dir otherwise
sliced = vnf_slice(vnf, slicedir, bend_at),
coord = axis=="X" ? [0,sign(bmax.z),0] : axis=="Y" ? [sign(bmax.z),0,0] : [sign(bmax.y),0,0],
new_vert = [for(p=sliced[0])
let(a=coord*p*180/(PI*r))
axis=="X"? [p.x, p.z*sin(a), p.z*cos(a)] :
axis=="Y"? [p.z*sin(a), p.y, p.z*cos(a)] :
[p.y*sin(a), p.y*cos(a), p.z]]
) [new_vert,sliced[1]];
// Section: Debugging Polyhedrons
/// Internal Module: _show_vertices()
/// Usage:
/// _show_vertices(vertices, [size])
/// Description:
/// Draws all the vertices in an array, at their 3D position, numbered by their
/// position in the vertex array. Also draws any children of this module with
/// transparency.
/// Arguments:
/// vertices = Array of point vertices.
/// size = The size of the text used to label the vertices. Default: 1
/// Example:
/// verts = [for (z=[-10,10], y=[-10,10], x=[-10,10]) [x,y,z]];
/// faces = [[0,1,2], [1,3,2], [0,4,5], [0,5,1], [1,5,7], [1,7,3], [3,7,6], [3,6,2], [2,6,4], [2,4,0], [4,6,7], [4,7,5]];
/// _show_vertices(vertices=verts, size=2) {
/// polyhedron(points=verts, faces=faces);
/// }
module _show_vertices(vertices, size=1) {
color("blue") {
dups = vector_search(vertices, EPSILON, vertices);
for (ind = dups){
numstr = str_join([for(i=ind) str(i)],",");
v = vertices[ind[0]];
translate(v) {
rot($vpr) back(size/8){
linear_extrude(height=size/10, center=true, convexity=10) {
text(text=numstr, size=size, halign="center");
}
}
sphere(size/10);
}
}
}
}
/// Internal Module: _show_faces()
/// Usage:
/// _show_faces(vertices, faces, [size=]);
/// Description:
/// Draws all the vertices at their 3D position, numbered in blue by their
/// position in the vertex array. Each face will have their face number drawn
/// in red, aligned with the center of face. All children of this module are drawn
/// with transparency.
/// Arguments:
/// vertices = Array of point vertices.
/// faces = Array of faces by vertex numbers.
/// size = The size of the text used to label the faces and vertices. Default: 1
/// Example(EdgesMed):
/// verts = [for (z=[-10,10], y=[-10,10], x=[-10,10]) [x,y,z]];
/// faces = [[0,1,2], [1,3,2], [0,4,5], [0,5,1], [1,5,7], [1,7,3], [3,7,6], [3,6,2], [2,6,4], [2,4,0], [4,6,7], [4,7,5]];
/// _show_faces(vertices=verts, faces=faces, size=2) {
/// polyhedron(points=verts, faces=faces);
/// }
module _show_faces(vertices, faces, size=1) {
vlen = len(vertices);
color("red") {
for (i = [0:1:len(faces)-1]) {
face = faces[i];
if (face[0] < 0 || face[1] < 0 || face[2] < 0 || face[0] >= vlen || face[1] >= vlen || face[2] >= vlen) {
echo("BAD FACE: ", vlen=vlen, face=face);
} else {
verts = select(vertices,face);
c = mean(verts);
v0 = verts[0];
v1 = verts[1];
v2 = verts[2];
dv0 = unit(v1 - v0);
dv1 = unit(v2 - v0);
nrm0 = cross(dv0, dv1);
nrm1 = UP;
axis = vector_axis(nrm0, nrm1);
ang = vector_angle(nrm0, nrm1);
theta = atan2(nrm0[1], nrm0[0]);
translate(c) {
rotate(a=180-ang, v=axis) {
zrot(theta-90)
linear_extrude(height=size/10, center=true, convexity=10) {
union() {
text(text=str(i), size=size, halign="center");
text(text=str("_"), size=size, halign="center");
}
}
}
}
}
}
}
}
// Module: vnf_debug()
// Usage:
// vnf_debug(vnfs, [faces], [vertices], [opacity], [size], [convexity]);
// Description:
// A drop-in module to replace `vnf_polyhedron()` to help debug vertices and faces.
// Draws all the vertices at their 3D position, numbered in blue by their
// position in the vertex array. Each face will have its face number drawn
// in red, aligned with the center of face. All given faces are drawn with
// transparency. All children of this module are drawn with transparency.
// Works best with Thrown-Together preview mode, to see reversed faces.
// You can set opacity to 0 if you want to supress the display of the polyhedron faces.
// .
// The vertex numbers are shown rotated to face you. As you rotate your polyhedron you
// can rerun the preview to display them oriented for viewing from a different viewpoint.
// Topics: Polyhedra, Debugging
// Arguments:
// vnf = vnf to display
// ---
// faces = if true display face numbers. Default: true
// vertices = if true display vertex numbers. Default: true
// opacity = Opacity of the polyhedron faces. Default: 0.5
// convexity = The max number of walls a ray can pass through the given polygon paths.
// size = The size of the text used to label the faces and vertices. Default: 1
// Example(EdgesMed):
// verts = [for (z=[-10,10], a=[0:120:359.9]) [10*cos(a),10*sin(a),z]];
// faces = [[0,1,2], [5,4,3], [0,3,4], [0,4,1], [1,4,5], [1,5,2], [2,5,3], [2,3,0]];
// vnf_debug([verts,faces], size=2);
module vnf_debug(vnf, faces=true, vertices=true, opacity=0.5, size=1, convexity=6 ) {
no_children($children);
if (faces)
_show_faces(vertices=vnf[0], faces=vnf[1], size=size);
if (vertices)
_show_vertices(vertices=vnf[0], size=size);
color([0.2, 1.0, 0, opacity])
vnf_polyhedron(vnf,convexity=convexity);
}
// Function&Module: vnf_validate()
// Usage: As Function
// fails = vnf_validate(vnf);
// Usage: As Module
// vnf_validate(vnf, [size]);
// Description:
// When called as a function, returns a list of non-manifold errors with the given VNF.
// Each error has the format `[ERR_OR_WARN,CODE,MESG,POINTS,COLOR]`.
// When called as a module, echoes the non-manifold errors to the console, and color hilites the
// bad edges and vertices, overlaid on a transparent gray polyhedron of the VNF.
// .
// Currently checks for these problems:
// .
// Type | Color | Code | Message
// ------- | -------- | ------------ | ---------------------------------
// WARNING | Yellow | BIG_FACE | Face has more than 3 vertices, and may confuse CGAL.
// WARNING | Brown | NULL_FACE | Face has zero area.
// ERROR | Cyan | NONPLANAR | Face vertices are not coplanar.
// ERROR | Brown | DUP_FACE | Multiple instances of the same face.
// ERROR | Orange | MULTCONN | Multiply Connected Geometry. Too many faces attached at Edge.
// ERROR | Violet | REVERSAL | Faces reverse across edge.
// ERROR | Red | T_JUNCTION | Vertex is mid-edge on another Face.
// ERROR | Blue | FACE_ISECT | Faces intersect.
// ERROR | Magenta | HOLE_EDGE | Edge bounds Hole.
// .
// Still to implement:
// - Overlapping coplanar faces.
// Arguments:
// vnf = The VNF to validate.
// size = The width of the lines and diameter of points used to highlight edges and vertices. Module only. Default: 1
// check_isects = If true, performs slow checks for intersecting faces. Default: false
// Example: BIG_FACE Warnings; Faces with More Than 3 Vertices. CGAL often will fail to accept that a face is planar after a rotation, if it has more than 3 vertices.
// vnf = skin([
// path3d(regular_ngon(n=3, d=100),0),
// path3d(regular_ngon(n=5, d=100),100)
// ], slices=0, caps=true, method="tangent");
// vnf_validate(vnf);
// Example: NONPLANAR Errors; Face Vertices are Not Coplanar
// a = [ 0, 0,-50];
// b = [-50,-50, 50];
// c = [-50, 50, 50];
// d = [ 50, 50, 60];
// e = [ 50,-50, 50];
// vnf = vnf_from_polygons([
// [a, b, e], [a, c, b], [a, d, c], [a, e, d], [b, c, d, e]
// ]);
// vnf_validate(vnf);
// Example: MULTCONN Errors; More Than Two Faces Attached to the Same Edge. This confuses CGAL, and can lead to failed renders.
// vnf = vnf_triangulate(linear_sweep(union(square(50), square(50,anchor=BACK+RIGHT)), height=50));
// vnf_validate(vnf);
// Example: REVERSAL Errors; Faces Reversed Across Edge
// vnf1 = skin([
// path3d(square(100,center=true),0),
// path3d(square(100,center=true),100),
// ], slices=0, caps=false);
// vnf = vnf_join([vnf1, vnf_from_polygons([
// [[-50,-50, 0], [ 50, 50, 0], [-50, 50, 0]],
// [[-50,-50, 0], [ 50,-50, 0], [ 50, 50, 0]],
// [[-50,-50,100], [-50, 50,100], [ 50, 50,100]],
// [[-50,-50,100], [ 50,-50,100], [ 50, 50,100]],
// ])]);
// vnf_validate(vnf);
// Example: T_JUNCTION Errors; Vertex is Mid-Edge on Another Face.
// vnf1 = skin([
// path3d(square(100,center=true),0),
// path3d(square(100,center=true),100),
// ], slices=0, caps=false);
// vnf = vnf_join([vnf1, vnf_from_polygons([
// [[-50,-50,0], [50,50,0], [-50,50,0]],
// [[-50,-50,0], [50,-50,0], [50,50,0]],
// [[-50,-50,100], [-50,50,100], [0,50,100]],
// [[-50,-50,100], [0,50,100], [0,-50,100]],
// [[0,-50,100], [0,50,100], [50,50,100]],
// [[0,-50,100], [50,50,100], [50,-50,100]],
// ])]);
// vnf_validate(vnf);
// Example: FACE_ISECT Errors; Faces Intersect
// vnf = vnf_join([
// vnf_triangulate(linear_sweep(square(100,center=true), height=100)),
// move([75,35,30],p=vnf_triangulate(linear_sweep(square(100,center=true), height=100)))
// ]);
// vnf_validate(vnf,size=2,check_isects=true);
// Example: HOLE_EDGE Errors; Edges Adjacent to Holes.
// vnf = skin([
// path3d(regular_ngon(n=4, d=100),0),
// path3d(regular_ngon(n=5, d=100),100)
// ], slices=0, caps=false);
// vnf_validate(vnf,size=2);
function vnf_validate(vnf, show_warns=true, check_isects=false) =
assert(is_vnf(vnf), "Invalid VNF")
let(
vnf = vnf_merge_points(vnf),
varr = vnf[0],
faces = vnf[1],
lvarr = len(varr),
edges = sort([
for (face=faces, edge=pair(face,true))
edge[0]<edge[1]? edge : [edge[1],edge[0]]
]),
dfaces = [
for (face=faces) let(
face=deduplicate_indexed(varr,face,closed=true)
) if(len(face)>=3)
face
],
face_areas = [
for (face = faces)
len(face) < 3? 0 :
polygon_area([for (k=face) varr[k]])
],
edgecnts = unique_count(edges),
uniq_edges = edgecnts[0],
issues = []
)
let(
big_faces = !show_warns? [] : [
for (face = faces)
if (len(face) > 3)
_vnf_validate_err("BIG_FACE", [for (i=face) varr[i]])
],
null_faces = !show_warns? [] : [
for (i = idx(faces)) let(
face = faces[i],
area = face_areas[i],
faceverts = [for (k=face) varr[k]]
)
if (is_num(area) && abs(area) < EPSILON)
_vnf_validate_err("NULL_FACE", faceverts)
],
issues = concat(big_faces, null_faces)
)
let(
bad_indices = [
for (face = faces, idx = face)
if (idx < 0 || idx >= lvarr)
_vnf_validate_err("BAD_INDEX", [idx])
],
issues = concat(issues, bad_indices)
) bad_indices? issues :
let(
repeated_faces = [
for (i=idx(dfaces), j=idx(dfaces))
if (i!=j) let(
face1 = dfaces[i],
face2 = dfaces[j]
) if (min(face1) == min(face2)) let(
min1 = min_index(face1),
min2 = min_index(face2)
) if (min1 == min2) let(
sface1 = list_rotate(face1,min1),
sface2 = list_rotate(face2,min2)
) if (sface1 == sface2)
_vnf_validate_err("DUP_FACE", [for (i=sface1) varr[i]])
],
issues = concat(issues, repeated_faces)
) repeated_faces? issues :
let(
multconn_edges = unique([
for (i = idx(uniq_edges))
if (edgecnts[1][i]>2)
_vnf_validate_err("MULTCONN", [for (i=uniq_edges[i]) varr[i]])
]),
issues = concat(issues, multconn_edges)
) multconn_edges? issues :
let(
reversals = unique([
for(i = idx(dfaces), j = idx(dfaces)) if(i != j)
for(edge1 = pair(faces[i],true))
for(edge2 = pair(faces[j],true))
if(edge1 == edge2) // Valid adjacent faces will never have the same vertex ordering.
if(_edge_not_reported(edge1, varr, multconn_edges))
_vnf_validate_err("REVERSAL", [for (i=edge1) varr[i]])
]),
issues = concat(issues, reversals)
) reversals? issues :
let(
t_juncts = unique([
for (v=idx(varr), edge=uniq_edges) let(
ia = edge[0],
ib = v,
ic = edge[1]
)
if (ia!=ib && ib!=ic && ia!=ic) let(
a = varr[ia],
b = varr[ib],
c = varr[ic]
)
if (!approx(a,b) && !approx(b,c) && !approx(a,c)) let(
pt = line_closest_point([a,c],b,SEGMENT)
)
if (approx(pt,b))
_vnf_validate_err("T_JUNCTION", [b])
]),
issues = concat(issues, t_juncts)
) t_juncts? issues :
let(
isect_faces = !check_isects? [] : unique([
for (i = [0:1:len(faces)-2]) let(
f1 = faces[i],
poly1 = select(varr, faces[i]),
plane1 = plane3pt(poly1[0], poly1[1], poly1[2]),
normal1 = [plane1[0], plane1[1], plane1[2]]
)
for (j = [i+1:1:len(faces)-1]) let(
f2 = faces[j],
poly2 = select(varr, f2),
val = poly2 * normal1
)
if( min(val)<=plane1[3] && max(val)>=plane1[3] ) let(
plane2 = plane_from_polygon(poly2),
normal2 = [plane2[0], plane2[1], plane2[2]],
val = poly1 * normal2
)
if( min(val)<=plane2[3] && max(val)>=plane2[3] ) let(
shared_edges = [
for (edge1 = pair(f1, true), edge2 = pair(f2, true))
if (edge1 == [edge2[1], edge2[0]]) 1
]
)
if (!shared_edges) let(
line = plane_intersection(plane1, plane2)
)
if (!is_undef(line)) let(
isects = polygon_line_intersection(poly1, line)
)
if (!is_undef(isects))
for (isect = isects)
if (len(isect) > 1) let(
isects2 = polygon_line_intersection(poly2, isect, bounded=true)
)
if (!is_undef(isects2))
for (seg = isects2)
if (seg[0] != seg[1])
_vnf_validate_err("FACE_ISECT", seg)
]),
issues = concat(issues, isect_faces)
) isect_faces? issues :
let(
hole_edges = unique([
for (i=idx(uniq_edges))
if (edgecnts[1][i]<2)
if (_pts_not_reported(uniq_edges[i], varr, t_juncts))
if (_pts_not_reported(uniq_edges[i], varr, isect_faces))
_vnf_validate_err("HOLE_EDGE", [for (i=uniq_edges[i]) varr[i]])
]),
issues = concat(issues, hole_edges)
) hole_edges? issues :
let(
nonplanars = unique([
for (i = idx(faces)) let(
face = faces[i],
area = face_areas[i],
faceverts = [for (k=face) varr[k]]
)
if (is_num(area) && abs(area) > EPSILON)
if (!is_coplanar(faceverts))
_vnf_validate_err("NONPLANAR", faceverts)
]),
issues = concat(issues, nonplanars)
) issues;
_vnf_validate_errs = [
["BIG_FACE", "WARNING", "cyan", "Face has more than 3 vertices, and may confuse CGAL"],
["NULL_FACE", "WARNING", "blue", "Face has zero area."],
["BAD_INDEX", "ERROR", "cyan", "Invalid face vertex index."],
["NONPLANAR", "ERROR", "yellow", "Face vertices are not coplanar"],
["DUP_FACE", "ERROR", "brown", "Multiple instances of the same face."],
["MULTCONN", "ERROR", "orange", "Multiply Connected Geometry. Too many faces attached at Edge"],
["REVERSAL", "ERROR", "violet", "Faces Reverse Across Edge"],
["T_JUNCTION", "ERROR", "magenta", "Vertex is mid-edge on another Face"],
["FACE_ISECT", "ERROR", "brown", "Faces intersect"],
["HOLE_EDGE", "ERROR", "red", "Edge bounds Hole"]
];
function _vnf_validate_err(name, extra) =
let(
info = [for (x = _vnf_validate_errs) if (x[0] == name) x][0]
) concat(info, [extra]);
function _pts_not_reported(pts, varr, reports) =
[
for (i = pts, report = reports, pt = report[3])
if (varr[i] == pt) 1
] == [];
function _edge_not_reported(edge, varr, reports) =
let(
edge = sort([for (i=edge) varr[i]])
) [
for (report = reports) let(
pts = sort(report[3])
) if (len(pts)==2 && edge == pts) 1
] == [];
module vnf_validate(vnf, size=1, show_warns=true, check_isects=false) {
faults = vnf_validate(
vnf, show_warns=show_warns,
check_isects=check_isects
);
for (fault = faults) {
err = fault[0];
typ = fault[1];
clr = fault[2];
msg = fault[3];
pts = fault[4];
echo(str(typ, " ", err, " (", clr ,"): ", msg, " at ", pts));
color(clr) {
if (is_vector(pts[0])) {
if (len(pts)==2) {
stroke(pts, width=size, closed=true, endcaps="butt", hull=false, $fn=8);
} else if (len(pts)>2) {
stroke(pts, width=size, closed=true, hull=false, $fn=8);
polyhedron(pts,[[for (i=idx(pts)) i]]);
} else {
move_copies(pts) sphere(d=size*3, $fn=18);
}
}
}
}
color([0.5,0.5,0.5,0.67]) vnf_polyhedron(vnf);
}
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap