////////////////////////////////////////////////////////////////////// // LibFile: vnf.scad // VNF structures, holding Vertices 'N' Faces for use with `polyhedron().` // To use, add the following lines to the beginning of your file: // ``` // use // use // ``` ////////////////////////////////////////////////////////////////////// include // 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. EMPTY_VNF = [[],[]]; // The standard empty VNF with no vertices or faces. // 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]))) && (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]; // 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_get_vertex() // Usage: // vvnf = vnf_get_vertex(vnf, p); // Description: // Finds the index number of the given vertex point `p` in the given VNF structure `vnf`. If said // point does not already exist in the VNF vertex list, it is added. Returns: `[INDEX, VNF]` where // INDEX if the index of the point, and VNF is the possibly modified new VNF structure. // If `p` is given as a list of points, then INDEX will be a list of indices. // Arguments: // vnf = The VNF structue to get the point index from. // p = The point, or list of points to get the index of. // Example: // vnf1 = vnf_get_vertex(p=[3,5,8]); // Returns: [0, [[[3,5,8]],[]]] // vnf2 = vnf_get_vertex(vnf1, p=[3,2,1]); // Returns: [1, [[[3,5,8],[3,2,1]],[]]] // vnf3 = vnf_get_vertex(vnf2, p=[3,5,8]); // Returns: [0, [[[3,5,8],[3,2,1]],[]]] // vnf4 = vnf_get_vertex(vnf3, p=[[1,3,2],[3,2,1]]); // Returns: [[1,2], [[[3,5,8],[3,2,1],[1,3,2]],[]]] function vnf_get_vertex(vnf=EMPTY_VNF, p) = let( p = is_vector(p)? [p] : p, res = set_union(vnf[0], p, get_indices=true) ) [res[0], [res[1],vnf[1]]]; // Function: vnf_add_face() // Usage: // vnf_add_face(vnf, pts); // Description: // Given a VNF structure and a list of face vertex points, adds the face to the VNF structure. // Returns the modified VNF structure `[VERTICES, FACES]`. It is up to the caller to make // sure that the points are in the correct order to make the face normal point outwards. // Arguments: // vnf = The VNF structure to add a face to. // pts = The vertex points for the face. function vnf_add_face(vnf=EMPTY_VNF, pts) = assert(is_vnf(vnf)) assert(is_path(pts)) let( res = set_union(vnf[0], pts, get_indices=true), face = deduplicate(res[0], closed=true) ) [ res[1], concat(vnf[1], len(face)>2? [face] : []) ]; // Function: vnf_add_faces() // Usage: // vnf_add_faces(vnf, faces); // Description: // Given a VNF structure and a list of faces, where each face is given as a list of vertex points, // adds the faces to the VNF structure. Returns the modified VNF structure `[VERTICES, FACES]`. // It is up to the caller to make sure that the points are in the correct order to make the face // normals point outwards. // Arguments: // vnf = The VNF structure to add a face to. // faces = The list of faces, where each face is given as a list of vertex points. function vnf_add_faces(vnf=EMPTY_VNF, faces) = assert(is_vnf(vnf)) assert(is_list(faces)) let( res = set_union(vnf[0], flatten(faces), get_indices=true), idxs = res[0], nverts = res[1], offs = cumsum([0, for (face=faces) len(face)]), ifaces = [ for (i=idx(faces)) [ for (j=idx(faces[i])) idxs[offs[i]+j] ] ] ) [ nverts, concat(vnf[1],ifaces) ]; // Function: vnf_merge() // Usage: // vnf = vnf_merge([VNF, VNF, VNF, ...]); // Description: // Given a list of VNF structures, merges them all into a single VNF structure. function vnf_merge(vnfs=[],_i=0,_acc=EMPTY_VNF) = (assert(is_vnf_list(vnfs)) _i>=len(vnfs))? _acc : vnf_merge( vnfs, _i=_i+1, _acc = let(base=len(_acc[0])) [ concat(_acc[0], vnfs[_i][0]), concat(_acc[1], [for (f=vnfs[_i][1]) [for (i=f) i+base]]), ] ); // Function: vnf_compact() // Usage: // cvnf = vnf_compact(vnf); // Description: // Takes a VNF and consolidates all duplicate vertices, and drops unreferenced vertices. function vnf_compact(vnf) = let( vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf, verts = vnf[0], faces = [ for (face=vnf[1]) [ for (i=face) verts[i] ] ] ) vnf_add_faces(faces=faces); // Function: vnf_triangulate() // Usage: // vnf2 = vnf_triangulate(vnf); // Description: // Forces triangulation of faces in the VNF that have more than 3 vertices. function vnf_triangulate(vnf) = let( vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf, verts = vnf[0] ) [verts, triangulate_faces(verts, vnf[1])]; // Function: vnf_vertex_array() // Usage: // vnf = vnf_vertex_array(points, [caps], [cap1], [cap2], [reverse], [col_wrap], [row_wrap], [vnf]); // Description: // Creates a VNF structure from a 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. // 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", and "quincunx". // vnf = If given, add all the vertices and faces to this existing VNF structure. // 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", vnf=EMPTY_VNF ) = assert((!caps)||(caps&&col_wrap)) assert(in_list(style,["default","alt","quincunx"])) let( pts = flatten(points), pcnt = len(pts), rows = len(points), cols = len(points[0]), errchk = [for (row=points) assert(len(row)==cols, "All rows much have the same number of columns.") 0], cap1 = first_defined([cap1,caps,false]), cap2 = first_defined([cap2,caps,false]), colcnt = cols - (col_wrap?0:1), rowcnt = rows - (row_wrap?0:1) ) vnf_merge([ vnf, [ concat( pts, style!="quincunx"? [] : [ for (r = [0:1:rowcnt-1]) ( for (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]]) ) ) ] ), concat( [ for (r = [0:1:rowcnt-1]) ( for (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) ) style=="quincunx"? ( let(i5 = pcnt + r*colcnt + c) reverse? [[i1,i2,i5],[i2,i3,i5],[i3,i4,i5],[i4,i1,i5]] : [[i1,i5,i2],[i2,i5,i3],[i3,i5,i4],[i4,i5,i1]] ) : style=="alt"? ( reverse? [[i1,i2,i4],[i2,i3,i4]] : [[i1,i4,i2],[i2,i4,i3]] ) : ( reverse? [[i1,i2,i3],[i1,i3,i4]] : [[i1,i3,i2],[i1,i4,i3]] ) ) ) ], !cap1? [] : [ reverse? [for (c = [0:1:cols-1]) c] : [for (c = [cols-1:-1:0]) c] ], !cap2? [] : [ reverse? [for (c = [cols-1:-1:0]) (rows-1)*cols + c] : [for (c = [0:1:cols-1]) (rows-1)*cols + c] ] ) ] ]); // 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. module vnf_polyhedron(vnf, convexity=2) { vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf; polyhedron(vnf[0], vnf[1], convexity=convexity); } // 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. function vnf_volume(vnf) = let( vnf = vnf_triangulate(vnf), verts = vnf[0] ) sum([ for(face_index=vnf[1]) let( face = select(verts, face_index), n = cross(face[2]-face[0],face[1]-face[0]) ) face[0] * n ])/6; // 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. // Algorithm from: https://wwwf.imperial.ac.uk/~rn/centroid.pdf function vnf_centroid(vnf) = let( vnf = vnf_triangulate(vnf), verts = vnf[0], val=sum([ for(face_index=vnf[1]) let( face = select(verts, face_index), n = cross(face[2]-face[0],face[1]-face[0]) ) [ face[0] * n, vmul(n, sqr(face[0] + face[1]) + sqr(face[0] + face[2]) + sqr(face[1] + face[2]) ) ] ]) ) val[1]/val[0]/8; 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; // Function: vnf_bend() // Usage: // bentvnf = vnf_bend(vnf); // Description: // Given a VNF that is entirely above, or entirely below the Z=0 plane, bends the VNF around the // Y axis, splitting up faces as necessary. Returns the bent VNF. Will error out if the VNF // straddles the Z=0 plane, or if the bent VNF would wrap more than completely around. 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],center=true), rect([20,100],center=true)); // 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],center=true), // 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],center=true), // 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],center=true), // 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]); function vnf_bend(vnf,r,d,axis="Z") = let( chk_axis = assert(in_list(axis,["X","Y","Z"])), vnf = vnf_triangulate(vnf), 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), width = axis=="X"? (bmax.y-bmin.y) : (bmax.x - bmin.x) ) assert(width <= 2*PI*r, "Shape would wrap more than completely around the cylinder.") 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."), min_ang = 180 * bmin.x / (PI * r), max_ang = 180 * bmax.x / (PI * r), ang_span = max_ang-min_ang, steps = ceil(segs(r) * ang_span/360), step = width / steps, bend_at = axis=="X"? [for(i = [1:1:steps-1]) i*step+bmin.y] : [for(i = [1:1:steps-1]) i*step+bmin.x], facepolys = [for (face=vnf[1]) select(verts,face)], splits = axis=="X"? split_polygons_at_each_y(facepolys, bend_at) : split_polygons_at_each_x(facepolys, bend_at), newtris = _triangulate_planar_convex_polygons(splits), bent_faces = [ for (tri = newtris) [ for (p = tri) let( a = axis=="X"? 180*p.y/(r*PI) * sign(bmax.z) : axis=="Y"? 180*p.x/(r*PI) * sign(bmax.z) : 180*p.x/(r*PI) * sign(bmax.y) ) 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] ] ] ) vnf_add_faces(faces=bent_faces); // Function&Module: vnf_validate() // Usage: As Function // fails = vnf_validate(vnf); // Usage: As Module // vnf_validate(vnf); // 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 | Orange | OVRPOP_EDGE | 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_add_faces(faces=[ // [a, b, e], [a, c, b], [a, d, c], [a, e, d], [b, c, d, e] // ]); // vnf_validate(vnf); // Example: OVRPOP_EDGE 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_add_faces(vnf=vnf1, faces=[ // [[-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_add_faces(vnf=vnf1, faces=[ // [[-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_merge([ // 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_path(vnf[0])) let( vnf = vnf_compact(vnf), varr = vnf[0], faces = vnf[1], edges = sort([ for (face=faces, edge=pair_wrap(face)) edge[0] 3) [ "WARNING", "BIG_FACE", "Face has more than 3 vertices, and may confuse CGAL", [for (i=face) varr[i]], "yellow" ] ], null_faces = !show_warns? [] : [ for (face = faces) let( face = deduplicate(face,closed=true) ) if (len(face)>=3) let( faceverts = [for (k=face) varr[k]], area = polygon_area(faceverts) ) if (is_num(area) && abs(area) < EPSILON) [ "WARNING", "NULL_FACE", str("Face has zero area: ",fmt_float(abs(area),15)), faceverts, "brown" ] ], nonplanars = unique([ for (face = faces) let( faceverts = [for (k=face) varr[k]] ) if (!points_are_coplanar(faceverts)) [ "ERROR", "NONPLANAR", "Face vertices are not coplanar", faceverts, "cyan" ] ]), overpop_edges = unique([ for (i=idx(uniq_edges)) if (edgecnts[1][i]>2) [ "ERROR", "OVRPOP_EDGE", "Too many faces attached at Edge", [for (i=uniq_edges[i]) varr[i]], "#f70" ] ]), reversals = unique([ for(i = idx(faces), j = idx(faces)) if(i != j) if(len(deduplicate(faces[i],closed=true))>=3) if(len(deduplicate(faces[j],closed=true))>=3) for(edge1 = pair_wrap(faces[i])) for(edge2 = pair_wrap(faces[j])) if(edge1 == edge2) // Valid adjacent faces will never have the same vertex ordering. if(_edge_not_reported(edge1, varr, overpop_edges)) [ "ERROR", "REVERSAL", "Faces Reverse Across Edge", [for (i=edge1) varr[i]], "violet" ] ]), t_juncts = unique([ for (v=idx(varr), edge=uniq_edges) if (v!=edge[0] && v!=edge[1]) let( a = varr[edge[0]], b = varr[v], c = varr[edge[1]], pt = segment_closest_point([a,c],b) ) if (pt == b) [ "ERROR", "T_JUNCTION", "Vertex is mid-edge on another Face", [b], "red" ] ]), isect_faces = !check_isects? [] : unique([ for (i = [0:1:len(faces)-2]) for (j = [i+1:1:len(faces)-1]) let( f1 = faces[i], f2 = faces[j], shared_edges = [ for (edge1 = pair_wrap(f1), edge2 = pair_wrap(f2)) let( e1 = edge1[0]1) let( poly2 = select(varr,f2), isects2 = polygon_line_intersection(poly2,isect,bounded=true) ) if (!is_undef(isects2)) for (seg=isects2) if (seg[0] != seg[1]) [ "ERROR", "FACE_ISECT", "Faces intersect", seg, "blue" ] ]), 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)) [ "ERROR", "HOLE_EDGE", "Edge bounds Hole", [for (i=uniq_edges[i]) varr[i]], "magenta" ] ]) ) concat( big_faces, null_faces, nonplanars, overpop_edges, reversals, t_juncts, isect_faces, hole_edges ); 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) { typ = fault[0]; err = fault[1]; msg = fault[2]; pts = fault[3]; clr = fault[4]; echo(str(typ, " ", err, ": ", msg, " at ", pts)); color(clr) { if (len(pts)==2) { stroke(pts, width=size); } else if (len(pts)>2) { stroke(pts, width=size, closed=true); polyhedron(pts,[[for (i=idx(pts)) i]]); } else { move_copies(pts) sphere(d=size*3, $fn=18); } } } color([0.5,0.5,0.5,0.5]) vnf_polyhedron(vnf); } // vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap