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1140 lines
47 KiB
OpenSCAD
1140 lines
47 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: vnf.scad
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// VNF structures, holding Vertices 'N' Faces for use with `polyhedron().`
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// Includes:
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// include <BOSL2/std.scad>
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//////////////////////////////////////////////////////////////////////
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include <triangulation.scad>
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// Section: Creating Polyhedrons with VNF Structures
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// VNF stands for "Vertices'N'Faces". VNF structures are 2-item lists, `[VERTICES,FACES]` where the
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// first item is a list of vertex points, and the second is a list of face indices into the vertex
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// list. Each VNF is self contained, with face indices referring only to its own vertex list.
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// You can construct a `polyhedron()` in parts by describing each part in a self-contained VNF, then
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// merge the various VNFs to get the completed polyhedron vertex list and faces.
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EMPTY_VNF = [[],[]]; // The standard empty VNF with no vertices or faces.
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// Function: is_vnf()
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// Usage:
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// bool = is_vnf(x);
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// Description:
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// Returns true if the given value looks like a VNF structure.
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function is_vnf(x) =
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is_list(x) &&
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len(x)==2 &&
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is_list(x[0]) &&
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is_list(x[1]) &&
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(x[0]==[] || (len(x[0])>=3 && is_vector(x[0][0]))) &&
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(x[1]==[] || is_vector(x[1][0]));
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// Function: is_vnf_list()
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// Description: Returns true if the given value looks passingly like a list of VNF structures.
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function is_vnf_list(x) = is_list(x) && all([for (v=x) is_vnf(v)]);
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// Function: vnf_vertices()
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// Description: Given a VNF structure, returns the list of vertex points.
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function vnf_vertices(vnf) = vnf[0];
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// Function: vnf_faces()
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// Description: Given a VNF structure, returns the list of faces, where each face is a list of indices into the VNF vertex list.
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function vnf_faces(vnf) = vnf[1];
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// Function: vnf_quantize()
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// Usage:
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// vnf2 = vnf_quantize(vnf,<q>);
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// Description:
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// Quantizes the vertex coordinates of the VNF to the given quanta `q`.
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// Arguments:
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// vnf = The VNF to quantize.
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// q = The quanta to quantize the VNF coordinates to.
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function vnf_quantize(vnf,q=pow(2,-12)) =
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[[for (pt = vnf[0]) quant(pt,q)], vnf[1]];
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// Function: vnf_get_vertex()
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// Usage:
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// vvnf = vnf_get_vertex(vnf, p);
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// Description:
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// Finds the index number of the given vertex point `p` in the given VNF structure `vnf`.
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// If said point does not already exist in the VNF vertex list, it is added to the returned VNF.
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// Returns: `[INDEX, VNF]` where INDEX is the index of the point in the returned VNF's vertex list,
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// and VNF is the possibly modified new VNF structure. If `p` is given as a list of points, then
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// the returned INDEX will be a list of indices.
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// Arguments:
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// vnf = The VNF structue to get the point index from.
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// p = The point, or list of points to get the index of.
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// Example:
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// vnf1 = vnf_get_vertex(p=[3,5,8]); // Returns: [0, [[[3,5,8]],[]]]
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// vnf2 = vnf_get_vertex(vnf1, p=[3,2,1]); // Returns: [1, [[[3,5,8],[3,2,1]],[]]]
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// vnf3 = vnf_get_vertex(vnf2, p=[3,5,8]); // Returns: [0, [[[3,5,8],[3,2,1]],[]]]
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// vnf4 = vnf_get_vertex(vnf3, p=[[1,3,2],[3,2,1]]); // Returns: [[1,2], [[[3,5,8],[3,2,1],[1,3,2]],[]]]
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function vnf_get_vertex(vnf=EMPTY_VNF, p) =
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let(
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isvec = is_vector(p),
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pts = isvec? [p] : p,
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res = set_union(vnf[0], pts, get_indices=true)
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) [
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(isvec? res[0][0] : res[0]),
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[ res[1], vnf[1] ]
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];
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// Function: vnf_add_face()
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// Usage:
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// vnf_add_face(vnf, pts);
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// Description:
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// Given a VNF structure and a list of face vertex points, adds the face to the VNF structure.
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// Returns the modified VNF structure `[VERTICES, FACES]`. It is up to the caller to make
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// sure that the points are in the correct order to make the face normal point outwards.
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// Arguments:
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// vnf = The VNF structure to add a face to.
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// pts = The vertex points for the face.
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function vnf_add_face(vnf=EMPTY_VNF, pts) =
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assert(is_vnf(vnf))
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assert(is_path(pts))
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let(
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res = set_union(vnf[0], pts, get_indices=true),
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face = deduplicate(res[0], closed=true)
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) [
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res[1],
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concat(vnf[1], len(face)>2? [face] : [])
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];
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// Function: vnf_add_faces()
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// Usage:
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// vnf_add_faces(vnf, faces);
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// Description:
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// Given a VNF structure and a list of faces, where each face is given as a list of vertex points,
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// adds the faces to the VNF structure. Returns the modified VNF structure `[VERTICES, FACES]`.
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// It is up to the caller to make sure that the points are in the correct order to make the face
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// normals point outwards.
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// Arguments:
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// vnf = The VNF structure to add a face to.
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// faces = The list of faces, where each face is given as a list of vertex points.
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function vnf_add_faces(vnf=EMPTY_VNF, faces) =
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assert(is_vnf(vnf))
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assert(is_list(faces))
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let(
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res = set_union(vnf[0], flatten(faces), get_indices=true),
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idxs = res[0],
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nverts = res[1],
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offs = cumsum([0, for (face=faces) len(face)]),
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ifaces = [
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for (i=idx(faces)) [
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for (j=idx(faces[i]))
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idxs[offs[i]+j]
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]
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]
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) [
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nverts,
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concat(vnf[1],ifaces)
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];
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// Function: vnf_merge()
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// Usage:
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// vnf = vnf_merge([VNF, VNF, VNF, ...], <cleanup>);
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// Description:
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// Given a list of VNF structures, merges them all into a single VNF structure.
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function vnf_merge(vnfs, cleanup=false) =
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let (
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offs = cumsum([
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0, for (vnf = vnfs) len(vnf[0])
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])
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) [
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[for (vnf=vnfs) each vnf[0]],
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[
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for (i = idx(vnfs))
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let(
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vnf = vnfs[i],
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verts = vnf[0],
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faces = vnf[1]
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)
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for (face = faces)
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let(
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dface = !cleanup ? face
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: deduplicate_indexed(verts, face, closed=true)
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)
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if (len(dface) >= 3)
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[ for (j = dface) offs[i] + j ]
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]
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];
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// Function: vnf_compact()
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// Usage:
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// cvnf = vnf_compact(vnf);
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// Description:
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// Takes a VNF and consolidates all duplicate vertices, and drops unreferenced vertices.
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function vnf_compact(vnf) =
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let(
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vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf,
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verts = vnf[0],
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faces = [
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for (face=vnf[1]) [
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for (i=face) verts[i]
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]
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]
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) vnf_add_faces(faces=faces);
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// Function: vnf_reverse_faces()
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// Usage:
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// rvnf = vnf_reverse_faces(vnf);
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// Description:
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// Reverses the facing of all the faces in the given VNF.
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function vnf_reverse_faces(vnf) =
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[vnf[0], [for (face=vnf[1]) reverse(face)]];
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// Function: vnf_triangulate()
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// Usage:
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// vnf2 = vnf_triangulate(vnf);
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// Description:
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// Forces triangulation of faces in the VNF that have more than 3 vertices.
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function vnf_triangulate(vnf) =
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let(
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vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf,
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verts = vnf[0]
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) [verts, triangulate_faces(verts, vnf[1])];
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// Function: vnf_vertex_array()
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// Usage:
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// vnf = vnf_vertex_array(points, <caps>, <cap1>, <cap2>, <reverse>, <col_wrap>, <row_wrap>, <vnf>);
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// Description:
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// Creates a VNF structure from a vertex list, by dividing the vertices into columns and rows,
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// adding faces to tile the surface. You can optionally have faces added to wrap the last column
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// back to the first column, or wrap the last row to the first. Endcaps can be added to either
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// the first and/or last rows. The style parameter determines how the quadrilaterals are divided into
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// triangles. The default style is an arbitrary, systematic subdivision in the same direction. The "alt" style
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// is the uniform subdivision in the other (alternate) direction. The "min_edge" style picks the shorter edge to
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// subdivide for each quadrilateral, so the division may not be uniform across the shape. The "quincunx" style
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// adds a vertex in the center of each quadrilateral and creates four triangles, and the "convex" style
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// chooses the locally convex subdivision.
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// Arguments:
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// points = A list of vertices to divide into columns and rows.
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// caps = If true, add endcap faces to the first AND last rows.
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// cap1 = If true, add an endcap face to the first row.
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// cap2 = If true, add an endcap face to the last row.
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// col_wrap = If true, add faces to connect the last column to the first.
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// row_wrap = If true, add faces to connect the last row to the first.
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// reverse = If true, reverse all face normals.
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// style = The style of subdividing the quads into faces. Valid options are "default", "alt", "min_edge", "quincunx", and "convex".
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// vnf = If given, add all the vertices and faces to this existing VNF structure.
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// Example(3D):
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// vnf = vnf_vertex_array(
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// points=[
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// for (h = [0:5:180-EPSILON]) [
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// for (t = [0:5:360-EPSILON])
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// cylindrical_to_xyz(100 + 12 * cos((h/2 + t)*6), t, h)
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// ]
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// ],
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// col_wrap=true, caps=true, reverse=true, style="alt"
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// );
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// vnf_polyhedron(vnf);
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// Example(3D): Both `col_wrap` and `row_wrap` are true to make a torus.
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// vnf = vnf_vertex_array(
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// points=[
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// for (a=[0:5:360-EPSILON])
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// apply(
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// zrot(a) * right(30) * xrot(90),
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// path3d(circle(d=20))
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// )
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// ],
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// col_wrap=true, row_wrap=true, reverse=true
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// );
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// vnf_polyhedron(vnf);
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// Example(3D): Möbius Strip. Note that `row_wrap` is not used, and the first and last profile copies are the same.
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// vnf = vnf_vertex_array(
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// points=[
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// for (a=[0:5:360]) apply(
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// zrot(a) * right(30) * xrot(90) * zrot(a/2+60),
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// path3d(square([1,10], center=true))
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// )
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// ],
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// col_wrap=true, reverse=true
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// );
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// vnf_polyhedron(vnf);
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// Example(3D): Assembling a Polyhedron from Multiple Parts
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// wall_points = [
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// for (a = [-90:2:90]) apply(
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// up(a) * scale([1-0.1*cos(a*6),1-0.1*cos((a+90)*6),1]),
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// path3d(circle(d=100))
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// )
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// ];
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// cap = [
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// for (a = [0:0.01:1+EPSILON]) apply(
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// up(90-5*sin(a*360*2)) * scale([a,a,1]),
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// wall_points[0]
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// )
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// ];
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// cap1 = [for (p=cap) down(90, p=zscale(-1, p=p))];
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// cap2 = [for (p=cap) up(90, p=p)];
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// vnf1 = vnf_vertex_array(points=wall_points, col_wrap=true);
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// vnf2 = vnf_vertex_array(points=cap1, col_wrap=true);
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// vnf3 = vnf_vertex_array(points=cap2, col_wrap=true, reverse=true);
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// vnf_polyhedron([vnf1, vnf2, vnf3]);
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function vnf_vertex_array(
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points,
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caps, cap1, cap2,
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col_wrap=false,
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row_wrap=false,
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reverse=false,
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style="default",
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vnf=EMPTY_VNF
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) =
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assert(!(any([caps,cap1,cap2]) && !col_wrap), "col_wrap must be true if caps are requested")
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assert(!(any([caps,cap1,cap2]) && row_wrap), "Cannot combine caps with row_wrap")
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assert(in_list(style,["default","alt","quincunx", "convex","min_edge"]))
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assert(is_consistent(points), "Non-rectangular or invalid point array")
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let(
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pts = flatten(points),
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pcnt = len(pts),
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rows = len(points),
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cols = len(points[0])
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)
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rows<=1 || cols<=1 ? vnf :
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let(
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cap1 = first_defined([cap1,caps,false]),
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cap2 = first_defined([cap2,caps,false]),
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colcnt = cols - (col_wrap?0:1),
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rowcnt = rows - (row_wrap?0:1),
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verts = [
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each pts,
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if (style=="quincunx")
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for (r = [0:1:rowcnt-1], c = [0:1:colcnt-1])
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let(
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i1 = ((r+0)%rows)*cols + ((c+0)%cols),
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i2 = ((r+1)%rows)*cols + ((c+0)%cols),
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i3 = ((r+1)%rows)*cols + ((c+1)%cols),
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i4 = ((r+0)%rows)*cols + ((c+1)%cols)
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)
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mean([pts[i1], pts[i2], pts[i3], pts[i4]])
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]
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)
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vnf_merge(cleanup=false, [
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vnf,
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[
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verts,
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[
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for (r = [0:1:rowcnt-1], c=[0:1:colcnt-1])
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each
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let(
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i1 = ((r+0)%rows)*cols + ((c+0)%cols),
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i2 = ((r+1)%rows)*cols + ((c+0)%cols),
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i3 = ((r+1)%rows)*cols + ((c+1)%cols),
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i4 = ((r+0)%rows)*cols + ((c+1)%cols),
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faces =
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style=="quincunx"?
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let(i5 = pcnt + r*colcnt + c)
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[[i1,i5,i2],[i2,i5,i3],[i3,i5,i4],[i4,i5,i1]]
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: style=="alt"?
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[[i1,i4,i2],[i2,i4,i3]]
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: style=="min_edge"?
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let(
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d42=norm(pts[i4]-pts[i2]),
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d13=norm(pts[i1]-pts[i3]),
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shortedge = d42<=d13 ? [[i1,i4,i2],[i2,i4,i3]]
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: [[i1,i3,i2],[i1,i4,i3]]
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)
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shortedge
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: style=="convex"?
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let( // Find normal for 3 of the points. Is the other point above or below?
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n = (reverse?-1:1)*cross(pts[i2]-pts[i1],pts[i3]-pts[i1]),
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convexfaces = n==0 ? [[i1,i4,i3]]
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: n*pts[i4] > n*pts[i1] ? [[i1,i4,i2],[i2,i4,i3]]
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: [[i1,i3,i2],[i1,i4,i3]]
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)
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convexfaces
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: [[i1,i3,i2],[i1,i4,i3]],
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// remove degenerate faces
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culled_faces= [for(face=faces)
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if (norm(verts[face[0]]-verts[face[1]])>EPSILON &&
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norm(verts[face[1]]-verts[face[2]])>EPSILON &&
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norm(verts[face[2]]-verts[face[0]])>EPSILON)
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face
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],
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rfaces = reverse? [for (face=culled_faces) reverse(face)] : culled_faces
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)
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rfaces,
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if (cap1) count(cols,reverse=!reverse),
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if (cap2) count(cols,(rows-1)*cols, reverse=reverse)
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]
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]
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]);
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// Function: vnf_tri_array()
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// Usage:
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// vnf = vnf_tri_array(points, <row_wrap>, <reverse>)
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// Description:
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// 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
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// the construction of triangular VNF patches. The resulting VNF can be wrapped along the rows by setting `row_wrap` to true.
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// Arguments:
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// points = List of point lists for each row
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// row_wrap = If true then add faces connecting the first row and last row. These rows must differ by at most 2 in length.
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// reverse = Set this to reverse the direction of the faces
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// Examples: Each row has one more point than the preceeding one.
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// pts = [for(y=[1:1:10]) [for(x=[0:y-1]) [x,y,y]]];
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// vnf = vnf_tri_array(pts);
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// vnf_wireframe(vnf,d=.1);
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// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
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// Examples: Each row has one more point than the preceeding one.
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// pts = [for(y=[0:2:10]) [for(x=[-y/2:y/2]) [x,y,y]]];
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// vnf = vnf_tri_array(pts);
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// vnf_wireframe(vnf,d=.1);
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// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
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// Example: Chaining two VNFs to construct a cone with one point length change between rows.
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// pts1 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[0,180]),10-z)];
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// pts2 = [for(z=[0:10]) path3d(arc(3+z,r=z/2+1, angle=[180,360]),10-z)];
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// vnf = vnf_tri_array(pts1,
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// vnf=vnf_tri_array(pts2));
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// color("green")vnf_wireframe(vnf,d=.1);
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// vnf_polyhedron(vnf);
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// Example: Cone with length change two between rows
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// pts1 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[0,180]),10-z)];
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// pts2 = [for(z=[0:1:10]) path3d(arc(3+2*z,r=z/2+1, angle=[180,360]),10-z)];
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// vnf = vnf_tri_array(pts1,
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// vnf=vnf_tri_array(pts2));
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// color("green")vnf_wireframe(vnf,d=.1);
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// vnf_polyhedron(vnf);
|
|
// Example: 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,d=.1);
|
|
// color("red")move_copies(flatten(pts)) sphere(r=.15,$fn=9);
|
|
function vnf_tri_array(points, row_wrap=false, reverse=false, vnf=EMPTY_VNF) =
|
|
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)))
|
|
])
|
|
vnf_merge(cleanup=true, [vnf, [flatten(points), faces]]);
|
|
|
|
|
|
|
|
// 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 of VNF to use for anchoring when `extent` is false. Default: `[0, 0, 0]`
|
|
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `"origin"`
|
|
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
|
|
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
|
|
module vnf_polyhedron(vnf, convexity=2, extent=true, cp=[0,0,0], anchor="origin", spin=0, orient=UP) {
|
|
vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
|
|
cp = is_def(cp) ? cp : vnf_centroid(vnf);
|
|
attachable(anchor,spin,orient, vnf=vnf, extent=extent, cp=cp) {
|
|
polyhedron(vnf[0], vnf[1], convexity=convexity);
|
|
children();
|
|
}
|
|
}
|
|
|
|
|
|
|
|
// Module: vnf_wireframe()
|
|
// Usage:
|
|
// vnf_wireframe(vnf, <r|d>);
|
|
// 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.
|
|
// Arguments:
|
|
// vnf = A vnf structure
|
|
// r|d = radius or diameter of the cylinders forming the wire frame. Default: r=1
|
|
// Example:
|
|
// $fn=32;
|
|
// ball = sphere(r=20, $fn=6);
|
|
// vnf_wireframe(ball,d=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,r=5);
|
|
module vnf_wireframe(vnf, r, d)
|
|
{
|
|
r = get_radius(r=r,d=d,dflt=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(r=r);
|
|
move_copies(vertex) sphere(r=r);
|
|
}
|
|
|
|
|
|
// 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_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) =
|
|
assert(is_vnf(vnf) && len(vnf[0])!=0 )
|
|
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, EPSILON), "The vnf has self-intersections.")
|
|
pos[1]/pos[0]/4;
|
|
|
|
|
|
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);
|
|
// 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, <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_add_faces(faces=[
|
|
// [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_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],
|
|
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 = segment_closest_point([a,c],b)
|
|
)
|
|
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 (!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);
|
|
}
|
|
|
|
|
|
// Section: VNF Transformations
|
|
|
|
// 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:
|
|
// vnf = cube(10,center=true);
|
|
// cutvnf = vnf_halfspace([-1,1,-1,0], vnf);
|
|
// vnf_polyhedron(cutvnf);
|
|
// Example: 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: 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: 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) =
|
|
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(
|
|
faceregion = project_plane(plane, newpaths),
|
|
facevnf = region_faces(faceregion,reverse=true)
|
|
)
|
|
vnf_merge([[newvert, faces_edges_vertices[0]], lift_plane(plane, facevnf)]);
|
|
|
|
|
|
function _assemble_paths(vertices, edges, paths=[],i=0) =
|
|
i==len(edges) ? paths :
|
|
norm(vertices[edges[i][0]]-vertices[edges[i][1]])<EPSILON ? echo(degen=i)_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);
|
|
|
|
|
|
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|