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1008 lines
39 KiB
OpenSCAD
1008 lines
39 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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// To use, add the following lines to the beginning of your file:
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// ```
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// use <BOSL2/std.scad>
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// use <BOSL2/vnf.scad>
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// ```
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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`. If said
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// point does not already exist in the VNF vertex list, it is added. Returns: `[INDEX, VNF]` where
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// INDEX if the index of the point, and VNF is the possibly modified new VNF structure.
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// If `p` is given as a list of points, then 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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p = is_vector(p)? [p] : p,
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res = set_union(vnf[0], p, get_indices=true)
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)
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[res[0], [res[1],vnf[1]]];
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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, ...]);
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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=[],_i=0,_acc=EMPTY_VNF) =
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(assert(is_vnf_list(vnfs)) _i>=len(vnfs))? _acc :
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vnf_merge(
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vnfs, _i=_i+1,
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_acc = let(base=len(_acc[0])) [
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concat(_acc[0], vnfs[_i][0]),
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concat(_acc[1], [for (f=vnfs[_i][1]) [for (i=f) i+base]]),
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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_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.
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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", and "quincunx".
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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((!caps)||(caps&&col_wrap))
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assert(in_list(style,["default","alt","quincunx"]))
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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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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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)
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rows<=1 || cols<=1 ? vnf :
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vnf_merge([
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vnf, [
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concat(
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pts,
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style!="quincunx"? [] : [
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for (r = [0:1:rowcnt-1]) (
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for (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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) mean([pts[i1], pts[i2], pts[i3], pts[i4]])
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)
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)
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]
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),
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concat(
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[
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for (r = [0:1:rowcnt-1]) (
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for (c = [0:1:colcnt-1]) 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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)
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style=="quincunx"? (
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let(i5 = pcnt + r*colcnt + c)
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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]]
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) : style=="alt"? (
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reverse? [[i1,i2,i4],[i2,i3,i4]] : [[i1,i4,i2],[i2,i4,i3]]
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) : (
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reverse? [[i1,i2,i3],[i1,i3,i4]] : [[i1,i3,i2],[i1,i4,i3]]
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)
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)
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)
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],
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!cap1? [] : [
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reverse?
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[for (c = [0:1:cols-1]) c] :
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[for (c = [cols-1:-1:0]) c]
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],
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!cap2? [] : [
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reverse?
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[for (c = [cols-1:-1:0]) (rows-1)*cols + c] :
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[for (c = [0:1:cols-1]) (rows-1)*cols + c]
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]
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)
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]
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]);
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// Module: vnf_polyhedron()
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// Usage:
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// vnf_polyhedron(vnf);
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// vnf_polyhedron([VNF, VNF, VNF, ...]);
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// Description:
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// Given a VNF structure, or a list of VNF structures, creates a polyhedron from them.
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// Arguments:
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// vnf = A VNF structure, or list of VNF structures.
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// convexity = Max number of times a line could intersect a wall of the shape.
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// extent = If true, calculate anchors by extents, rather than intersection. Default: true.
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// cp = Centerpoint of VNF to use for anchoring when `extent` is false. Default: `[0, 0, 0]`
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// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `"origin"`
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// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0`
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// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP`
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module vnf_polyhedron(vnf, convexity=2, extent=true, cp=[0,0,0], anchor="origin", spin=0, orient=UP) {
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vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
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cp = is_def(cp) ? cp : vnf_centroid(vnf);
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attachable(anchor,spin,orient, vnf=vnf, extent=extent, cp=cp) {
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polyhedron(vnf[0], vnf[1], convexity=convexity);
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children();
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}
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}
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// Module: vnf_wireframe()
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// Usage:
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// vnf_wireframe(vnf, [r|d]);
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// Description:
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// 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.
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// Arguments:
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// vnf = A vnf structure
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// r|d = radius or diameter of the cylinders forming the wire frame. Default: r=1
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// Example:
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// $fn=32;
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// ball = sphere(r=20, $fn=6);
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// vnf_wireframe(ball,d=1);
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// Example:
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// include<BOSL2/polyhedra.scad>
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// $fn=32;
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// cube_oct = regular_polyhedron_info("vnf", name="cuboctahedron", or=20);
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// vnf_wireframe(cube_oct);
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// 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.
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// include<BOSL2/polyhedra.scad>
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// $fn=8;
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// octahedron = regular_polyhedron_info("vnf", name="octahedron", or=20);
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// vnf_wireframe(octahedron,r=5);
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module vnf_wireframe(vnf, r, d)
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{
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r = get_radius(r=r,d=d,dflt=1);
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vertex = vnf[0];
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edges = unique([for (face=vnf[1], i=idx(face))
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sort([face[i], select(face,i+1)])
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]);
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for (e=edges) extrude_from_to(vertex[e[0]],vertex[e[1]]) circle(r=r);
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move_copies(vertex) sphere(r=r);
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}
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// Function: vnf_volume()
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// Usage:
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// vol = vnf_volume(vnf);
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// Description:
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// Returns the volume enclosed by the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
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// no holes; otherwise the results are undefined. Returns a positive volume if face direction is clockwise and a negative volume
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// if face direction is counter-clockwise.
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// Divide the polyhedron into tetrahedra with the origin as one vertex and sum up the signed volume.
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function vnf_volume(vnf) =
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let(verts = vnf[0])
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sum([
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for(face=vnf[1], j=[1:1:len(face)-2])
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cross(verts[face[j+1]], verts[face[j]]) * verts[face[0]]
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])/6;
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// Function: vnf_centroid()
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// Usage:
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// vol = vnf_centroid(vnf);
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// Description:
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// Returns the centroid of the given manifold VNF. The VNF must describe a valid polyhedron with consistent face direction and
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// no holes; otherwise the results are undefined.
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// Divide the solid up into tetrahedra with the origin as one vertex. The centroid of a tetrahedron is the average of its vertices.
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// The centroid of the total is the volume weighted average.
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function vnf_centroid(vnf) =
|
|
let(
|
|
verts = vnf[0],
|
|
vol = 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]]
|
|
) cross(v2,v1)*v0
|
|
]),
|
|
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
|
|
)
|
|
(v0+v1+v2)*vol
|
|
])
|
|
)
|
|
pos/vol/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);
|
|
// 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]<edge[1]? edge : [edge[1],edge[0]]
|
|
]),
|
|
edgecnts = unique_count(edges),
|
|
uniq_edges = edgecnts[0],
|
|
big_faces = !show_warns? [] : [
|
|
for (face = faces)
|
|
if (len(face) > 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]],
|
|
area = polygon_area(faceverts)
|
|
)
|
|
if (is_num(area) && abs(area) > EPSILON)
|
|
if (!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]]
|
|
)
|
|
if (a != b && b != c && a != c) let(
|
|
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]<edge1[1]? edge1 : [edge1[1],edge1[0]],
|
|
e2 = edge2[0]<edge2[1]? edge2 : [edge2[1],edge2[0]]
|
|
) if (e1==e2) 1
|
|
]
|
|
)
|
|
if (!shared_edges) let(
|
|
plane1 = plane3pt_indexed(varr, f1[0], f1[1], f1[2]),
|
|
plane2 = plane3pt_indexed(varr, f2[0], f2[1], f2[2]),
|
|
line = plane_intersection(plane1, plane2)
|
|
)
|
|
if (!is_undef(line)) let(
|
|
poly1 = select(varr,f1),
|
|
isects = polygon_line_intersection(poly1,line)
|
|
)
|
|
if (!is_undef(isects))
|
|
for (isect=isects)
|
|
if (len(isect)>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);
|
|
}
|
|
|
|
// Section: VNF transformations
|
|
//
|
|
|
|
// Function: vnf_halfspace(halfspace, vnf)
|
|
// Usage:
|
|
// vnf_halfspace([a,b,c,d], vnf)
|
|
// Description:
|
|
// returns the intersection of the VNF with the given half-space.
|
|
// Arguments:
|
|
// halfspace = half-space to intersect with, given as the four coefficients of the affine inequation a\*x+b\*y+c\*z≥ d.
|
|
|
|
function _vnf_halfspace_pts(halfspace, points, faces,
|
|
inside=undef, coords=[], map=[]) =
|
|
/* Recursive function to compute the intersection of points (and edges,
|
|
* but not faces) with with the half-space.
|
|
* Parameters:
|
|
* halfspace a vector(4)
|
|
* points a list of points3d
|
|
* faces a list of indexes in points
|
|
* inside a vector{bool} determining which points belong to the
|
|
* half-space; if undef, it is initialized at first loop.
|
|
* coords the coordinates of the points in the intersection
|
|
* map the logical map (old point) → (new point(s)):
|
|
* if point i is kept, then map[i] = new-index-for-i;
|
|
* if point i is dropped, then map[i] = [[j1, k1], [j2, k2], …],
|
|
* where points j1,… are kept (old index)
|
|
* and k1,… are the matching intersections (new index).
|
|
* Returns the triple [coords, map, inside].
|
|
*
|
|
*/
|
|
let(i=len(map), n=len(coords)) // we are currently processing point i
|
|
// termination test:
|
|
i >= len(points) ? [ coords, map, inside ] :
|
|
let(inside = !is_undef(inside) ? inside :
|
|
[for(x=points) halfspace*concat(x,[-1]) >= 0],
|
|
pi = points[i])
|
|
// inside half-space: keep the point (and reindex)
|
|
inside[i] ? _vnf_halfspace_pts(halfspace, points, faces, inside,
|
|
concat(coords, [pi]), concat(map, [n]))
|
|
: // else: compute adjacent vertices (adj)
|
|
let(adj = unique([for(f=faces) let(m=len(f), j=search(i, f)[0])
|
|
each if(j!=undef) [f[(j+1)%m], f[(j+m-1)%m]] ]),
|
|
// filter those which lie in half-space:
|
|
adj2 = [for(x=adj) if(inside[x]) x],
|
|
zi = halfspace*concat(pi, [-1]))
|
|
_vnf_halfspace_pts(halfspace, points, faces, inside,
|
|
// new points: we append all these intersection points
|
|
concat(coords, [for(j=adj2) let(zj=halfspace*concat(points[j],[-1]))
|
|
(zi*points[j]-zj*pi)/(zi-zj)]),
|
|
// map: we add the info
|
|
concat(map, [[for(y=enumerate(adj2)) [y[1], n+y[0]]]]));
|
|
function _vnf_halfspace_face(face, map, inside, i=0,
|
|
newface=[], newedge=[], exit) =
|
|
/* Recursive function to intersect a face of the VNF with the half-plane.
|
|
* Arguments:
|
|
* face: the list of points of the face (old indices).
|
|
* map: as produced by _vnf_halfspace_pts
|
|
* inside: vector{bool} containing half-space info
|
|
* i: index for iteration
|
|
* exit: boolean; is first point in newedge an exit or an entrance from
|
|
* half-space?
|
|
* newface: list of (new indexes of) points on the face
|
|
* newedge: list of new points on the plane (even number of points)
|
|
* Return value: [newface, new-edges], where new-edges is a list of
|
|
* pairs [entrance-node, exit-node] (new indices).
|
|
*/
|
|
// termination condition:
|
|
(i >= len(face)) ? [ newface,
|
|
// if exit==true then we return newedge[1,0], newedge[3,2], ...
|
|
// otherwise newedge[0,1], newedge[2,3], ...;
|
|
// all edges are oriented (entrance->exit), so that by following the
|
|
// arrows we obtain a correctly-oriented face:
|
|
let(k = exit ? 0 : 1)
|
|
[for(i=[0:2:len(newedge)-2]) [newedge[i+k], newedge[i+1-k]]] ]
|
|
: // recursion case: p is current point on face, q is next point
|
|
let(p = face[i], q = face[(i+1)%len(face)],
|
|
// if p is inside half-plane, keep it in the new face:
|
|
newface0 = inside[p] ? concat(newface, [map[p]]) : newface)
|
|
// if the current segment does not intersect, this is all:
|
|
inside[p] == inside[q] ? _vnf_halfspace_face(face, map, inside, i+1,
|
|
newface0, newedge, exit)
|
|
: // otherwise, we must add the intersection point:
|
|
// rename the two points p,q as inner and outer point:
|
|
let(in = inside[p] ? p : q, out = p+q-in,
|
|
inter=[for(a=map[out]) if(a[0]==in) a[1]][0])
|
|
_vnf_halfspace_face(face, map, inside, i+1,
|
|
concat(newface0, [inter]),
|
|
concat(newedge, [inter]),
|
|
is_undef(exit) ? inside[p] : exit);
|
|
function _vnf_halfspace_path_search_edge(edge, paths, i=0, ret=[undef,undef]) =
|
|
/* given an oriented edge [x,y] and a set of oriented paths,
|
|
* returns the indices [i,j] of paths [before, after] given edge
|
|
*/
|
|
// termination condition
|
|
i >= len(paths) ? ret:
|
|
_vnf_halfspace_path_search_edge(edge, paths, i+1,
|
|
[last(paths[i]) == edge[0] ? i : ret[0],
|
|
paths[i][0] == edge[1] ? i : ret[1]]);
|
|
function _vnf_halfspace_paths(edges, i=0, paths=[]) =
|
|
/* given a set of oriented edges [x,y],
|
|
returns all paths [x,y,z,..] that may be formed from these edges.
|
|
A closed path will be returned with equal first and last point.
|
|
i: index of currently examined edge
|
|
*/
|
|
i >= len(edges) ? paths : // termination condition
|
|
let(e=edges[i], s = _vnf_halfspace_path_search_edge(e, paths))
|
|
_vnf_halfspace_paths(edges, i+1,
|
|
// we keep all paths untouched by e[i]
|
|
concat([for(i=[0:1:len(paths)-1]) if(i!= s[0] && i != s[1]) paths[i]],
|
|
is_undef(s[0])? (
|
|
// fresh e: create a new path
|
|
is_undef(s[1]) ? [e] :
|
|
// e attaches to beginning of previous path
|
|
[concat([e[0]], paths[s[1]])]
|
|
) :// edge attaches to end of previous path
|
|
is_undef(s[1]) ? [concat(paths[s[0]], [e[1]])] :
|
|
// edge merges two paths
|
|
s[0] != s[1] ? [concat(paths[s[0]], paths[s[1]])] :
|
|
// edge closes a loop
|
|
[concat(paths[s[0]], [e[1]])]));
|
|
function vnf_halfspace(_arg1=_undef, _arg2=_undef,
|
|
halfspace=_undef, vnf=_undef) =
|
|
// here is where we wish that OpenSCAD had array lvalues...
|
|
let(args=get_named_args([_arg1, _arg2], [[halfspace],[vnf]]),
|
|
halfspace=args[0], vnf=args[1])
|
|
assert(is_vector(halfspace, 4),
|
|
"half-space must be passed as a length 4 affine form")
|
|
assert(is_vnf(vnf), "must pass a vnf")
|
|
// read points
|
|
let(tmp1=_vnf_halfspace_pts(halfspace, vnf[0], vnf[1]),
|
|
coords=tmp1[0], map=tmp1[1], inside=tmp1[2],
|
|
// cut faces and generate edges
|
|
tmp2= [for(f=vnf[1]) _vnf_halfspace_face(f, map, inside)],
|
|
newfaces=[for(x=tmp2) if(x[0]!=[]) x[0]],
|
|
newedges=[for(x=tmp2) each x[1]],
|
|
// generate new faces
|
|
paths=_vnf_halfspace_paths(newedges),
|
|
loops=[for(p=paths) if(p[0] == last(p)) p])
|
|
[coords, concat(newfaces, loops)];
|
|
|
|
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|