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311 lines
11 KiB
OpenSCAD
311 lines
11 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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// Function: is_vnf()
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// Description: Returns true if the given value looks passingly like a VNF structure.
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function is_vnf(x) = is_list(x) && len(x)==2 && is_list(x[0]) && is_list(x[1]) && (x[0]==[] || is_vector(x[0][0])) && (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_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=[[],[]], p) =
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is_path(p)? _vnf_get_vertices(vnf, p) :
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assert(is_vnf(vnf))
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assert(is_vector(p))
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let(
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p = quant(p,1/1024), // OpenSCAD internally quantizes objects to 1/1024.
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v = search([p], vnf[0])[0]
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) [
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v != []? v : len(vnf[0]),
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[
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concat(vnf[0], v != []? [] : [p]),
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vnf[1]
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]
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];
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// Internal use only
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function _vnf_get_vertices(vnf=[[],[]], pts, _i=0, _idxs=[]) =
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_i>=len(pts)? [_idxs, vnf] :
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let(
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vvnf = vnf_get_vertex(vnf, pts[_i])
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) _vnf_get_vertices(vvnf[1], pts, _i=_i+1, _idxs=concat(_idxs,[vvnf[0]]));
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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=[[],[]], 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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vvnf = vnf_get_vertex(vnf, pts),
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face = deduplicate(vvnf[0], closed=true),
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vnf2 = vvnf[1]
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) [
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vnf_vertices(vnf2),
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concat(vnf_faces(vnf2), 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=[[],[]], faces, _i=0) =
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(assert(is_vnf(vnf)) assert(is_list(faces)) _i>=len(faces))? vnf :
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vnf_add_faces(vnf_add_face(vnf, faces[_i]), faces, _i=_i+1);
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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=[[],[]]) =
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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_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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) [vnf[0], triangulate_faces(vnf[0], vnf[1])];
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// Function: vnf_vertex_array()
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// Usage:
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// vnf = vnf_vertex_array(points, cols, [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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// cols = The number of points in a column.
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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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// affine3d_apply(
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// circle(d=20),
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// [xrot(90), right(30), zrot(a)]
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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]) affine3d_apply(
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// square([1,10], center=true),
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// [zrot(a/2+60), xrot(90), right(30), zrot(a)]
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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]) affine3d_apply(
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// circle(d=100),
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// [scale([1-0.1*cos(a*6), 1-0.1*cos((a+90)*6), 1]), up(a)]
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// )
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// ];
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// cap = [
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// for (a = [0:0.01:1+EPSILON]) affine3d_apply(
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// wall_points[0],
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// [scale([a,a,1]), up(90-5*sin(a*360*2))]
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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=[[],[]]
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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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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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errchk = [for (row=points) assert(len(row)==cols, "All rows much have the same number of columns.") 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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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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module vnf_polyhedron(vnf, convexity=2) {
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vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf;
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polyhedron(vnf[0], vnf[1], convexity=convexity);
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}
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// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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