916 lines
32 KiB
JavaScript
916 lines
32 KiB
JavaScript
/** Copyright Stewart Allen <sa@grid.space> -- All Rights Reserved */
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"use strict";
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// dep: ext.earcut
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// dep: mesh.geom
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gapp.register("mesh.tool", [], (root, exports) => {
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const { mesh } = root;
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const { geom } = mesh;
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const { Vector3 } = THREE;
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const empty = 0xffffffff;
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/**
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* tool for identiying defects and healing them
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* copied from base/mesh which is used by KM. the
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* two need to be merged. earcut needs to be migrated
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* to base.util.triagulate
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*/
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mesh.tool = class MeshTool {
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constructor(params = {}) {
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this.precision = Math.pow(10, params.precision || 6);
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}
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checkVertices(vertices, mod) {
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if (!vertices) {
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throw "missing vertices";
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}
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if (mod && vertices.length % mod !== 0) {
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throw "invalid vertices";
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}
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return vertices;
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}
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getIndex() {
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if (!this.indexed) {
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throw "missing index";
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}
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return this.indexed;
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}
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listZ() {
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let verts = this.checkVertices(this.uvert).group(3);
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let zs = new Set();
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for (let vert of verts) {
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zs.add(vert[2]);
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}
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return Array.from(zs).sort((a,b) => a - b);
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}
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flattenZ(faceIdxs) {
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let { uvert, faces } = this;
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let zsum = 0;
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let zunq = [];
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for (let faceIdx of faceIdxs) {
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let fv1 = faces[faceIdx * 3 + 0];
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let fv2 = faces[faceIdx * 3 + 1];
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let fv3 = faces[faceIdx * 3 + 2];
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let z1 = uvert[fv1 + 2];
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let z2 = uvert[fv2 + 2];
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let z3 = uvert[fv3 + 2];
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zunq.push(z1,z2,z3);
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zsum = zsum + z1 + z2 + z3;
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}
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let zavg = ((( zsum / (faceIdxs.length * 3) ) * 10000 ) | 0) / 10000;
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for (let faceIdx of faceIdxs) {
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let fv1 = faces[faceIdx * 3 + 0];
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let fv2 = faces[faceIdx * 3 + 1];
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let fv3 = faces[faceIdx * 3 + 2];
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uvert[fv1 + 2] = zavg;
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uvert[fv2 + 2] = zavg;
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uvert[fv3 + 2] = zavg;
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}
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return { unique: zunq.sort().uniq(), average: zavg };
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}
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/**
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* @param {number[]} vertices non-indexed
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*/
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generateFaces(vertices, opt = {}) {
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this.checkVertices(vertices, 3);
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let doClean = opt.clean !== false;
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let doDedup = opt.dedup !== false;
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let round = Math.pow(10, opt.round || 0);
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let faces = [];
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let fcac = {}; // seen face hash
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let fnew = []; // accumulate vertex triplets
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let nuvt = []; // new vertex list
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let hash = {}; // find vertex matches
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let prec = this.precision;
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let dups = 0;
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let cull = 0;
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if (round > 1) {
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for (let i=0, l=vertices.length; i<l; i++) {
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vertices[i] = ((vertices[i] * round) | 0) / round;
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}
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}
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for (let i=0, l=vertices.length; i<l; i += 3) {
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let x = vertices[i];
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let y = vertices[i+1];
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let z = vertices[i+2];
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let key = [
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(x * prec) | 0,
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(y * prec) | 0,
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(z * prec) | 0
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].join('');
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let vpos = hash[key];
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if (vpos === undefined) {
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// add new vertex x,y,z and hash entry with index
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hash[key] = vpos = nuvt.length;
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nuvt.push(x);
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nuvt.push(y);
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nuvt.push(z);
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}
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if (doClean) {
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// add vertex position to face accumulator
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fnew.push(vpos);
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if (fnew.length === 3) {
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// check and emit face if it's unique
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// cull invalid faces (has 2 or more shared vertices)
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if (fnew[0] === fnew[1] || fnew[0] === fnew[2] || fnew[1] === fnew[2]) {
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fnew = [];
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cull++;
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continue;
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}
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if (doDedup) {
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let key = fnew.slice().sort().join('-');
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// drop duplicate faces (sort handles reverse order)
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if (!fcac[key]) {
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faces.appendAll(fnew);
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fcac[key] = key;
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} else {
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dups++;
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}
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} else {
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faces.appendAll(fnew);
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}
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fnew = [];
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}
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} else {
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faces.push(vpos);
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}
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}
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this.stats = {cull, dups, faces: faces.length/3};
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// unique vertex array
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this.uvert = nuvt;
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// unique face array. elements are offset into vertices
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this.faces = faces;
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return this;
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}
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// todo: supercede generatedFaces() for patch()
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// face record: vi1, vi2, vi3, nx, ny, nz
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// vi = vertex index
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// n = normal
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// af = adjacent face index
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index(vertices) {
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this.vertices = this.checkVertices(vertices, 3);
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const prec = this.precision;
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const vcount = vertices.length / 3;
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const fcount = vcount / 3;
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const vround = vertices.map(v => (v * prec) | 0);
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// side records [ vi0, vi1, fn1, fn2 ]
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const sides = new Uint32Array(fcount * 4 * 3).fill(empty);
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// map of side index to face count
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const srecs = {};
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// side extended records when face count exceeds 2 (bad mesh)
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const sideExt = {};
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// face record array [ nx, ny, nz, sn0, sn1, sn2 ]
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const faces = new Float32Array(fcount * 6);
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// vertex key to vertex index
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const vimap = {};
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// normal key to normal index
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const nimap = {};
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// side key to side index
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const simap = {};
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// tmp face vertex indices
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const vinds = [ 0, 0, 0 ];
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// tmp face raw vertex offset
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const viraw = [ 0, 0, 0 ];
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// tmp vector array
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const vects = [ new Vector3(), new Vector3(), new Vector3() ];
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// i=vround index, fi=faces record index
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// vi=vinds index % 3, x,y,z = tmp vars
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// fn=next face index, vn=next vertex index, sn=next side index
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for (let i=0, l=vround.length, fn=0, vn=0, sn=0, fi=0, vi=0, x, y, z; i<l; ) {
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const vroot = i;
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// create unique vertex map
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vects[vi].set(x = vround[i++], y = vround[i++], z = vround[i++]);
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let key = x + ',' + y + ',' + z;
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// vertex index
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let vid = vimap[key];
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if (vid === undefined) {
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vid = vimap[key] = vn++;
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}
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viraw[vi] = vroot;
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vinds[vi++] = vid;
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// completed record for a face
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if (vi === 3) {
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// create indexed unique normal map
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const cfn = THREE.computeFaceNormal(...vects);
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const [ v0, v1, v2 ] = vinds;
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// create consistent side order for index key
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const s0 = (v0 < v1 ? v0 + "," + v1 : v1 + "," +v0);
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const s1 = (v1 < v2 ? v1 + "," + v2 : v2 + "," +v1);
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const s2 = (v2 < v0 ? v2 + "," + v0 : v0 + "," +v2);
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// for storing raw vertex offset in side record
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const [ vr0, vr1, vr2 ] = viraw;
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// store face indexes into sdrec array for each side
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const smap = [ s0, s1, s2 ].map((key,ki) => {
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let sid = simap[key], sdoff, sdcnt;
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if (sid === undefined) {
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sid = simap[key] = sn++;
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sdcnt = srecs[sid] = 1;
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sdoff = sid * 4;
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sides[sdoff] = viraw[ki];
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sides[sdoff + 1] = viraw[(ki + 1) % 3];
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} else {
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sdoff = sid * 4;
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sdcnt = ++srecs[sid];
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}
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if (sdcnt > 2) {
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(sideExt[sid] = sideExt[sid] ||
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[ sides[sdoff], sides[sdoff + 1], sides[sdoff + 2], sides[sdoff + 3] ]
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).push(fn);
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} else {
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sides[sdoff + sdcnt + 1] = fn;
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}
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return sid;
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});
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faces[fi++] = cfn.x;
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faces[fi++] = cfn.y;
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faces[fi++] = cfn.z;
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faces[fi++] = smap[0];
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faces[fi++] = smap[1];
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faces[fi++] = smap[2];
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vi = 0;
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fn++;
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}
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}
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this.indexed = {
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faces, sides, sideExt
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};
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}
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getAdjacentFaces(face) {
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const { faces, sides } = this.getIndex();
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const foff = face * 6;
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const s0 = faces[foff + 3];
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const s1 = faces[foff + 4];
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const s2 = faces[foff + 5];
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const farr = [
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sides[s0 * 4 + 2],
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sides[s0 * 4 + 3],
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sides[s1 * 4 + 2],
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sides[s1 * 4 + 3],
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sides[s2 * 4 + 2],
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sides[s2 * 4 + 3]
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].filter(f => f !== empty && f !== face);
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if (!farr.length) {
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console.log(`no adjacent faces to ${face}`);
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return [];
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}
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return farr;
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}
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// depends on index() being run first
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findConnectedSurface(faces, radians, filterZ, found = {}) {
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const norms = this.getIndex().faces;
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if (filterZ !== undefined) {
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// optional filter to z normal >= value
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faces = faces.filter(f => norms[f * 6 + 2] >= filterZ);
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}
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const checked = {};
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const check = faces.slice();
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for (let face of faces) {
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found[face] = 1;
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}
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while (check.length) {
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const face = check.shift();
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const froot = face * 6;
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if (filterZ !== undefined && norms[froot + 2] < filterZ) {
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continue;
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}
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const fadj = this.getAdjacentFaces(face);
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for (let f of fadj) {
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if (found[f] || checked[f]) {
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continue;
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}
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const aroot = f * 6;
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let sum = 0;
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for (let i=0; i<3; i++) {
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sum += Math.pow(norms[froot + i] - norms[aroot + i], 2);
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}
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const fn = Math.sqrt(sum);
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if (fn <= radians) {
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faces.push(f);
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check.push(f)
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checked[f] = 1;
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found[f] = 1;
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}
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}
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}
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return faces;
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}
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// given a list of faces (indices), return an array of closed
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// polylines that represent the outlines of each discrete island
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generateOutlines(list) {
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const { faces, sides } = this.getIndex();
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const prec = this.precision;
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const verts = this.vertices;
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const lines = {};
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const point = {};
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const pindx = {};
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let pnext = 0;
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function vert2point(v) {
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const x = verts[v];
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const y = verts[v + 1];
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const z = verts[v + 2];
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const key = ((x * prec) | 0) + ',' + ((y * prec) | 0) + ',' + ((z * prec) | 0);
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const rec = point[key];
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if (rec === undefined) {
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pindx[pnext] = { x, y, z, to: [] };
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return point[key] = pnext++;
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} else {
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return rec;
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}
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}
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function addLine(s) {
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if (s === empty) return;
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const v0 = vert2point(sides[s * 4]);
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const v1 = vert2point(sides[s * 4 + 1]);
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const key = v0 < v1 ? v0 + ',' + v1 : v1 +',' + v0;
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const rec = lines[key];
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if (rec) {
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rec.del = true;
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} else {
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lines[key] = { v0, v1 };
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}
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}
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for (let face of list) {
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const foff = face * 6;
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addLine(faces[foff + 3]);
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addLine(faces[foff + 4]);
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addLine(faces[foff + 5]);
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}
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const pairs = Object.values(lines).filter(l => !l.del);
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for (let line of pairs) {
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const { v0, v1 } = line;
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const p0 = pindx[v0];
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const p1 = pindx[v1];
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p0.to.push(v1);
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p1.to.push(v0);
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}
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let curr;
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let outs = [ ];
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for (let prec of Object.values(pindx)) {
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if (prec.used || prec.to.length === 0) continue;
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outs.push(curr = []);
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while (prec) {
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let { to, x, y, z } = prec;
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if (to.length < 2) {
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throw `invalid to ${to.length} @ ${x},${y},${z}`;
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}
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prec.used = true;
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curr.push({ x, y, z });
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const t0 = pindx[to[0]];
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const t1 = pindx[to[1]];
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if (!t0.used) {
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prec = t0;
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} else if (!t1.used) {
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prec = t1;
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} else {
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prec = undefined;
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}
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}
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}
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// console.log({lines, pairs, pindx, outs});
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return outs;
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}
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// depends on index() being run first
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isolateBodies() {
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const verts = this.checkVertices(this.vertices);
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const bodies = [];
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const used = {};
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for (let i=0, l=verts.length / 9; i<l; i++) {
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if (used[i]) {
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continue;
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}
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const body = this.findConnectedSurface([i], Infinity, undefined, used);
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if (body.length) {
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// todo: pre-allocate known length
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// then copy array regions from verts to bverts
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const bverts = [];
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for (let f of body) {
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bverts.push(...verts.slice(f*9, f*9+9));
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}
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bodies.push(bverts);
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}
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}
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return bodies;
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}
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/**
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* finds edge lines which are line segments on a single face.
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* construct ordered line maps with array of connected edges.
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* connect lines into polys. earcut polys into new faces.
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* requires generateFaces() be run first
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*/
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patch(opt = { merge: true }) {
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let vertices = this.checkVertices(this.uvert);
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let faces = this.faces;
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let hash = {}; // key to line map
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let vmap = {}; // vertext to line map
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let lines = [];
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class Line {
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constructor(v1, v2) {
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this.v1 = v1;
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this.v2 = v2;
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this.faces = [];
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}
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addFace(face) {
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if (this.faces.indexOf(face) < 0) {
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this.faces.push(face);
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} else if (false) {
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console.log('adding face to line twice', this, face);
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}
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return this;
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}
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adjacentUnused() {
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return vmap[this.v1]
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.concat(vmap[this.v2])
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.filter(l => l !== this && !l.used && l.faces.length === 1);
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}
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adjacentUsed() {
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return vmap[this.v1]
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.concat(vmap[this.v2])
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.filter(l => l !== this && l.used && l.faces.length === 1);
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}
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touches(line) {
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return this.v1 === line.v1 ||
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this.v1 === line.v2 ||
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this.v2 === line.v1 ||
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this.v2 === line.v2;
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}
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unitVector() {
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if (this.unit !== undefined) {
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return this.unit;
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}
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let v1 = this.v1;
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let v2 = this.v2;
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let d = [
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vertices[v1] - vertices[v2],
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vertices[v1 + 1] - vertices[v2 + 1],
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vertices[v1 + 2] - vertices[v2 + 2],
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];
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let max = Math.max(...d.map(v => Math.abs(v)));
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// console.log({d, max});
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return this.unit = d.map(v => v / max);
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}
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}
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function diffUnitVector(uv1, uv2) {
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let diff = 0;
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for (let i=0; i<3; i++) {
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diff += Math.abs(uv1[i] - uv2[i]);
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}
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return diff;
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}
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function getLine(v1, v2) {
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let s1 = vertices[v1] + vertices[v1+1]*1000 + vertices[v1+2]*100000;
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let s2 = vertices[v2] + vertices[v2+1]*1000 + vertices[v2+2]*100000;
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let key = s1 <= s2 ? [v1,v2].join('-') : [v2,v1].join('-');
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let line = hash[key];
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if (!line) {
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// point order will be swapped for reconstructed faces
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// to preserve chirality (assuming face normals are correct)
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line = hash[key] = new Line(v1, v2);
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line.key = key;
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lines.push(line);
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let lm1 = vmap[v1] = vmap[v1] || [];
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let lm2 = vmap[v2] = vmap[v2] || [];
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lm1.push(line);
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lm2.push(line);
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}
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return line;
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}
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function getXYZ(v) {
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return {x: vertices[v], y: vertices[v+1], z: vertices[v+2]};
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}
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for (let i=0, l=this.faces.length; i<l; i += 3) {
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let v1 = faces[i];
|
|
let v2 = faces[i+1];
|
|
let v3 = faces[i+2];
|
|
let l1 = getLine(v1, v2).addFace(i);
|
|
let l2 = getLine(v2, v3).addFace(i);
|
|
let l3 = getLine(v3, v1).addFace(i);
|
|
}
|
|
|
|
// array of unique line segment records with vertices
|
|
// and a list of faces. one = edge, two = inside
|
|
// all lines should be inside or object is not manifold
|
|
// but does not preclude self-intersecting geometries
|
|
this.lines = lines;
|
|
|
|
// lines belonging to only one face are on the edge of a hole
|
|
let edges = this.edges = lines.filter(l => l.faces.length === 1);
|
|
|
|
// arrays of connected edges that form a closed loop
|
|
let loops = this.loops = [];
|
|
|
|
// connect edge lines into closed loops
|
|
for (let i=0, l=edges.length; i<l; i++) {
|
|
let line = edges[i];
|
|
if (line.used) {
|
|
continue;
|
|
}
|
|
// cannot start on split
|
|
if (line.adjacentUnused().length > 2) {
|
|
// console.log('cannot start on a split');
|
|
continue;
|
|
}
|
|
// line.used = true;
|
|
let loop = [ ];
|
|
// build line through adjacent lines
|
|
while (true) {
|
|
let adjacent = line.adjacentUnused();
|
|
if (adjacent.length === 0) {
|
|
let first = loop[0];
|
|
let last = loop.last();
|
|
loop.open = loop.length < 3
|
|
|| (first.v1 !== last.v1
|
|
&& first.v2 !== last.v2
|
|
&& first.v1 !== last.v2
|
|
&& first.v2 !== last.v1);
|
|
// console.log({term: line, adj: line.adjacentUsed(), open, loop});
|
|
break;
|
|
} else if (adjacent.length === 1) {
|
|
if (line.v2 !== adjacent[0].v1) {
|
|
let tmp = adjacent[0].v1;
|
|
adjacent[0].v1 = adjacent[0].v2;
|
|
adjacent[0].v2 = tmp;
|
|
// console.log('chirality mismatch fixed');
|
|
}
|
|
line = adjacent[0];
|
|
} else if (adjacent.length === 2) {
|
|
// follow edges according to chirality
|
|
line = adjacent[0].v1 === line.v2 ?
|
|
adjacent[0] :
|
|
adjacent[1]
|
|
} else {
|
|
// console.log('error adjacent', line, adjacent, loops.length, loop.length);
|
|
line.split = adjacent;
|
|
line = adjacent[0];
|
|
}
|
|
loop.push(line);
|
|
line.used = true;
|
|
}
|
|
if (loop.length) {
|
|
loops.push(loop);
|
|
}
|
|
}
|
|
|
|
// attempt to connect open loops
|
|
if (loops.length > 1) {
|
|
outer: for (let i=0; i<loops.length-1; i++) {
|
|
let l1 = loops[i];
|
|
if (!(l1 && l1.open)) {
|
|
continue;
|
|
}
|
|
for (let j=i+1; j<loops.length; j++) {
|
|
let l2 = loops[j];
|
|
if (!(l2 && l2.open)) {
|
|
continue;
|
|
}
|
|
let nuloop;
|
|
if (l1[0].touches(l2[0])) {
|
|
nuloop = [...l2.reverse(), ...l1];
|
|
} else if (l1[0].touches(l2.last())) {
|
|
nuloop = [...l2, ...l1];
|
|
} else if (l1.last().touches(l2[0])) {
|
|
nuloop = [...l1, ...l2];
|
|
} else if (l1.last().touches(l2.last())) {
|
|
nuloop = [...l1, ...l2.reverse()];
|
|
}
|
|
if (nuloop) {
|
|
nuloop.open = true;
|
|
loops.push(nuloop);
|
|
loops[i] = loops[j] = undefined;
|
|
continue outer;
|
|
}
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
// store invalid loops for display / culling
|
|
this.shorts = loops.filter(l => l && l.length <= 2);
|
|
// console.log({edges, loops, shorts: this.shorts});
|
|
|
|
// filter out null and short loops
|
|
this.loops = loops = loops.filter(l => l && l.length > 2);
|
|
// console.log({loops_filtered: loops});
|
|
|
|
// rotate/flatten to Z plane and use earcut to generate faces
|
|
// because earcut emits point indexes, no need to un-rotate
|
|
function emitLoop(loop) {
|
|
let lastPoint;
|
|
let pindex = [];
|
|
let points = [];
|
|
let dx = 0, dy = 0, dz = 0;
|
|
|
|
// gather points, find axis with least deviaton to swap with Z
|
|
let loop1 = loop.slice();
|
|
loop1.push(loop[0]);
|
|
for (let i=0; i<loop1.length; i++) {
|
|
let line = loop1[i];
|
|
let nextPoint;
|
|
if (line.v1 === lastPoint) {
|
|
nextPoint = line.v2;
|
|
} else {
|
|
nextPoint = line.v1;
|
|
}
|
|
if (i < loop1.length - 1) {
|
|
pindex.push(nextPoint);
|
|
points.push([
|
|
vertices[nextPoint],
|
|
vertices[nextPoint+1],
|
|
vertices[nextPoint+2]
|
|
]);
|
|
}
|
|
if (lastPoint >= 0) {
|
|
dx = Math.max(dx, Math.abs(vertices[lastPoint] - vertices[nextPoint]));
|
|
dy = Math.max(dy, Math.abs(vertices[lastPoint+1] - vertices[nextPoint+1]));
|
|
dz = Math.max(dz, Math.abs(vertices[lastPoint+2] - vertices[nextPoint+2]));
|
|
}
|
|
lastPoint = nextPoint;
|
|
}
|
|
|
|
// swap Z axis with least delta axis
|
|
let swap = 2;
|
|
if (dy < dx && dy < dz) {
|
|
// swap y,z
|
|
swap = 1;
|
|
} else if (dx < dy && dx < dz) {
|
|
// swap x,z
|
|
swap = 0;
|
|
}
|
|
if (swap < 2) {
|
|
// swap x or y for z axes
|
|
for (let point of points) {
|
|
let tmpz = point[2];
|
|
point[2] = point[swap];
|
|
point[swap] = tmpz;
|
|
}
|
|
}
|
|
|
|
return { index: pindex, points: points.flat(), swap };
|
|
}
|
|
|
|
// given a loop with holes, emit faces
|
|
function emitFaces(loop) {
|
|
let { index, points } = loop;
|
|
let ec = earcut(points, undefined, 3);
|
|
// map earcut point indexes back to vertex indexes
|
|
return ec.map(p => index[p]);
|
|
}
|
|
|
|
function emitTop(rec) {
|
|
let points = rec.loop.points.slice();
|
|
let index = rec.loop.index.slice();
|
|
let holes = [];
|
|
for (let inner of rec.inner) {
|
|
holes.push(points.length / 3);
|
|
points.appendAll(inner.loop.points);
|
|
index.appendAll(inner.loop.index);
|
|
}
|
|
let ec = earcut(points, holes, 3);
|
|
return ec.map(p => index[p]);
|
|
}
|
|
|
|
// new patch areas
|
|
let areas = this.areas = [];
|
|
|
|
if (opt.compound) {
|
|
// group loops by normal (using swap as crude proxy for now)
|
|
// then attempt to nest them (find holes)
|
|
let polys = loops.map(loop => {
|
|
return emitLoop(loop);
|
|
});
|
|
|
|
// return nested mapping
|
|
let nested = geom.nest(polys.map(p => p.points));
|
|
// recover and map loops from point arrays
|
|
for (let rec of nested) {
|
|
rec.loop = polys.filter(loop => loop.points === rec.points)[0];
|
|
}
|
|
|
|
// extract tops which have nesting depth mod 2 === 0
|
|
let tops = nested.filter(rec => rec.depth % 2 === 0);
|
|
for (let top of tops) {
|
|
areas.push(emitTop(top));
|
|
}
|
|
} else {
|
|
// create area faces covering loops
|
|
for (let loop of loops) {
|
|
let l2 = emitLoop(loop);
|
|
let fs = emitFaces(l2);
|
|
areas.push(fs);
|
|
}
|
|
}
|
|
|
|
// auto-merge newly found enclosed areas
|
|
if (opt.merge) {
|
|
this.merge();
|
|
}
|
|
|
|
// de-reference loops and edges
|
|
if (opt.mapped) {
|
|
this.mapped = {
|
|
edges: this.expandLoop(this.edges),
|
|
areas: this.areas.map(a => this.expandArray(a))
|
|
};
|
|
}
|
|
|
|
return this;
|
|
}
|
|
|
|
// add vertex data from given index into array
|
|
appendVertex(index, array = []) {
|
|
let vertx = this.uvert;
|
|
array.push(vertx[index++]);
|
|
array.push(vertx[index++]);
|
|
array.push(vertx[index]);
|
|
return array;
|
|
}
|
|
|
|
// add vertices from a vertex index list to an array
|
|
expandArray(indices, array = []) {
|
|
for (let i of indices) {
|
|
this.appendVertex(i, array);
|
|
}
|
|
return array;
|
|
}
|
|
|
|
// turn loop into XYZ vertex array
|
|
expandLoop(loop, array = []) {
|
|
for (let line of loop) {
|
|
this.appendVertex(line.v1, array);
|
|
this.appendVertex(line.v2, array);
|
|
}
|
|
return array;
|
|
}
|
|
|
|
// merge generated poly areas into faces
|
|
merge() {
|
|
for (let area of this.areas || []) {
|
|
this.faces.appendAll(area);
|
|
}
|
|
}
|
|
|
|
// return non-indexed vertex list (for compatibility)
|
|
unrolled() {
|
|
let out = [];
|
|
for (let face of this.faces) {
|
|
this.appendVertex(face, out);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
// returns points array for a polygon
|
|
// extrusion and twist is handled in work.js
|
|
generateGear(numTeeth, module, pressureAngle, offset) {
|
|
// Adapted from: Public Domain Parametric Involute Spur Gear by Leemon Baird, 2011, Leemon@Leemon.com http://www.thingiverse.com/thing:5505
|
|
// see also http://grabcad.com/questions/tutorial-how-to-model-involute-gears-in-solidworks-and-show-design-intent
|
|
|
|
// const pitch_radius = (numTeeth * module) / 2;
|
|
const pi = Math.PI;
|
|
|
|
// degrees to radians
|
|
function degrees_to_radians(theta) { return theta / 180 * pi; }
|
|
|
|
// polar to cartesian
|
|
function polar(r, theta) { return [r * Math.sin(theta), r * Math.cos(theta)]; }
|
|
|
|
// point on involute curve
|
|
function q6(b, s, t, d) { return polar(d, s * (iang(b, d) + t)); }
|
|
|
|
// unwind this many degrees to go from r1 to r2
|
|
function iang(r1, r2) { return Math.sqrt((r2 / r1) * (r2 / r1) - 1) - Math.acos(r1 / r2); }
|
|
|
|
// radius a fraction f up the curved side of the tooth
|
|
function q7(f, r, b, r2, t, s) { return q6(b, s, t, (1 - f) * Math.max(b, r) + f * r2); }
|
|
|
|
// lerp q7 0..1 with a given # steps
|
|
function qf(steps, r, b, r2, t, s) {
|
|
let res = [];
|
|
let step = 1/steps;
|
|
for (let f=0; f <= 1; f += step) {
|
|
res.push(q7(f, r, b, r2, t, s));
|
|
}
|
|
return res;
|
|
}
|
|
|
|
// rotate an array of 2d points
|
|
function rotate(points_array, angle) {
|
|
let answer = [];
|
|
for (let i = 0; i < points_array.length; i++) {
|
|
let x = points_array[i][0];
|
|
let y = points_array[i][1];
|
|
let xr = x * Math.cos(angle) - y * Math.sin(angle);
|
|
let yr = y * Math.cos(angle) + x * Math.sin(angle);
|
|
answer.push([xr, yr]);
|
|
}
|
|
return answer;
|
|
}
|
|
|
|
// gear parameter setup
|
|
let mm_per_tooth = module * pi; // mm size of one gear tooth
|
|
let clearance = offset/2 || 0; // freedom between two gear centers
|
|
let backlash = offset || 0; // freedom between two gear contact points
|
|
let pressure_angle = degrees_to_radians(pressureAngle);
|
|
let gear = [];
|
|
let pitch;
|
|
|
|
// involute gear maker
|
|
{
|
|
let p = mm_per_tooth * numTeeth / pi / 2; // radius of pitch circle
|
|
let c = p + mm_per_tooth / pi - clearance; // radius of outer circle
|
|
let b = p * Math.cos(pressure_angle); // radius of base circle
|
|
let r = p - (c - p) - clearance; // radius of root circle
|
|
let t = mm_per_tooth / 2 - backlash / 2; // tooth thickness at pitch circle
|
|
let k = -iang(b, p) - t / 2 / p; // angle where involute meets base circle on side of tooth
|
|
let f = 10 + ((p/5) | 0); // increase number of tooth curve points on larger gears
|
|
let points = [ // [x,y] points for a single gear tooth
|
|
polar(r, -pi / numTeeth),
|
|
polar(r, r < b ? k : -pi / numTeeth),
|
|
...qf(f, r, b, c, k, 1),
|
|
...qf(f, r, b, c, k, -1).reverse(),
|
|
polar(r, r < b ? -k : pi / numTeeth),
|
|
// polar(r, 3.142 / numTeeth) // omit b/c overlaps start when rotated
|
|
];
|
|
|
|
// create all gear teeth by rotating the first tooth
|
|
for (var i = 0; i < numTeeth; i++) {
|
|
gear.appendAll(rotate(points, -i * 2 * pi / numTeeth));
|
|
}
|
|
|
|
pitch = p.round(3);
|
|
mesh.log(`gear pitch radius: ${pitch}`);
|
|
}
|
|
|
|
return { gear, pitch };
|
|
}
|
|
|
|
generateThreads(height, radius, turns, depth, steps, taper) {
|
|
let verts = [];
|
|
let zstep = height / turns;
|
|
let rstep = (Math.PI * 2) / steps;
|
|
let z2step = zstep / steps;
|
|
let points = []
|
|
let iter = 0;
|
|
let iter_max = turns * steps + steps;
|
|
let mute_min = Math.round(steps * 2.5);
|
|
let mute_max = iter_max - mute_min;
|
|
for (let turn=0; turn<turns; turn++) {
|
|
for (let step=0; step<steps; step++) {
|
|
iter++;
|
|
let itern = iter + steps;
|
|
let rm = radius - depth;
|
|
let rx = true &&
|
|
taper && iter < mute_min ? rm + (iter / mute_min) * depth :
|
|
taper && iter > mute_max ? rm + ((iter_max - iter) / mute_min) * depth :
|
|
radius;
|
|
let rxt = true &&
|
|
taper && itern < mute_min ? rm + (itern / mute_min) * depth :
|
|
taper && itern > mute_max ? rm + ((iter_max - itern) / mute_min) * depth :
|
|
radius;
|
|
let angle0 = rstep * step - Math.PI/2;
|
|
let z0 = (zstep * turn) + (z2step * step);
|
|
let x0 = Math.cos(angle0) * (rm);
|
|
let y0 = Math.sin(angle0) * (rm);
|
|
let x1 = Math.cos(angle0) * (rx);
|
|
let y1 = Math.sin(angle0) * (rx);
|
|
let x1t = Math.cos(angle0) * (rxt);
|
|
let y1t = Math.sin(angle0) * (rxt);
|
|
let p0 = [ x1t, y1t, z0 + zstep/2 ];
|
|
let p1 = [ x0, y0, z0 ];
|
|
let p2 = [ x1, y1, z0 - zstep/2 ];
|
|
let [ pp0, pp1, pp2 ] = points;
|
|
if (pp0 && pp1 && pp2) {
|
|
verts.push(...pp0, ...pp1, ...p0);
|
|
verts.push(...p0, ...pp1, ...p1);
|
|
verts.push(...pp1, ...pp2, ...p1);
|
|
verts.push(...p1, ...pp2, ...p2);
|
|
}
|
|
points = [ p0, p1, p2 ];
|
|
}
|
|
}
|
|
return verts;
|
|
}
|
|
|
|
};
|
|
|
|
});
|