Christian Lawson-Perfect
bdf1890ac0
I've gathered the vector and matrix functions in Point and Matrix classes. Going to make the building functions part of a builder class. You can drag to pan the view. Clicking a tile highlights it. Each tile is labelled with a number, but it gets reflected when there's an odd number of iterations - need to fix that.
673 lines
18 KiB
JavaScript
673 lines
18 KiB
JavaScript
// derived from https://cs.uwaterloo.ca/~csk/spectre/spectre.js
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const {PI, cos, sin} = Math;
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function radians(degrees) {
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return degrees * PI / 180;
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}
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let num_pieces = 0;
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class Point {
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constructor(x,y) {
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this.x = x;
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this.y = y;
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}
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add( q ) {
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return { x : this.x + q.x, y : this.y + q.y };
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}
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sub( q ) {
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return { x : this.x - q.x, y : this.y - q.y };
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}
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frame( p, q, a, b ) {
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return{ x : this.x + a*p.x + b*q.x, y : this.y + a*p.y + b*q.y };
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}
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}
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class Matrix {
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constructor(mat) {
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this.mat = mat;
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}
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determinant() {
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const T = this.mat;
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const det = T[0]*T[4] - T[1]*T[3];
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}
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inverse() {
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const T = this.mat;
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const det = this.determinant();
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return new Matrix([
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T[4]/det,
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-T[1]/det,
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(T[1]*T[5]-T[2]*T[4])/det,
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-T[3]/det,
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T[0]/det,
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(T[2]*T[3]-T[0]*T[5])/det
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]);
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}
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mul( other ) {
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const A = this.mat;
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const B = other.mat;
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return new Matrix([
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A[0]*B[0] + A[1]*B[3],
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A[0]*B[1] + A[1]*B[4],
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A[0]*B[2] + A[1]*B[5] + A[2],
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A[3]*B[0] + A[4]*B[3],
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A[3]*B[1] + A[4]*B[4],
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A[3]*B[2] + A[4]*B[5] + A[5]
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]);
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}
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// Rotation matrix
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static rotation( ang ) {
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const c = cos( ang );
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const s = sin( ang );
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return new Matrix([c, -s, 0, s, c, 0]);
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}
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static scale(x,y) {
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return new Matrix([x,0,0,0,y,0]);
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}
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static translate( tx, ty ) {
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return new Matrix([1, 0, tx, 0, 1, ty]);
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}
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// Translation matrix moving p to q
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static translateTo( p, q ) {
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return Matrix.translate( q.x - p.x, q.y - p.y );
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}
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transform( P ) {
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const M = this.mat;
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return new Point(M[0]*P.x + M[1]*P.y + M[2], M[3]*P.x + M[4]*P.y + M[5]);
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}
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}
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const ident = new Matrix([1,0,0,0,1,0]);
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const spectre = [
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new Point(0, 0),
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new Point(1.0, 0.0),
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new Point(1.5, -0.8660254037844386),
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new Point(2.366025403784439, -0.36602540378443865),
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new Point(2.366025403784439, 0.6339745962155614),
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new Point(3.366025403784439, 0.6339745962155614),
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new Point(3.866025403784439, 1.5),
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new Point(3.0, 2.0),
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new Point(2.133974596215561, 1.5),
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new Point(1.6339745962155614, 2.3660254037844393),
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new Point(0.6339745962155614, 2.3660254037844393),
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new Point(-0.3660254037844386, 2.3660254037844393),
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new Point(-0.866025403784439, 1.5),
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new Point(0.0, 1.0)
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];
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const base_quad = [spectre[3], spectre[5], spectre[7], spectre[11]];
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function getsvg(event) {
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let t = event.target;
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while(t && t.tagName.toLowerCase()!='svg') {
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t = t.parentElement;
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}
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return t;
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}
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function getcoords(event) {
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const t = getsvg(event);
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if(!t) {
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return;
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}
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const point = t.createSVGPoint()
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point.x = event.clientX
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point.y = event.clientY
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const position = point.matrixTransform(t.getScreenCTM().inverse())
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return position;
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}
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// Match unit interval to line segment p->q
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function matchSeg( p, q )
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{
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return [q.x-p.x, p.y-q.y, p.x, q.y-p.y, q.x-p.x, p.y];
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};
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// Match line segment p1->q1 to line segment p2->q2
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function matchTwo( p1, q1, p2, q2 )
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{
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return matchSeg( p2, q2 ).mul(matchSeg( p1, q1 ).inverse());
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};
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function drawPolygon( shape, T, f, s, w )
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{
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beginShape();
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for( let p of shape ) {
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const tp = T.transform( p );
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vertex( tp.x, tp.y );
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}
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endShape( CLOSE );
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}
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class Shape
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{
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constructor( pts, quad) {
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this.pts = pts;
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this.quad = quad;
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this.pts = [pts[pts.length-1]];
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for( const p of pts ) {
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const prev = this.pts[this.pts.length-1];
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const v = p.sub(prev);
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const w = new Point( -v.y, v.x );
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this.pts.push( prev.frame(v, w, 0.5, -0.3 ) );
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this.pts.push( prev.frame(v, w, 0.5, 0.3 ) );
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this.pts.push( p );
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}
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}
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streamSVG( S, stream ) {
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const tpts = this.pts.map(p => S.transform( p ));
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const [a,c,e,b,d,f] = S.mat;
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const matS = [a,b,c,d,e,f].map(p=>p.toFixed(3));
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num_pieces += 1;
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stream.push(`<g class="tile">
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<use href="#spectre" transform="matrix(${matS.join(',')}) "/>
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<text font-size="0.5" dominant-baseline="middle" text-anchor="middle" transform="matrix(${matS.join(',')}) translate(1 1.6)">${num_pieces}</text>
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<text font-size="1" dominant-baseline="middle" text-anchor="middle" transform="matrix(${matS.join(',')}) translate(1 1)">↑</text>
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</g>`);
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}
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bounds(S) {
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const points = this.pts.map(p => S.transform(p));
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return {
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minx: Math.min(...points.map(p => p.x)),
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miny: Math.min(...points.map(p => p.y)),
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maxx: Math.max(...points.map(p => p.x)),
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maxy: Math.max(...points.map(p => p.y)),
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};
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}
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* flatten(S) {
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const points = this.pts.map(p => S.transform(p));
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const ymax = Math.max(...points.map(p => p.y));
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yield {points, ymax, shape: this};
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}
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}
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class Meta {
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constructor() {
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this.geoms = [];
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this.quad = [];
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}
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addChild( g, T ) {
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this.geoms.push( { geom : g, xform: T } );
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}
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draw( S ) {
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for( let g of this.geoms ) {
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g.geom.draw( S.mul( g.xform ) );
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}
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}
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streamSVG( S, stream ) {
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const {minx,miny,maxx,maxy} = this.bounds(S);
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for( let g of this.geoms ) {
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g.geom.streamSVG( S.mul(g.xform), stream );
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}
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}
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bounds(S) {
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const sub_bounds = this.geoms.map(g => g.geom.bounds(S.mul(g.xform)));
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return {
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minx: Math.min(...sub_bounds.map(b=>b.minx)),
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miny: Math.min(...sub_bounds.map(b=>b.miny)),
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maxx: Math.max(...sub_bounds.map(b=>b.maxx)),
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maxy: Math.max(...sub_bounds.map(b=>b.maxy)),
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};
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}
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* flatten(S) {
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for(let g of this.geoms) {
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yield* g.geom.flatten(S.mul(g.xform));
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}
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}
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}
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function tiles(level, label) {
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let quad;
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let out = [];
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let transform;
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if(level == 0) {
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transform = ident;
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quad = base_quad;
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switch(label) {
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case 'Delta':
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case 'Theta':
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case 'Lambda':
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case 'Xi':
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case 'Pi':
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case 'Sigma':
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case 'Phi':
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case 'Psi':
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out.push(ident);
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case 'Gamma':
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const mystic = new Meta();
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out.push(ident);
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out.push(Matrix.translate( spectre[8].x, spectre[8].y ).mul( Matrix.rotation( PI / 6 ) ));
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}
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} else {
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/*
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* Each of the subtiles is identical, but rotated and translated.
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*
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* Produce transformation matrices Ts for each of the subtiles: they're formed by rotating the quad and then matching up a pair of points.
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*
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* The whole thing is then reflected.
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*
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* The layout of subtiles depends on the larger tile.
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*
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*/
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const labels = [
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'Delta',
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'Theta',
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'Lambda',
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'Xi',
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'Pi',
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'Sigma',
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'Phi',
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'Psi'
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];
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const sublevels = Object.fromEntries(labels.map(label => tiles(level-1, label)));
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const subquad = sublevels['Delta'].quad;
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const reflection = Matrix.scale(-1,1);
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// How to get from each subtile to the next.
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const t_rules = [
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[60, 3, 1],
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[0, 2, 0],
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[60, 3, 1],
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[60, 3, 1],
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[0, 2, 0],
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[60, 3, 1],
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[-120, 3, 3]
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];
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let Ts = [ident];
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let total_ang = 0;
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let rot = ident;
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let tquad = [...subquad];
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for( const [ang,from,to] of t_rules ) {
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total_ang += ang;
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if( ang != 0 ) {
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rot = Matrix.rotation( radians( total_ang ) );
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tquad = subquad.map(q => rot.transform(q));
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}
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const ttt = Matrix.translateTo( tquad[to], Ts[Ts.length-1].transform( subquad[from] ) );
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Ts.push( ttt.mul( rot ) );
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}
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Ts = Ts.map(t => mul(reflection, t));
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// Now build the actual supertiles, labelling appropriately.
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const super_rules = {
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'Gamma' : ['Pi','Delta','null','Theta','Sigma','Xi','Phi','Gamma'],
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'Delta' : ['Xi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
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'Theta' : ['Psi','Delta','Pi','Phi','Sigma','Pi','Phi','Gamma'],
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'Lambda' : ['Psi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
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'Xi' : ['Psi','Delta','Pi','Phi','Sigma','Psi','Phi','Gamma'],
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'Pi' : ['Psi','Delta','Xi','Phi','Sigma','Psi','Phi','Gamma'],
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'Sigma' : ['Xi','Delta','Xi','Phi','Sigma','Pi','Lambda','Gamma'],
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'Phi' : ['Psi','Delta','Psi','Phi','Sigma','Pi','Phi','Gamma'],
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'Psi' : ['Psi','Delta','Psi','Phi','Sigma','Psi','Phi','Gamma']
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};
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const super_quad = [
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Ts[6].transform(subquad[2] ),
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Ts[5].transform(subquad[1] ),
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Ts[3].transform(subquad[2] ),
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Ts[0].transform(subquad[1] ) ];
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}
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return {quad, tiles: out};
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}
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function buildSpectreBase()
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{
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const ret = {};
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for( lab of ['Delta', 'Theta', 'Lambda', 'Xi',
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'Pi', 'Sigma', 'Phi', 'Psi'] ) {
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ret[lab] = new Shape( spectre, base_quad, lab );
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}
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const mystic = new Meta();
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mystic.addChild( new Shape( spectre, base_quad, 'Gamma1' ), ident );
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mystic.addChild( new Shape( spectre, base_quad, 'Gamma2' ),
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Matrix.translate( spectre[8].x, spectre[8].y ).mul( Matrix.rotation( PI / 6 ) ) );
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mystic.quad = base_quad;
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ret['Gamma'] = mystic;
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return ret;
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}
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function buildHatTurtleBase( hat_dominant )
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{
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const r3 = 1.7320508075688772;
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const hr3 = 0.8660254037844386;
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function hexPt( x, y ) {
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return new Point( x + 0.5*y, -hr3*y );
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}
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function hexPt2( x, y ) {
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return new Point( x + hr3*y, -0.5*y );
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}
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const hat = [
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hexPt(-1, 2), hexPt(0, 2), hexPt(0, 3), hexPt(2, 2), hexPt(3, 0),
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hexPt(4, 0), hexPt(5,-1), hexPt(4,-2), hexPt(2,-1), hexPt(2,-2),
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hexPt( 1, -2), hexPt(0,-2), hexPt(-1,-1), hexPt(0, 0) ];
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const turtle = [
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hexPt(0,0), hexPt(2,-1), hexPt(3,0), hexPt(4,-1), hexPt(4,-2),
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hexPt(6,-3), hexPt(7,-5), hexPt(6,-5), hexPt(5,-4), hexPt(4,-5),
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hexPt(2,-4), hexPt(0,-3), hexPt(-1,-1), hexPt(0,-1)
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];
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const hat_keys = [
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hat[3], hat[5], hat[7], hat[11]
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];
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const turtle_keys = [
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turtle[3], turtle[5], turtle[7], turtle[11]
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];
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const ret = {};
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if( hat_dominant ) {
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for( lab of ['Delta', 'Theta', 'Lambda', 'Xi',
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'Pi', 'Sigma', 'Phi', 'Psi'] ) {
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ret[lab] = new Shape( hat, hat_keys, lab );
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}
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const mystic = new Meta();
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mystic.addChild( new Shape( hat, hat_keys, 'Gamma1' ), ident );
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mystic.addChild( new Shape( turtle, turtle_keys, 'Gamma2' ),
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Matrix.translate( hat[8].x, hat[8].y ) );
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mystic.quad = hat_keys;
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ret['Gamma'] = mystic;
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} else {
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for( lab of ['Delta', 'Theta', 'Lambda', 'Xi',
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'Pi', 'Sigma', 'Phi', 'Psi'] ) {
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ret[lab] = new Shape( turtle, turtle_keys, lab );
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}
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const mystic = new Meta();
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mystic.addChild( new Shape( turtle, turtle_keys, 'Gamma1' ), ident );
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mystic.addChild( new Shape( hat, hat_keys, 'Gamma2' ),
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Matrix.translate( turtle[9].x, turtle[9].y ).mul( Matrix.rotation( PI/3 ) ) );
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mystic.quad = turtle_keys;
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ret['Gamma'] = mystic;
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}
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return ret;
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}
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function buildHexBase()
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{
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const hr3 = 0.8660254037844386;
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const hex = [
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new Point(0, 0),
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new Point(1.0, 0.0),
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new Point(1.5, hr3),
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new Point(1, 2*hr3),
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new Point(0, 2*hr3),
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new Point(-0.5, hr3)
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];
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const hex_keys = [ hex[1], hex[2], hex[3], hex[5] ];
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const ret = {};
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for( lab of ['Gamma', 'Delta', 'Theta', 'Lambda', 'Xi',
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'Pi', 'Sigma', 'Phi', 'Psi'] ) {
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ret[lab] = new Shape( hex, hex_keys, lab );
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}
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return ret;
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}
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function buildSupertiles( sys )
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{
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// First, use any of the nine-unit tiles in sys to obtain
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// a list of transformation matrices for placing tiles within
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// supertiles.
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const quad = sys['Delta'].quad;
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const R = new Matrix([-1,0,0,0,1,0]);
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const t_rules = [
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[60, 3, 1], [0, 2, 0], [60, 3, 1], [60, 3, 1],
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[0, 2, 0], [60, 3, 1], [-120, 3, 3] ];
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const Ts = [ident];
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let total_ang = 0;
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let rot = ident;
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const tquad = [...quad];
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for( const [ang,from,to] of t_rules ) {
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total_ang += ang;
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if( ang != 0 ) {
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rot = Matrix.rotation( radians( total_ang ) );
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for( i = 0; i < 4; ++i ) {
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tquad[i] = rot.transform(quad[i] );
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}
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}
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const ttt = Matrix.translateTo( tquad[to],
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Ts[Ts.length-1].transform(quad[from] ) );
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Ts.push( ttt.mul( rot ) );
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}
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for( let idx = 0; idx < Ts.length; ++idx ) {
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Ts[idx] = R.mul( Ts[idx] );
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}
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// Now build the actual supertiles, labelling appropriately.
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const super_rules = {
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'Gamma' : ['Pi','Delta','null','Theta','Sigma','Xi','Phi','Gamma'],
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'Delta' : ['Xi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
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'Theta' : ['Psi','Delta','Pi','Phi','Sigma','Pi','Phi','Gamma'],
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'Lambda' : ['Psi','Delta','Xi','Phi','Sigma','Pi','Phi','Gamma'],
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'Xi' : ['Psi','Delta','Pi','Phi','Sigma','Psi','Phi','Gamma'],
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'Pi' : ['Psi','Delta','Xi','Phi','Sigma','Psi','Phi','Gamma'],
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'Sigma' : ['Xi','Delta','Xi','Phi','Sigma','Pi','Lambda','Gamma'],
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'Phi' : ['Psi','Delta','Psi','Phi','Sigma','Pi','Phi','Gamma'],
|
|
'Psi' : ['Psi','Delta','Psi','Phi','Sigma','Psi','Phi','Gamma'] };
|
|
const super_quad = [
|
|
Ts[6].transform(quad[2] ),
|
|
Ts[5].transform(quad[1] ),
|
|
Ts[3].transform(quad[2] ),
|
|
Ts[0].transform(quad[1] ) ];
|
|
|
|
const ret = {};
|
|
|
|
for( const [lab, subs] of Object.entries( super_rules ) ) {
|
|
const sup = new Meta();
|
|
for( let idx = 0; idx < 8; ++idx ) {
|
|
if( subs[idx] == 'null' ) {
|
|
continue;
|
|
}
|
|
sup.addChild( sys[subs[idx]], Ts[idx] );
|
|
}
|
|
sup.quad = super_quad;
|
|
|
|
ret[lab] = sup;
|
|
}
|
|
|
|
return ret;
|
|
}
|
|
|
|
/* modified from https://css-tricks.com/converting-color-spaces-in-javascript/
|
|
*/
|
|
function hexToHSL(H) {
|
|
const [r,g,b] = [0,1,2].map(i=>H.slice(2*i+1,2*i+3)).map(n=>parseInt(n,16)/255);
|
|
let cmin = Math.min(r,g,b),
|
|
cmax = Math.max(r,g,b),
|
|
delta = cmax - cmin,
|
|
h = 0,
|
|
s = 0,
|
|
l = 0;
|
|
|
|
if (delta == 0)
|
|
h = 0;
|
|
else if (cmax == r)
|
|
h = ((g - b) / delta) % 6;
|
|
else if (cmax == g)
|
|
h = (b - r) / delta + 2;
|
|
else
|
|
h = (r - g) / delta + 4;
|
|
|
|
h = Math.round(h * 60);
|
|
|
|
if (h < 0)
|
|
h += 360;
|
|
|
|
l = (cmax + cmin) / 2;
|
|
s = delta == 0 ? 0 : delta / (1 - Math.abs(2 * l - 1));
|
|
s = +(s * 100).toFixed(1);
|
|
l = +(l * 100).toFixed(1);
|
|
|
|
return {h,s,l};
|
|
}
|
|
|
|
let last_num_iterations;
|
|
|
|
function get_settings() {
|
|
return Object.fromEntries(
|
|
Array.from(document.querySelectorAll('input,textarea')).map(i => [i.id, i.type=='number' ? i.valueAsNumber : i.value])
|
|
);
|
|
}
|
|
|
|
function rebuild() {
|
|
num_pieces = 0;
|
|
const svg = document.querySelector('svg');
|
|
const settings = get_settings();
|
|
let sys = buildSpectreBase(false);
|
|
|
|
for(let i=0;i<settings.num_iterations;i++) {
|
|
sys = buildSupertiles( sys );
|
|
}
|
|
|
|
sys = sys['Delta'];
|
|
window.sys = sys;
|
|
|
|
const drawing = [];
|
|
const board = svg.querySelector('#board');
|
|
board.innerHTML = '';
|
|
sys.streamSVG(ident, drawing);
|
|
board.innerHTML = drawing.join(' ');
|
|
|
|
const viewbox = svg.getBoundingClientRect();
|
|
function visit(g, t) {
|
|
for(let c of g.children) {
|
|
visit(c, t+Math.random()*10-5);
|
|
}
|
|
if(g.tagName=='path') {
|
|
const b = g.getBoundingClientRect();
|
|
const x = (b.x - viewbox.x) / viewbox.width;
|
|
const y = (b.y - viewbox.y) / viewbox.height;
|
|
g.style.color = '#ccc';
|
|
}
|
|
}
|
|
visit(board,50);
|
|
|
|
svg.addEventListener('click', e => {
|
|
console.log('click');
|
|
if(!last_click) {
|
|
return;
|
|
}
|
|
let tile = e.target;
|
|
while(tile && !tile.classList.contains('tile')) {
|
|
tile = tile.parentElement;
|
|
}
|
|
if(!tile) {
|
|
return;
|
|
}
|
|
|
|
for(let el of svg.querySelectorAll('.highlight')) {
|
|
el.classList.remove('highlight');
|
|
}
|
|
tile.classList.add('highlight');
|
|
});
|
|
}
|
|
|
|
function update_display() {
|
|
const settings = get_settings();
|
|
const svg = document.querySelector('svg');
|
|
//const bounds = sys.bounds(ident);
|
|
svg.setAttribute('viewBox',`${settings.ox - settings.scale/2} ${settings.oy - settings.scale/2} ${settings.scale} ${settings.scale}`);
|
|
const mx = spectre.map(p=>p.x).reduce((a,b)=>a+b)/spectre.length;
|
|
const my = spectre.map(p=>p.y).reduce((a,b)=>a+b)/spectre.length;
|
|
document.getElementById('spectre').setAttribute('transform',`translate(${mx},${my}) translate(${-mx},${-my})`);
|
|
|
|
if(settings.num_iterations != last_num_iterations) {
|
|
rebuild();
|
|
last_num_iterations = settings.num_iterations;
|
|
}
|
|
}
|
|
|
|
for(let i of document.querySelectorAll('input')) {
|
|
i.addEventListener('input', update_display);
|
|
i.addEventListener('change', update_display)
|
|
}
|
|
|
|
update_display();
|
|
|
|
let opos;
|
|
let dragging;
|
|
let pan = {x:0, y:0};
|
|
let npan = pan;
|
|
let last_click = false;
|
|
|
|
const svg = document.querySelector('svg');
|
|
svg.addEventListener('pointerdown', e => {
|
|
opos = getcoords(e);
|
|
dragging = true;
|
|
console.log('dragstart');
|
|
});
|
|
|
|
svg.addEventListener('pointermove', e => {
|
|
if(!dragging) {
|
|
return;
|
|
}
|
|
const pos = getcoords(e);
|
|
npan = {x: pan.x + pos.x - opos.x, y: pan.y + pos.y - opos.y};
|
|
document.getElementById('board').setAttribute('transform', `translate(${npan.x} ${npan.y})`);
|
|
});
|
|
|
|
svg.addEventListener('pointerup', e => {
|
|
dragging = false;
|
|
const [dx,dy] = [npan.x - pan.x, npan.y - pan.y];
|
|
const d = Math.sqrt(dx*dx + dy*dy);
|
|
console.log(d);
|
|
last_click = d < 0.5;
|
|
pan = npan;
|
|
console.log('dragend');
|
|
});
|
|
|