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Un/curling Golden Squares with Continuous Intermediate Squares
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| function generateTransformations(T, n) { | |
| let T_n = {scale:1, angle:0, t_x:0, t_y:0}; | |
| let matrices = [T_n]; | |
| for (let i = 0; i < n; i++) { | |
| T_n = composeTransformations(T_n, T) | |
| matrices.push(T_n); | |
| } | |
| return matrices | |
| } | |
| function composeTransformations(T_1, T_2) { | |
| return { | |
| 'scale': T_1.scale * T_2.scale, | |
| 'angle': T_1.angle + T_2.angle, | |
| 't_x': T_2.scale * T_1.t_x * Math.cos(T_2.angle) - T_2.scale * T_1.t_y * Math.sin(T_2.angle) + T_2.t_x, | |
| 't_y': T_2.scale * T_1.t_x * Math.sin(T_2.angle) + T_2.scale * T_1.t_y * Math.cos(T_2.angle) + T_2.t_y | |
| } | |
| } | |
| function nthRoot(T, n) { | |
| let C = function(n, theta, r) { | |
| return (1-r*Math.cos(theta)-r**(n+1)*Math.cos((n+1)*theta)+r**(n+2)*Math.cos(n*theta))/(1-2*r*Math.cos(theta)+r**2) | |
| } | |
| let S = function(n, theta, r) { | |
| return (r*Math.sin(theta)-r**(n+1)*Math.sin((n+1)*theta)+r**(n+2)*Math.sin((n)*theta))/(1-2*r*Math.cos(theta)+r**2) | |
| } | |
| let detM = C(n-1, T.angle/n, T.scale**(1/n))**2 + S(n-1, T.angle/n, T.scale**(1/n))**2; | |
| let new_t_x = (T.t_x * C(n-1, T.angle/n, T.scale**(1/n)) + T.t_y * S(n-1, T.angle/n, T.scale**(1/n)))/detM; | |
| let new_t_y = (T.t_x * -S(n-1, T.angle/n, T.scale**(1/n)) + T.t_y * C(n-1, T.angle/n, T.scale**(1/n)))/detM; | |
| return { | |
| 'scale':(T.scale)**(1/n), | |
| 'angle':T.angle/n, | |
| 't_x':new_t_x, | |
| 't_y':new_t_y | |
| }; | |
| } | |
| function getMatrixTransformation(T) { | |
| let a = T.scale * Math.cos(T.angle), | |
| b = T.scale * Math.sin(T.angle), | |
| c = -T.scale * Math.sin(T.angle), | |
| d = T.scale * Math.cos(T.angle), | |
| e = T.t_x, | |
| f = T.t_y; | |
| return `matrix(${a},${b},${c},${d},${e},${f})`; | |
| } | |
| class GoldenCurl { | |
| constructor(el) { | |
| this.depth = 7; | |
| this.step = 130; | |
| this.frameTime = 15; | |
| this.width = 960; | |
| this.height = 500; | |
| this.scale = d3.scaleLinear().domain([0,1]).range([0,130]) | |
| d3.select(el).select('a') | |
| .on('mouseenter', () => { this._pause = false; this.play(); }) | |
| .on('mouseout', () => { this.pause() }); | |
| this.svg = d3.select('svg') | |
| .attr("width", this.width) | |
| .attr("height", this.height) | |
| this.lowerLayer = this.svg.append("g").attr('transform', 'translate(30,30)') | |
| this.upperLayer = this.svg.append("g").attr('transform', 'translate(30,30)') | |
| this.play(); | |
| } | |
| async update() { | |
| this.step += 1; | |
| this.step %= 200; | |
| return this.step; | |
| } | |
| draw() { | |
| let n = d3.easeQuadIn(d3.easeQuadInOut(Math.min(this.step/100, 2 - this.step/100))) * 8 + 1; // number of interpolated squares | |
| let angle = -Math.PI / 2 + d3.easeQuadInOut(Math.min(this.step/100, 2 - this.step/100)) * Math.PI; | |
| let T = {scale:Math.sqrt(5)*0.5-0.5, angle:angle, t_x: this.scale(1), t_y: this.scale(1)} | |
| let mainSquareTransformations = generateTransformations(T, this.depth); | |
| let interpolatedSquareTransformations = generateTransformations(nthRoot(T, n), this.depth * n); | |
| let color = d3.scaleSequential(d3.interpolateRainbow).domain([0, 5*n]); | |
| let mainSquares = this.upperLayer.selectAll(".mainSquare").data(mainSquareTransformations); | |
| mainSquares | |
| .enter() | |
| .append("rect") | |
| .attr("class", "mainSquare") | |
| .attr("width", this.scale(1)) | |
| .attr("height", this.scale(1)) | |
| .attr("stroke", "white") | |
| .attr("stroke-width", d => `${2/d.scale}px`) | |
| .attr("transform", getMatrixTransformation) | |
| .attr("fill", "none") | |
| .merge(mainSquares) | |
| .attr("transform", getMatrixTransformation) | |
| let interpolatedSquares = this.lowerLayer.selectAll(".square").data(interpolatedSquareTransformations); | |
| interpolatedSquares | |
| .enter() | |
| .append("rect") | |
| .attr("class", "square") | |
| .attr("width", this.scale(1)) | |
| .attr("height", this.scale(1)) | |
| .merge(interpolatedSquares) | |
| .attr("transform", getMatrixTransformation) | |
| .attr("fill", function(d, i) { return color(i); }) | |
| .attr('fill-opacity', 0.25) | |
| .attr("stroke", function(d, i) { return color(i); }) | |
| .attr("stroke-width", d => `${2/d.scale}px`) | |
| interpolatedSquares.exit() | |
| .remove(); | |
| } | |
| play() { | |
| if (!this._pause) { | |
| this.update().then(this.draw()).then(setTimeout(() => {this.play();}, this.frameTime)); | |
| } | |
| } | |
| pause() { | |
| this._pause = true; | |
| } | |
| } |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| body { | |
| background: black; | |
| } | |
| </style> | |
| <svg width="960" height="500"></svg> | |
| <script src="https://cdnjs.cloudflare.com/ajax/libs/d3/5.15.1/d3.js"></script> | |
| <script src="golden.js"></script> | |
| <script> | |
| let goldenCurl = new GoldenCurl(d3.select('svg').node()) | |
| </script> |
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