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September 12, 2017 07:39
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Visualize inscribed lines in jordan curves
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<!DOCTYPE html> | |
<html lang="en"> | |
<head> | |
<meta charset="UTF-8"> | |
<meta name="viewport" content="width=device-width, initial-scale=1.0"> | |
<title>Jordan Curve Inscribed Lines</title> | |
<style> | |
body { font-family: monospace; } | |
.canvas-section { display: inline-block; } | |
canvas { border: 1px solid black; } | |
</style> | |
</head> | |
<body> | |
<h1>Visualization of Jordan Curve Inscribed Lines</h1> | |
<div class="canvas-section"> | |
<h2>Curve</h2> | |
<canvas id="drawing-canvas" width="512" height="512"></canvas> | |
</div> | |
<div class="canvas-section"> | |
<h2>Inscribed Line Angles</h2> | |
<canvas id="angle-canvas" width="512" height="512"></canvas> | |
</div> | |
<div class="canvas-section"> | |
<h2>Inscribed Line Lengths</h2> | |
<canvas id="length-canvas" width="512" height="512"></canvas> | |
</div> | |
<script> | |
const drawingCanvas = document.getElementById("drawing-canvas"); | |
const angleCanvas = document.getElementById("angle-canvas"); | |
const lengthCanvas = document.getElementById("length-canvas"); | |
const drawingCtx = drawingCanvas.getContext("2d"); | |
const angleCtx = angleCanvas.getContext("2d"); | |
const lengthCtx = lengthCanvas.getContext("2d"); | |
let curvePoints = []; | |
let drawing = false; | |
const lineLength = function(a, b) { | |
return Math.hypot(b.x - a.x, b.y - a.y); //euclidean distance | |
}; | |
const lineAngle = function(a, b) { | |
const x = a.x - b.x; | |
const y = a.y - b.y; | |
return 2 * (y < 0 ? Math.atan(-y / -x) : Math.atan(y / x)); | |
}; | |
const radiansToDegrees = function(rads) { | |
return rads / (Math.PI / 180); | |
}; | |
const getAtCircular = function(curve, i) { | |
return curve[i % curve.length]; | |
}; | |
const indexCurve = function(curvePoints) { | |
let len = 0; | |
let minX = Infinity, minY = Infinity, maxX = 0, maxY = 0; | |
const index = Array(curvePoints.length); | |
for (let i = 0; i < curvePoints.length; i++) { | |
index[i] = len; | |
let a = curvePoints[i]; | |
let b = getAtCircular(curvePoints, i + 1); | |
len += lineLength(a, b); | |
//find minimum bounding box | |
if (a.x < minX) minX = a.x; | |
if (a.y < minY) minY = a.y; | |
if (a.x > maxX) maxX = a.x; | |
if (a.y > maxY) maxY = a.y; | |
} | |
return { | |
tIndex: index.map(d => d / len), | |
maxBoundingLen: lineLength({x: minX, y: minY}, {x: maxX, y: maxY}) | |
}; | |
}; | |
const getSegmentParameter = function(t, t0, t1) { | |
return (t - t0) / (t1 - t0); | |
}; | |
const lerpPoints = function(t, p0, p1) { | |
return { | |
x: (1 - t) * p0.x + t * p1.x, | |
y: (1 - t) * p0.y + t * p1.y | |
}; | |
}; | |
const getParametricPoint = function(curvePoints, tIndex, t) { | |
let l = 0; r = tIndex.length; | |
while (r - l > 1) { | |
let m = Math.floor((r + l) / 2); | |
let tM = tIndex[m]; | |
if (tM < t) l = m; | |
else if (tM > t) r = m; | |
else {l = m; break} | |
} | |
const t0 = tIndex[l]; //0.95 | |
const t1 = getAtCircular(tIndex, l + 1) || 1; | |
return lerpPoints( | |
getSegmentParameter(t, t0, t1), | |
curvePoints[l], | |
getAtCircular(curvePoints, l + 1) | |
); | |
}; | |
const render = function(curvePoints) { | |
const {tIndex, maxBoundingLen} = indexCurve(curvePoints); | |
//todo: parallelize on GPU | |
for (let y = 0; y < angleCanvas.height; y++) { | |
const pointB = getParametricPoint(curvePoints, tIndex, y / angleCanvas.height); | |
//start from y because symmetric | |
for (let x = 0; x < angleCanvas.width; x++) { | |
const pointA = getParametricPoint(curvePoints, tIndex, x / angleCanvas.width); | |
const distance = lineLength(pointA, pointB) / maxBoundingLen; | |
const angle = lineAngle(pointA, pointB); | |
angleCtx.fillStyle = `hsl(${Math.floor(radiansToDegrees(angle))}, ${100}%, ${50}%)`; | |
angleCtx.fillRect(x, y, 1, 1); | |
lengthCtx.fillStyle = `hsl(${0}, ${0}%, ${Math.floor(distance * 100)}%)`; | |
lengthCtx.fillRect(x, y, 1, 1); | |
} | |
} | |
}; | |
const getPoint = function(e) { | |
const rect = drawingCanvas.getBoundingClientRect(); | |
return { | |
x: Math.floor(e.clientX - rect.left), | |
y: Math.floor(e.clientY - rect.top), | |
}; | |
}; | |
const drawLine = function(ctx, a, b) { | |
ctx.beginPath(); | |
ctx.moveTo(a.x, a.y); | |
ctx.lineTo(b.x, b.y); | |
ctx.stroke(); | |
}; | |
drawingCanvas.onmousedown = function(e) { | |
drawingCtx.clearRect(0, 0, drawingCanvas.width, drawingCanvas.height); | |
curvePoints = []; | |
drawing = true; | |
curvePoints.push(getPoint(e)); | |
}; | |
drawingCanvas.onmouseup = function(e) { | |
drawLine( | |
drawingCtx, | |
curvePoints[curvePoints.length - 1], | |
curvePoints[0] | |
); | |
drawing = false; | |
window.requestAnimationFrame(() => render(curvePoints)); | |
}; | |
drawingCanvas.onmousemove = function(e) { | |
if (!drawing) return; | |
curvePoints.push(getPoint(e)); | |
drawLine( | |
drawingCtx, | |
curvePoints[curvePoints.length - 2], | |
curvePoints[curvePoints.length - 1] | |
); | |
}; | |
</script> | |
</body> | |
</html> |
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