Compute points and angles along a bezier curve

.block

license: mit
height: 320
border: no

README.md

Compute points and angles along a bezier curve

Given the end points and control points along a bezier curve, this code shows how to get any point and any angle along the curve.

dist.js

function quadraticPath(t){return"M"+t.start[0]+","+t.start[1]+" Q"+t.control[0]+","+t.control[1]+" "+t.end[0]+","+t.end[1]}function interpolateQuadraticBezier(t,r,a){return function(n){return[Math.pow(1-n,2)*t[0]+2*(1-n)*n*r[0]+Math.pow(n,2)*a[0],Math.pow(1-n,2)*t[1]+2*(1-n)*n*r[1]+Math.pow(n,2)*a[1]]}}function interpolateQuadraticBezierAngle(t,r,a){return function(n){var e=2*(1-n)*(r[0]-t[0])+2*n*(a[0]-r[0]),o=2*(1-n)*(r[1]-t[1])+2*n*(a[1]-r[1]);return Math.atan2(o,e)*(180/Math.PI)}}function cubicPath(t){return"M"+t.start[0]+","+t.start[1]+" C"+t.control1[0]+","+t.control1[1]+" "+t.control2[0]+","+t.control2[1]+" "+t.end[0]+","+t.end[1]}function interpolateCubicBezier(t,r,a,n){return function(e){return[Math.pow(1-e,3)*t[0]+3*Math.pow(1-e,2)*e*r[0]+3*(1-e)*Math.pow(e,2)*a[0]+Math.pow(e,3)*n[0],Math.pow(1-e,3)*t[1]+3*Math.pow(1-e,2)*e*r[1]+3*(1-e)*Math.pow(e,2)*a[1]+Math.pow(e,3)*n[1]]}}function interpolateCubicBezierAngle(t,r,a,n){return function(e){var o=3*Math.pow(1-e,2)*(r[0]-t[0])+6*(1-e)*e*(a[0]-r[0])+3*Math.pow(e,2)*(n[0]-a[0]),c=3*Math.pow(1-e,2)*(r[1]-t[1])+6*(1-e)*e*(a[1]-r[1])+3*Math.pow(e,2)*(n[1]-a[1]);return Math.atan2(c,o)*(180/Math.PI)}}function drawQuadratic(t){var r=g.append("g").attr("class","quadratic");r.append("text").text("Quadratic Bezier").attr("dy","0.4em"),r.append("circle").attr("r",5).attr("class","start-point").attr("cx",t.start[0]).attr("cy",t.start[1]),r.append("circle").attr("r",5).attr("class","end-point").attr("cx",t.end[0]).attr("cy",t.end[1]),r.append("circle").attr("r",3).attr("class","control-point").attr("cx",t.control[0]).attr("cy",t.control[1]),r.append("path").attr("class","curve").attr("d",quadraticPath(t));var a=interpolateQuadraticBezier(t.start,t.control,t.end),n=d3.range(10).map(function(t,r,n){return a(t/(n.length-1))});r.selectAll(".interpolated-point").data(n).enter().append("circle").attr("class","interpolated-point").attr("r",3).attr("cx",function(t){return t[0]}).attr("cy",function(t){return t[1]});var e=interpolateQuadraticBezierAngle(t.start,t.control,t.end),o=d3.range(3).map(function(t,r,n){var o=t/(n.length-1);return{t:o,position:a(o),angle:e(o)}});return r.selectAll(".rotated-point").data(o).enter().append("path").attr("d","M12,0 L-5,-8 L0,0 L-5,8 Z").attr("class","rotated-point").attr("transform",function(t){return"translate("+t.position[0]+", "+t.position[1]+") rotate("+t.angle+")"}),console.log("QUADRATIC"),console.log(JSON.stringify(t)),console.log(JSON.stringify(o,null,2)),r}function drawCubic(t){var r=g.append("g").attr("class","cubic").attr("transform","translate(250, 0)");r.append("text").text("Cubic Bezier").attr("dy","0.4em"),r.append("circle").attr("r",5).attr("class","start-point").attr("cx",t.start[0]).attr("cy",t.start[1]),r.append("circle").attr("r",5).attr("class","end-point").attr("cx",t.end[0]).attr("cy",t.end[1]),r.append("circle").attr("r",3).attr("class","control-point").attr("cx",t.control1[0]).attr("cy",t.control1[1]),r.append("circle").attr("r",3).attr("class","control-point").attr("cx",t.control2[0]).attr("cy",t.control2[1]),r.append("path").attr("class","curve").attr("d",cubicPath(t));var a=interpolateCubicBezier(t.start,t.control1,t.control2,t.end),n=d3.range(10).map(function(t,r,n){return a(t/(n.length-1))});r.selectAll(".interpolated-point").data(n).enter().append("circle").attr("class","interpolated-point").attr("r",3).attr("cx",function(t){return t[0]}).attr("cy",function(t){return t[1]});var e=interpolateCubicBezierAngle(t.start,t.control1,t.control2,t.end),o=d3.range(3).map(function(t,r,n){var o=t/(n.length-1);return{t:o,position:a(o),angle:e(o)}});return r.selectAll(".rotated-point").data(o).enter().append("path").attr("d","M12,0 L-5,-8 L0,0 L-5,8 Z").attr("class","rotated-point").attr("transform",function(t){return"translate("+t.position[0]+", "+t.position[1]+") rotate("+t.angle+")"}),console.log("CUBIC"),console.log(JSON.stringify(t)),console.log(JSON.stringify(o,null,2)),r}var width=500,height=300,padding={top:10,right:10,bottom:10,left:10},svg=d3.select("body").append("svg").attr("width",width).attr("height",height),g=svg.append("g").attr("transform","translate("+padding.left+", "+padding.top+")");drawQuadratic({start:[0,70],end:[200,100],control:[160,20]}),drawCubic({start:[0,70],end:[200,100],control1:[40,180],control2:[160,20]});
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width = 500;\nconst height = 300;\nconst padding = { top: 10, right: 10, bottom: 10, left: 10 };\n\n\nconst svg = d3.select('body').append('svg')\n\t\t.attr('width', width)\n\t\t.attr('height', height);\n\nconst g = svg.append('g')\n\t\t.attr('transform', `translate(${padding.left}, ${padding.top})`)\n\n\nfunction quadraticPath(q) {\n\treturn `M${q.start[0]},${q.start[1]} Q${q.control[0]},${q.control[1]} ${q.end[0]},${q.end[1]}`;\n}\n\n// B(t) = (1 - t)^2P0 + 2(1 - t)tP1 + t^2P2\nfunction interpolateQuadraticBezier(start, control, end) {\n\t// 0 <= t <= 1\n\treturn function interpolator(t) {\n\t\treturn [\n\t\t\t(Math.pow(1 - t, 2) * start[0]) +\n      (2 * (1 - t) * t * control[0]) +\n      (Math.pow(t, 2) * end[0]),\n      (Math.pow(1 - t, 2) * start[1]) +\n      (2 * (1 - t) * t * control[1]) +\n      (Math.pow(t, 2) * end[1]),\n\t\t];\n\t};\n}\n\n// B'(t) = 2(1 - t)(P1 - P0) + 2t(P2 - P1)\nfunction interpolateQuadraticBezierAngle(start, control, end) {\n\t// 0 <= t <= 1\n\treturn function interpolator(t) {\n\t\tconst tangentX = (2 * (1 - t) * (control[0] - start[0])) +\n\t\t\t\t\t\t\t\t\t\t (2 * t * (end[0] - control[0]));\n\t\tconst tangentY = (2 * (1 - t) * (control[1] - start[1])) +\n\t\t\t\t\t\t\t\t\t\t (2 * t * (end[1] - control[1]));\n\n\t\treturn Math.atan2(tangentY, tangentX) * (180 / Math.PI);\n\t}\n}\n\nfunction cubicPath(c) {\n\treturn `M${c.start[0]},${c.start[1]} C${c.control1[0]},${c.control1[1]} ${c.control2[0]},${c.control2[1]} ${c.end[0]},${c.end[1]}`;\n}\n\n// B(t) = (1 - t)^3P0 + 3(1 - t)^2tP1 + 3(1 - t)t^2P2 + t^3P3\nfunction interpolateCubicBezier(start, control1, control2, end) {\n\t// 0 <= t <= 1\n\treturn function interpolator(t) {\n\t\treturn [\n      (Math.pow(1 - t, 3) * start[0]) +\n      (3 * Math.pow(1 - t, 2) * t * control1[0]) +\n      (3 * (1 - t) * Math.pow(t, 2) * control2[0]) +\n\t\t\t(Math.pow(t, 3) * end[0]),\n\t\t\t(Math.pow(1 - t, 3) * start[1]) +\n      (3 * Math.pow(1 - t, 2) * t * control1[1]) +\n      (3 * (1 - t) * Math.pow(t, 2) * control2[1]) +\n\t\t\t(Math.pow(t, 3) * end[1]),\n\t\t];\n\t};\n}\n\n// B'(t) = 3(1- t)^2(P1 - P0) + 6(1 - t)t(P2 - P1) + 3t^2(P3 - P2)\nfunction interpolateCubicBezierAngle(start, control1, control2, end) {\n\t// 0 <= t <= 1\n\treturn function interpolator(t) {\n\t\tconst tangentX =  (3 * Math.pow(1 - t, 2) * (control1[0] - start[0])) +\n\t\t\t\t\t\t\t\t\t\t\t(6 * (1 - t) * t * (control2[0] - control1[0])) +\n\t\t\t\t\t\t\t\t\t\t\t(3 * Math.pow(t, 2) * (end[0] - control2[0]));\n\t\tconst tangentY =  (3 * Math.pow(1 - t, 2) * (control1[1] - start[1])) +\n\t\t\t\t\t\t\t\t\t\t\t(6 * (1 - t) * t * (control2[1] - control1[1])) +\n\t\t\t\t\t\t\t\t\t\t\t(3 * Math.pow(t, 2) * (end[1] - control2[1]));\n\n\t\treturn Math.atan2(tangentY, tangentX) * (180 / Math.PI);\n\t}\n}\n\n\n// draw a quadratic bezier curve\nfunction drawQuadratic(quadratic) {\n\tconst gQuadratic = g.append('g')\n\t\t.attr('class', 'quadratic');\n\n\tgQuadratic.append('text')\n\t\t.text('Quadratic Bezier')\n\t\t.attr('dy', '0.4em')\n\n\t// draw the points\n\tgQuadratic.append('circle')\n\t\t.attr('r', 5)\n\t\t.attr('class', 'start-point')\n\t\t.attr('cx', quadratic.start[0])\n\t\t.attr('cy', quadratic.start[1])\n\n\tgQuadratic.append('circle')\n\t\t.attr('r', 5)\n\t\t.attr('class', 'end-point')\n\t\t.attr('cx', quadratic.end[0])\n\t\t.attr('cy', quadratic.end[1])\n\n\tgQuadratic.append('circle')\n\t\t.attr('r', 3)\n\t\t.attr('class', 'control-point')\n\t\t.attr('cx', quadratic.control[0])\n\t\t.attr('cy', quadratic.control[1])\n\n\t// draw the path\n\tgQuadratic.append('path')\n\t\t.attr('class', 'curve')\n\t\t.attr('d', quadraticPath(quadratic));\n\n\tconst quadraticInterpolator = interpolateQuadraticBezier(quadratic.start, quadratic.control, quadratic.end);\n\tconst interpolatedPoints = d3.range(10).map((d, i, a) => quadraticInterpolator(d / (a.length - 1)));\n\n\tgQuadratic.selectAll('.interpolated-point').data(interpolatedPoints)\n\t\t.enter()\n\t\t\t.append('circle')\n\t\t\t\t.attr('class', 'interpolated-point')\n\t\t\t\t.attr('r', 3)\n\t\t\t\t.attr('cx', d => d[0])\n\t\t\t\t.attr('cy', d => d[1]);\n\n\n\tconst quadraticAngleInterpolator = interpolateQuadraticBezierAngle(quadratic.start, quadratic.control, quadratic.end);\n\n\tconst rotatedPoints = d3.range(3).map((d, i, a) => {\n\t\tconst t = d / (a.length - 1);\n\t\treturn {\n\t\t\tt: t,\n\t\t\tposition: quadraticInterpolator(t),\n\t\t\tangle: quadraticAngleInterpolator(t),\n\t\t};\n\t});\n\n\tgQuadratic.selectAll('.rotated-point').data(rotatedPoints)\n\t\t.enter()\n\t\t\t.append('path')\n\t\t\t\t.attr('d', 'M12,0 L-5,-8 L0,0 L-5,8 Z')\n\t\t\t\t.attr('class', 'rotated-point')\n\t\t\t\t.attr('transform', d => `translate(${d.position[0]}, ${d.position[1]}) rotate(${d.angle})`)\n\n\n\tconsole.log('QUADRATIC');\n\tconsole.log(JSON.stringify(quadratic));\n\tconsole.log(JSON.stringify(rotatedPoints, null, 2))\n\n\treturn gQuadratic;\n}\n\n\nfunction drawCubic(cubic) {\n\tconst gCubic = g.append('g')\n\t\t.attr('class', 'cubic')\n\t\t.attr('transform', 'translate(250, 0)');\n\n\tgCubic.append('text')\n\t\t.text('Cubic Bezier')\n\t\t.attr('dy', '0.4em')\n\n\t// draw the points\n\tgCubic.append('circle')\n\t\t.attr('r', 5)\n\t\t.attr('class', 'start-point')\n\t\t.attr('cx', cubic.start[0])\n\t\t.attr('cy', cubic.start[1])\n\n\tgCubic.append('circle')\n\t\t.attr('r', 5)\n\t\t.attr('class', 'end-point')\n\t\t.attr('cx', cubic.end[0])\n\t\t.attr('cy', cubic.end[1])\n\n\tgCubic.append('circle')\n\t\t.attr('r', 3)\n\t\t.attr('class', 'control-point')\n\t\t.attr('cx', cubic.control1[0])\n\t\t.attr('cy', cubic.control1[1])\n\n\tgCubic.append('circle')\n\t\t.attr('r', 3)\n\t\t.attr('class', 'control-point')\n\t\t.attr('cx', cubic.control2[0])\n\t\t.attr('cy', cubic.control2[1])\n\n\t// draw the path\n\tgCubic.append('path')\n\t\t.attr('class', 'curve')\n\t\t.attr('d', cubicPath(cubic));\n\n\tconst cubicInterpolator = interpolateCubicBezier(cubic.start, cubic.control1, cubic.control2, cubic.end);\n\tconst interpolatedPoints = d3.range(10).map((d, i, a) => cubicInterpolator(d / (a.length - 1)));\n\n\tgCubic.selectAll('.interpolated-point').data(interpolatedPoints)\n\t\t.enter()\n\t\t\t.append('circle')\n\t\t\t\t.attr('class', 'interpolated-point')\n\t\t\t\t.attr('r', 3)\n\t\t\t\t.attr('cx', d => d[0])\n\t\t\t\t.attr('cy', d => d[1]);\n\n\n\tconst cubicAngleInterpolator = interpolateCubicBezierAngle(cubic.start, cubic.control1, cubic.control2, cubic.end);\n\n\tconst rotatedPoints = d3.range(3).map((d, i, a) => {\n\t\tconst t = d / (a.length - 1);\n\t\treturn {\n\t\t\tt: t,\n\t\t\tposition: cubicInterpolator(t),\n\t\t\tangle: cubicAngleInterpolator(t),\n\t\t};\n\t});\n\n\tgCubic.selectAll('.rotated-point').data(rotatedPoints)\n\t\t.enter()\n\t\t\t.append('path')\n\t\t\t\t.attr('d', 'M12,0 L-5,-8 L0,0 L-5,8 Z')\n\t\t\t\t.attr('class', 'rotated-point')\n\t\t\t\t.attr('transform', d => `translate(${d.position[0]}, ${d.position[1]}) rotate(${d.angle})`)\n\n\n\tconsole.log('CUBIC');\n\tconsole.log(JSON.stringify(cubic));\n\tconsole.log(JSON.stringify(rotatedPoints, null, 2))\n\n\treturn gCubic;\n}\n\n\nconst quadratic = { start: [0, 70], end: [200, 100], control: [160, 20] };\ndrawQuadratic(quadratic);\n\nconst cubic = { start: [0, 70], end: [200, 100], control1: [40, 180], control2: [160, 20] };\ndrawCubic(cubic);\n"]}

index.html

<!DOCTYPE html>
<title>Compute points and angles along a bezier curve</title>
<link href='style.css' rel='stylesheet' />
<body>
	<script src='https://d3js.org/d3.v4.min.js'></script>
	<script src='dist.js'></script>
</body>

preview.png

script.js

const width = 500;
const height = 300;
const padding = { top: 10, right: 10, bottom: 10, left: 10 };


const svg = d3.select('body').append('svg')
		.attr('width', width)
		.attr('height', height);

const g = svg.append('g')
		.attr('transform', `translate(${padding.left}, ${padding.top})`)


function quadraticPath(q) {
	return `M${q.start[0]},${q.start[1]} Q${q.control[0]},${q.control[1]} ${q.end[0]},${q.end[1]}`;
}

// B(t) = (1 - t)^2P0 + 2(1 - t)tP1 + t^2P2
function interpolateQuadraticBezier(start, control, end) {
	// 0 <= t <= 1
	return function interpolator(t) {
		return [
			(Math.pow(1 - t, 2) * start[0]) +
      (2 * (1 - t) * t * control[0]) +
      (Math.pow(t, 2) * end[0]),
      (Math.pow(1 - t, 2) * start[1]) +
      (2 * (1 - t) * t * control[1]) +
      (Math.pow(t, 2) * end[1]),
		];
	};
}

// B'(t) = 2(1 - t)(P1 - P0) + 2t(P2 - P1)
function interpolateQuadraticBezierAngle(start, control, end) {
	// 0 <= t <= 1
	return function interpolator(t) {
		const tangentX = (2 * (1 - t) * (control[0] - start[0])) +
										 (2 * t * (end[0] - control[0]));
		const tangentY = (2 * (1 - t) * (control[1] - start[1])) +
										 (2 * t * (end[1] - control[1]));

		return Math.atan2(tangentY, tangentX) * (180 / Math.PI);
	}
}

function cubicPath(c) {
	return `M${c.start[0]},${c.start[1]} C${c.control1[0]},${c.control1[1]} ${c.control2[0]},${c.control2[1]} ${c.end[0]},${c.end[1]}`;
}

// B(t) = (1 - t)^3P0 + 3(1 - t)^2tP1 + 3(1 - t)t^2P2 + t^3P3
function interpolateCubicBezier(start, control1, control2, end) {
	// 0 <= t <= 1
	return function interpolator(t) {
		return [
      (Math.pow(1 - t, 3) * start[0]) +
      (3 * Math.pow(1 - t, 2) * t * control1[0]) +
      (3 * (1 - t) * Math.pow(t, 2) * control2[0]) +
			(Math.pow(t, 3) * end[0]),
			(Math.pow(1 - t, 3) * start[1]) +
      (3 * Math.pow(1 - t, 2) * t * control1[1]) +
      (3 * (1 - t) * Math.pow(t, 2) * control2[1]) +
			(Math.pow(t, 3) * end[1]),
		];
	};
}

// B'(t) = 3(1- t)^2(P1 - P0) + 6(1 - t)t(P2 - P1) + 3t^2(P3 - P2)
function interpolateCubicBezierAngle(start, control1, control2, end) {
	// 0 <= t <= 1
	return function interpolator(t) {
		const tangentX =  (3 * Math.pow(1 - t, 2) * (control1[0] - start[0])) +
											(6 * (1 - t) * t * (control2[0] - control1[0])) +
											(3 * Math.pow(t, 2) * (end[0] - control2[0]));
		const tangentY =  (3 * Math.pow(1 - t, 2) * (control1[1] - start[1])) +
											(6 * (1 - t) * t * (control2[1] - control1[1])) +
											(3 * Math.pow(t, 2) * (end[1] - control2[1]));

		return Math.atan2(tangentY, tangentX) * (180 / Math.PI);
	}
}


// draw a quadratic bezier curve
function drawQuadratic(quadratic) {
	const gQuadratic = g.append('g')
		.attr('class', 'quadratic');

	gQuadratic.append('text')
		.text('Quadratic Bezier')
		.attr('dy', '0.4em')

	// draw the points
	gQuadratic.append('circle')
		.attr('r', 5)
		.attr('class', 'start-point')
		.attr('cx', quadratic.start[0])
		.attr('cy', quadratic.start[1])

	gQuadratic.append('circle')
		.attr('r', 5)
		.attr('class', 'end-point')
		.attr('cx', quadratic.end[0])
		.attr('cy', quadratic.end[1])

	gQuadratic.append('circle')
		.attr('r', 3)
		.attr('class', 'control-point')
		.attr('cx', quadratic.control[0])
		.attr('cy', quadratic.control[1])

	// draw the path
	gQuadratic.append('path')
		.attr('class', 'curve')
		.attr('d', quadraticPath(quadratic));

	const quadraticInterpolator = interpolateQuadraticBezier(quadratic.start, quadratic.control, quadratic.end);
	const interpolatedPoints = d3.range(10).map((d, i, a) => quadraticInterpolator(d / (a.length - 1)));

	gQuadratic.selectAll('.interpolated-point').data(interpolatedPoints)
		.enter()
			.append('circle')
				.attr('class', 'interpolated-point')
				.attr('r', 3)
				.attr('cx', d => d[0])
				.attr('cy', d => d[1]);


	const quadraticAngleInterpolator = interpolateQuadraticBezierAngle(quadratic.start, quadratic.control, quadratic.end);

	const rotatedPoints = d3.range(3).map((d, i, a) => {
		const t = d / (a.length - 1);
		return {
			t: t,
			position: quadraticInterpolator(t),
			angle: quadraticAngleInterpolator(t),
		};
	});

	gQuadratic.selectAll('.rotated-point').data(rotatedPoints)
		.enter()
			.append('path')
				.attr('d', 'M12,0 L-5,-8 L0,0 L-5,8 Z')
				.attr('class', 'rotated-point')
				.attr('transform', d => `translate(${d.position[0]}, ${d.position[1]}) rotate(${d.angle})`)


	console.log('QUADRATIC');
	console.log(JSON.stringify(quadratic));
	console.log(JSON.stringify(rotatedPoints, null, 2))

	return gQuadratic;
}


function drawCubic(cubic) {
	const gCubic = g.append('g')
		.attr('class', 'cubic')
		.attr('transform', 'translate(250, 0)');

	gCubic.append('text')
		.text('Cubic Bezier')
		.attr('dy', '0.4em')

	// draw the points
	gCubic.append('circle')
		.attr('r', 5)
		.attr('class', 'start-point')
		.attr('cx', cubic.start[0])
		.attr('cy', cubic.start[1])

	gCubic.append('circle')
		.attr('r', 5)
		.attr('class', 'end-point')
		.attr('cx', cubic.end[0])
		.attr('cy', cubic.end[1])

	gCubic.append('circle')
		.attr('r', 3)
		.attr('class', 'control-point')
		.attr('cx', cubic.control1[0])
		.attr('cy', cubic.control1[1])

	gCubic.append('circle')
		.attr('r', 3)
		.attr('class', 'control-point')
		.attr('cx', cubic.control2[0])
		.attr('cy', cubic.control2[1])

	// draw the path
	gCubic.append('path')
		.attr('class', 'curve')
		.attr('d', cubicPath(cubic));

	const cubicInterpolator = interpolateCubicBezier(cubic.start, cubic.control1, cubic.control2, cubic.end);
	const interpolatedPoints = d3.range(10).map((d, i, a) => cubicInterpolator(d / (a.length - 1)));

	gCubic.selectAll('.interpolated-point').data(interpolatedPoints)
		.enter()
			.append('circle')
				.attr('class', 'interpolated-point')
				.attr('r', 3)
				.attr('cx', d => d[0])
				.attr('cy', d => d[1]);


	const cubicAngleInterpolator = interpolateCubicBezierAngle(cubic.start, cubic.control1, cubic.control2, cubic.end);

	const rotatedPoints = d3.range(3).map((d, i, a) => {
		const t = d / (a.length - 1);
		return {
			t: t,
			position: cubicInterpolator(t),
			angle: cubicAngleInterpolator(t),
		};
	});

	gCubic.selectAll('.rotated-point').data(rotatedPoints)
		.enter()
			.append('path')
				.attr('d', 'M12,0 L-5,-8 L0,0 L-5,8 Z')
				.attr('class', 'rotated-point')
				.attr('transform', d => `translate(${d.position[0]}, ${d.position[1]}) rotate(${d.angle})`)


	console.log('CUBIC');
	console.log(JSON.stringify(cubic));
	console.log(JSON.stringify(rotatedPoints, null, 2))

	return gCubic;
}


const quadratic = { start: [0, 70], end: [200, 100], control: [160, 20] };
drawQuadratic(quadratic);

const cubic = { start: [0, 70], end: [200, 100], control1: [40, 180], control2: [160, 20] };
drawCubic(cubic);

style.css

.start-point {
  fill: #fff;
  stroke: #0bb;
}

.end-point {
  fill: #fff;
  stroke: #0bb;
}

.control-point {
  fill: tomato;
}

.curve {
  fill: none;
  stroke: #0bb;
  stroke-width: 2px;
}

.interpolated-point {
  fill: #077;
}

.rotated-point {
  fill: #af84e6;
  stroke: #660cd0;
}

thumbnail.png

Thank you very much for the good demo. You solution helped to implement proper rotation (orientation) of arrowheads with reactflow.dev library.

Awesome, thanks for sharing!