Interpolate path
Created
June 9, 2020 18:44
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Metaball interpolation
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<html> | |
<header> | |
<title>Metaballs PIXIjs</title> | |
<style> | |
html, body { | |
margin: 0; | |
font-family: sans-serif; | |
} | |
</style> | |
</header> | |
<body> | |
<svg width="960" height="500"> | |
<g transform="translate(480,250)"> | |
<!-- elements will be inserted here --> | |
</g> | |
</svg> | |
<script src="https://d3js.org/d3.v5.min.js"></script> | |
<script> | |
// some sample data | |
let data=[ | |
{x:40, y:0, r:10}, | |
{x:20, y:40, r:15}, | |
{x:-20, y:40, r:20}, | |
{x:-40, y:0, r:25}, | |
{x:-20, y:-40, r:6}, | |
{x:20, y:-40, r:12} | |
] | |
data.forEach(d=>d.c=[d.x,d.y]); | |
let d=''; | |
for (let i=0; i<data.length; i++) { | |
const circles = data.slice(0,3); | |
data.push(data.shift()); | |
// calculate points and handles for metaball path | |
const pointsAndHandles=curvesBetweenCircles(circles[0].r, circles[1].r, circles[0].c, circles[1].c); | |
// calculate for the next one, to draw arch (this could be optimized) | |
const next=curvesBetweenCircles(circles[1].r, circles[2].r, circles[1].c, circles[2].c); | |
// set the starting point of the path ONLY in case it is the first circle | |
if (i===0) d+=`M ${pointsAndHandles.p[1][0]},${pointsAndHandles.p[1][1]} `; | |
// draw bezier curve and arc | |
d+=`C ${pointsAndHandles.h[1][0]},${pointsAndHandles.h[1][1]} ${pointsAndHandles.h[3][0]},${pointsAndHandles.h[3][1]} ${pointsAndHandles.p[3][0]},${pointsAndHandles.p[3][1]}` | |
d+=`A ${next.r1}, ${next.r1}, 1, 0, 1, ${next.p[1][0]}, ${next.p[1][1]}` | |
} | |
// close the path | |
d+='Z' | |
// draw the path | |
d3.select('svg > g') | |
.append('path') | |
.attr('d',d) | |
.attr('fill','#CDDC39') | |
.attr('stroke','#7CB342'); | |
// draw the circles and numbers for visual feedback | |
data.forEach((c,i)=>{ | |
d3.select('svg > g') | |
.append('circle') | |
.attr('r',c.r) | |
.attr('cx',c.x) | |
.attr('cy',c.y) | |
.attr('fill','rgba(255,255,255,0.4)'); | |
d3.select('svg > g') | |
.append('text') | |
.attr('x',c.x) | |
.attr('y',c.y+3) | |
.attr('text-anchor','middle') | |
.attr('font-size','9') | |
.text(i) | |
}) | |
/** | |
* Based on Metaball script by SATO Hiroyuki | |
* http://shspage.com/aijs/en/#metaball | |
*/ | |
function curvesBetweenCircles(radius1, radius2, center1, center2, handleSize = 2.4, v = 0.5) { | |
const HALF_PI = Math.PI / 2; | |
const d = dist(center1, center2); | |
let u1 = 0, u2 = 0; | |
if (radius1 === 0 || radius2 === 0 || d <= Math.abs(radius1 - radius2)) { | |
return null; | |
} | |
if (d < radius1 + radius2) { | |
u1 = Math.acos( | |
(radius1 * radius1 + d * d - radius2 * radius2) / (2 * radius1 * d), | |
); | |
u2 = Math.acos( | |
(radius2 * radius2 + d * d - radius1 * radius1) / (2 * radius2 * d), | |
); | |
} | |
// All the angles | |
const angleBetweenCenters = angle(center2, center1); | |
const maxSpread = Math.acos((radius1 - radius2) / d); | |
const angle1 = angleBetweenCenters + u1 + (maxSpread - u1) * v; | |
const angle2 = angleBetweenCenters - u1 - (maxSpread - u1) * v; | |
const angle3 = angleBetweenCenters + Math.PI - u2 - (Math.PI - u2 - maxSpread) * v; | |
const angle4 = angleBetweenCenters - Math.PI + u2 + (Math.PI - u2 - maxSpread) * v; | |
// Points | |
const p1 = getVector(center1, angle1, radius1); | |
const p2 = getVector(center1, angle2, radius1); | |
const p3 = getVector(center2, angle3, radius2); | |
const p4 = getVector(center2, angle4, radius2); | |
// Define handle length by the | |
// distance between both ends of the curve | |
const totalRadius = radius1 + radius2; | |
const d2Base = Math.min(v * handleSize, dist(p1, p3) / totalRadius); | |
// Take into account when circles are overlapping | |
const d2 = d2Base * Math.min(1, d * 2 / (radius1 + radius2)); | |
const r1 = radius1 * d2; | |
const r2 = radius2 * d2; | |
const h1 = getVector(p1, angle1 - HALF_PI, r1); | |
const h2 = getVector(p2, angle2 + HALF_PI, r1); | |
const h3 = getVector(p3, angle3 + HALF_PI, r2); | |
const h4 = getVector(p4, angle4 - HALF_PI, r2); | |
return { | |
p : [ p1, p2, p3, p4 ], | |
h : [ h1, h2, h3, h4 ], | |
escaped : d > radius1, | |
r : radius2, | |
r1 : radius1 | |
} | |
} | |
/** | |
* Utils | |
*/ | |
function moveTo([x, y] = [0, 0], element) { | |
element.setAttribute('cx', x); | |
element.setAttribute('cy', y); | |
} | |
function line([x1, y1] = [0, 0], [x2, y2] = [0, 0], element) { | |
element.setAttribute('x1', x1); | |
element.setAttribute('y1', y1); | |
element.setAttribute('x2', x2); | |
element.setAttribute('y2', y2); | |
} | |
function dist([x1, y1], [x2, y2]) { | |
return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5; | |
} | |
function angle([x1, y1], [x2, y2]) { | |
return Math.atan2(y1 - y2, x1 - x2); | |
} | |
function getVector([cx, cy], a, r) { | |
return [cx + r * Math.cos(a), cy + r * Math.sin(a)]; | |
} | |
</script> | |
</body> | |
</html> |
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