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# spite/superellipsoid

Last active Sep 2, 2021
distorts an icosahedron sphere into a superellipsoid
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 // https://en.wikipedia.org/wiki/Superellipsoid function c(w, m) { const cv = Math.cos(w); return Math.sign(cv) * Math.abs(cv) ** m; } function s(w, m) { const sv = Math.sin(w); return Math.sign(sv) * Math.abs(sv) ** m; } function getSuperEllipsoidPoint(theta, phi) { // radii const A = 1; const B = 1; const C = 1; // https://en.wikipedia.org/wiki/Superellipsoid#/media/File:Superellipsoid_collection.png // r = 2/e, t = 2/n const r = 4; const t = 4; const x = A * c(theta, 2 / t) * c(phi, 2 / r); const y = B * c(theta, 2 / t) * s(phi, 2 / r); const z = C * s(theta, 2 / t); return { x, y, z }; } const v0 = new Vector3(); const v1 = new Vector3(); const v2 = new Vector3(); function getSuperEllipsoidNormal(theta, phi) { const e = 0.00001; const { x: x0, y: y0, z: z0 } = getSuperEllipsoidPoint(theta, phi); const { x: x1, y: y1, z: z1 } = getSuperEllipsoidPoint(theta + e, phi); const { x: x2, y: y2, z: z2 } = getSuperEllipsoidPoint(theta, phi + e); v0.set(x0, y0, z0); v1.set(x1, y1, z1).sub(v0); v2.set(x2, y2, z2).sub(v0); v0.crossVectors(v1, v2); return { x: v0.x, y: v0.y, z: v0.z }; } function createSuperEllipsoid() { const geometry = new IcosahedronBufferGeometry(1, 10); const vertices = geometry.attributes.position.array; const normals = geometry.attributes.normal.array; const v = new Vector3(); for (let i = 0; i < vertices.length; i += 3) { v.set(vertices[i], vertices[i + 1], vertices[i + 2]); const theta = Math.atan2(Math.sqrt(v.x ** 2 + v.y ** 2), v.z) + Math.PI / 2; const phi = Math.atan2(v.y, v.x); const { x, y, z } = getSuperEllipsoidPoint(theta, phi); vertices[i] = x; vertices[i + 1] = y; vertices[i + 2] = z; const { x: nx, y: ny, z: nz } = getSuperEllipsoidNormal(theta, phi); normals[i] = nx; normals[i + 1] = ny; normals[i + 2] = nz; } return geometry; } const geometry2 = createSuperEllipsoid();
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