Published
Edited
Apr 18, 2020
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Mathematical Easter Egg Coloring
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WebGL
drawEgg = regl({
vert: `
precision highp float;
attribute vec3 aPosition, aNormal;
uniform mat4 projectionView;
uniform float time;
varying vec3 position, normal;
void main () {
position = aPosition;
normal = aNormal;
gl_Position = projectionView * vec4(position, 1);
}
`,
frag: `
precision highp float;
varying vec3 position, normal;
uniform vec3 eye; // Position of the camera, for use in lighting
uniform float time;
vec3 applyGamma (vec3 c, float gamma) {
return vec3(pow(c.r, gamma), pow(c.g, gamma), pow(c.b, gamma));
}
void main () {
// Define your coloring function here!
vec3 color = vec3(
0.5 +
0.3 * cos(position * 5.0) *
sin(position * 10.0 - 4.0 * time)
);
gl_FragColor = vec4(applyGamma(color, (1.0 / 2.2)), 1);
}
`,
attributes: {
aPosition: regl.prop('positions'),
aNormal: regl.prop('normals')
},
cull: { enable: true, face: 'back' },
elements: regl.prop('cells')
})
function egg(x, y, z) {
return y * y + Math.pow(1.2, y * 2) * 1.9 * (x * x + z * z) - 1;
}
domain = [[-1, 1], [-1, 1], [-1, 1]]
resolution = [100, 100, 100]
mesh = {
// Precompute the offset and slope so that converting grid coordinates to scalars is a bit faster.
const b = domain.map((b, i) => [b[0], (b[1] - b[0]) / (resolution[i] - 1)]);
// Use ndarray-proxy to create an ndarray that lazily returns the values of the function on a grid
const gridValues = ndarrayProxy(resolution, (i, j, k) =>
egg(b[0][0] + i * b[0][1], b[1][0] + j * b[1][1], b[2][0] + k * b[2][1])
);
const mesh = surfaceNets(gridValues);
// The positions in the mesh above are all in terms of grid coordinates.
// We scale them to our domain.
for (var i = 0; i < mesh.positions.length; i++) {
const p = mesh.positions[i];
p[0] = b[0][0] + b[0][1] * p[0];
p[1] = b[1][0] + b[1][1] * p[1];
p[2] = b[2][0] + b[2][1] * p[2];
}
mesh.normals = angleNormals(mesh.cells, mesh.positions);
return mesh;
}
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