Spherical Harmonics Shader (Three.js Coordinates)

This time using the equations / coordinate system used in THREE.SphericalHarmonics3

by Matt

HTML

<base href="https://rawcdn.githack.com/mrdoob/three.js/r152/examples/" />
<script async src="https://cdn.jsdelivr.net/npm/[email protected]/dist/es-module-shims.js"></script>
<script type="importmap">
	{
		"imports": {
			"three": "https://cdn.jsdelivr.net/npm/[email protected]/build/three.module.js",
			"three/addons/": "https://cdn.jsdelivr.net/npm/[email protected]/examples/jsm/",
			"lil-gui": "https://cdn.jsdelivr.net/npm/[email protected]/dist/lil-gui.esm.min.js"
		}
	}
</script>

<template id="vertex-shader">

varying vec3 vPosition;

void main() {
  vPosition = position;
  
  gl_Position = projectionMatrix * modelViewMatrix * vec4(position, 1.0);
}
</template>

<template id="fragment-shader">

#define WHITE vec3(1., 1., 1.)


// Reference: https://www.shadertoy.com/view/lsfXWH

uniform vec3 colorPos;
uniform vec3 colorNeg;

uniform float f0_0;

uniform float f1_0;
uniform float f1_1;
uniform float f1_2;

uniform float f2_0;
uniform float f2_1;
uniform float f2_2;
uniform float f2_3;
uniform float f2_4;

varying vec3 vPosition;

vec3 color_ramp(float x) {
  float step0 = -1.0;
  float step1 = 0.0;
  float step2 = 1.0;

  vec3 color;
  color = mix(colorNeg, WHITE, smoothstep(step0, step1, x));
  color = mix(color, colorPos, smoothstep(step1, step2, x));

  return color;
}

float SH3(vec3 normal, float[9] coeff) {
  float target;
  float x = normal.x, y = normal.y, z = normal.z;
  
  // band 0
  target += coeff[ 0 ] * 0.282095;
  
  // band 1
  target += coeff[ 1 ] * 0.488603 * y;
  target += coeff[ 2 ] * 0.488603 * z;
  target += coeff[ 3 ] * 0.488603 * x;
  
  // band 2
  target += coeff[ 4 ] * 1.092548 * ( x * y );
  target += coeff[ 5 ] * 1.092548 * ( y * z );
  target += coeff[ 6 ] * 0.315392 * ( 3.0 * z * z - 1.0 );
  target += coeff[ 7 ] * 1.092548 * ( x * z );
  target += coeff[ 8 ] * 0.546274 * ( x * x - y * y );
  
  return target;
}

void main() {
  
  float factor = 0.;
  
  float[9] coeff = float[9](f0_0, f1_0, f1_1, f1_2, f2_0, f2_1, f2_2, f2_3,...

CSS

canvas {
	position: fixed;
	inset: 0;
}

JavaScript

/**
 * Reference: https://www.shadertoy.com/view/lsfXWH
 */

import * as THREE from 'three'
import { OrbitControls } from 'three/addons/controls/OrbitControls.js'
import { GUI } from 'lil-gui'

let scene, camera, renderer
let mesh, orbitControls, clock
let params

init().then(animate)

async function init() {

	params = {
		colorPos: "#ff0000",
		colorNeg: "#0000ff",
    l0: [0],
    l1: [0,0,0],
    l2: [0,0,0,0,0],
	}
	
	scene = new THREE.Scene()
	scene.background = new THREE.Color('black')

	camera = new THREE.PerspectiveCamera(75, undefined, 0.1, 1000)
	camera.position.set(1, 2, 3)
	
	clock = new THREE.Clock()

	const directionalLight = new THREE.DirectionalLight('white')
	directionalLight.position.set(2, 3, 4)
	scene.add(directionalLight)

	const ambientLight = new THREE.AmbientLight('white', 0.3)
	scene.add(ambientLight)

	renderer = new THREE.WebGLRenderer({ antialias: true })
	document.body.appendChild(renderer.domElement)

	orbitControls = new OrbitControls(camera, renderer.domElement)

	const grid = new THREE.GridHelper()
	grid.position.y = -1
	scene.add(grid)
  
  const axes = new THREE.AxesHelper(2)
  //scene.add(axes)
  
  const vertexShader = document.querySelector("#vertex-shader").content.textContent
  const fragmentShader = document.querySelector("#fragment-shader").content.textContent
	const uniforms = {
  	colorPos: { value: new THREE.Color(params.colorPos) },
  	colorNeg: { value: new THREE.Color(params.colorNeg) },
    f0_0: { value: params.l0[0] },
    f1_0: { value: params.l1[0] },
    f1_1: { value: params.l1[1] },
    f1_2: { value: params.l1[2] },
    f2_0: { value: params.l2[0] },
    f2_1: { value: params.l2[1] },
    f2_2: { value: params.l2[2] },
    f2_3: { value: params.l2[3] },
    f2_4: { value: params.l2[4] },
  }
  
	const geometry = new THREE.SphereGeometry(1, 128, 64)
	const material = new THREE.ShaderMaterial({
  	uniforms,
  	vertexShader,
    fragmentShader,
  })
  
	mesh = new THREE.Mesh(geometry,...