Three.js. How do I use a custom material for a scene background rather then color or texture?

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The docs for scene say a color or texture can be used for scene.background. I would like to use a ShaderMaterial with my own custom shaders. How can I do this?

Specifically, I want to paint a color ramp behind the foreground elements. Here is the fragment shader:

uniform vec2 uXYPixel;
void main() {
    vec2 xy = vec2(gl_FragCoord.x/uXYPixel.x, gl_FragCoord.y/uXYPixel.y);
    gl_FragColor.rgb = vec3(xy.x, xy.y, 0);
    gl_FragColor.a = 1.0;
}

uXYPixel is a uniform vec2 with the values window.innerWidth, window.innerHeight

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You'd need to manually create two render passes. One that renders the background plane with a simple Camera, and the second one that renders the rest of the scene. You can use the most basic Camera class since you won't be using transformation or projection matrices:

// Set renderer with no autoclear
var renderer = new THREE.WebGLRenderer();
renderer.autoClear = false;
document.body.append(renderer.domElement);
renderer.setSize(window.innerWidth, window.innerHeight);

// Set up background scene
var bgScene = new THREE.Scene();
var bgCam = new THREE.Camera();
var bgGeom = new THREE.PlaneBufferGeometry(2, 2);
var bgMat = new THREE.ShaderMaterial({
    // Add shader stuff in here
    // ..
    // Disable depth so it doesn't interfere with foreground scene
    depthTest: false,
    depthWrite: false
});
var bgMesh = new THREE.Mesh(bgGeom, bgMat);
bgScene.add(bgMesh);

// Set up regular scene
var scene = new THREE.Scene();
var cam = new THREE.PerspectiveCamera(45, w/h, 1, 100);

function update() {
    // Clear previous frame
    renderer.clear();

    // Background render pass
    renderer.render(bgScene, bgCam);

    // Foreground render pass
    renderer.render(scene, cam);

    requestAnimationFrame(update);
}

update();

Here you can see a working example.

Notice that the renderer's autoClear = false attribute makes sure it doesn't clear the buffer in between each render() call; you'll have to clear it manually at the beginning of each frame.