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Lighting 3D SDFs

Video Lecture

Section Video Links
Lighting 3D SDFs Lighting 3D SDFs

Description

In this lesson we will add,

  • Lambertian Reflectance,

  • Ambient Lighting,

  • Phong Specular Reflection

Working Example

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Lambertian Reflectance

Lambertian reflectance is a simple diffuse lighting model where the intensity of light reflected off a surface is proportional to the cosine of the angle between the surface normal and the light direction.

const normal = getNormal(position, distance)

const lightPosition = vec3(5, 5, 5) // Position the light in the 3D scene
const lightDirection = normalize(lightPosition.sub(position)) // Normalize the direction to the light source
const diffuse = clamp(dot(normal, lightDirection), 0, 1) // Get the dot product of the normal and lightDirection. The closer these two values are together, the brighter the color to return.

const finalColour = diffuse

return finalColour

Ambient lighting

Ambient lighting simulates indirect lighting by providing a base level of illumination, regardless of the light direction.

Adding ambient lighting will allow us to see the parts of the scene that are hidden from the light.

const normal = getNormal(position, distance)

const lightPosition = vec3(5, 5, 5)
const lightDirection = normalize(lightPosition.sub(position))
const diffuse = clamp(dot(normal, lightDirection), 0, 1)

const ambientStrength = 0.01 // Adjust to control the ambient effect
const ambient = vec3(1).mul(ambientStrength)

const finalColour = diffuse.add(ambient)

return finalColour

Now with the ambient, it also lights the background. We can override the background. I.e, the part where the accumulatedDistance is greater than cameraFar.

We can set a default color, black in this example, and then only color with diffuse and ambient where the raymarcher hit a shape in the scene.

const finalColour = vec3(0).toVar()

If(accumulatedDistance.lessThan(cameraFar), () => {
  const normal = getNormal(position, distance)

  const lightPosition = vec3(5, 5, 5)
  const lightDirection = normalize(lightPosition.sub(position))
  const diffuse = clamp(dot(normal, lightDirection), 0, 1)

  const ambientStrength = 0.01
  const ambient = vec3(1).mul(ambientStrength)

  finalColour.assign(diffuse.add(ambient))
})

return finalColour

Phong Specular Reflection

The Phong reflection model adds a specular calculation to simulate shiny surfaces.

We will calculate the direction from the hit surface to the position of the camera (ray origin).

We will be able to manage the shininess, strength and colour of the specular reflection.

const viewDirection = normalize(rayOrigin.sub(position)) // Camera direction // ray origin
const shineDirection = reflect(lightDirection.negate(), normal) // Reflect light about the normal

const shininess = 32.0 // Higher = sharper highlights
const specularStrength = 0.5 // Controls how intense the specular reflection is

const specularIntensity = pow(
  clamp(dot(viewDirection, shineDirection), 0.0, 1.0),
  shininess
).mul(specularStrength)
const specularColour = vec3(1.0, 0.05, 0.3) // Tint for the specular highlights (warm tone)
const specularComponent = specularColour.mul(specularIntensity) // Apply color tint

finalColour.assign(ambient.add(diffuse).add(specularComponent))

In the video, we will also add GUI controls to manage the ambientStrength, shininess, specularStrength, specularColour, ambientColour and diffuseColour.

finalColour.assign(ambientColour.mul(ambient).add(diffuseColour.mul(diffuse)).add(specularComponent))

Start Script

./src/main.ts

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import './style.css'
import * as THREE from 'three/webgpu'
import {
  positionLocal,
  Fn,
  If,
  Loop,
  Break,
  float,
  vec2,
  vec3,
  min,
  max,
  length,
  normalize,
  cross,
  dot,
  time,
  sin,
  cos,
  abs,
  negate,
  uniform,
  pow,
  reflect,
  mix,
  color,
  clamp,
} from 'three/tsl'
import { OrbitControls } from 'three/addons/controls/OrbitControls.js'
import { GUI } from 'three/addons/libs/lil-gui.module.min.js'

const scene = new THREE.Scene()

const camera = new THREE.PerspectiveCamera(
  53,
  window.innerWidth / window.innerHeight,
  0.1,
  1000
)
camera.position.set(-5, 5, 4)

const renderer = new THREE.WebGPURenderer()
renderer.setSize(window.innerWidth, window.innerHeight)
document.body.appendChild(renderer.domElement)
renderer.setAnimationLoop(animate)

window.addEventListener('resize', function () {
  camera.aspect = window.innerWidth / window.innerHeight
  camera.updateProjectionMatrix()
  renderer.setSize(window.innerWidth, window.innerHeight)
})

const controls = new OrbitControls(camera, renderer.domElement)
controls.enableDamping = true
controls.target.y = 0.25

const options = {
  zoom: 0,
  maxSteps: 256,
  surfaceDistance: 0.0001,
  cameraNear: 0.1,
  cameraFar: 128.0,
  // ambientStrength: 0.01,
  // shininess: 32,
  // specularStrength: 0.5,
  // diffuseColour: new THREE.Color(0.1, 0.4, 1.0),
  // specularColour: new THREE.Color(1.0, 0.05, 0.3),
  // ambientColour: new THREE.Color(0.2, 1, 0.2)
}

const camPos = uniform(new THREE.Vector3())
const camTarget = uniform(new THREE.Vector3())
const zoom = uniform(options.zoom)
const maxSteps = uniform(options.maxSteps)
const surfaceDistance = uniform(options.surfaceDistance)
const cameraNear = uniform(options.cameraNear)
const cameraFar = uniform(options.cameraFar)
// const ambientStrength = uniform(options.ambientStrength)
// const shininess = uniform(options.shininess)
// const specularStrength = uniform(options.specularStrength)
// const diffuseColour = uniform(options.diffuseColour)
// const specularColour = uniform(options.specularColour)
// const ambientColour = uniform(options.ambientColour)

// @ts-ignore
const rotateAroundAxis = Fn(([position, axis, radians]) => {
  axis = normalize(axis)

  const cosTheta = cos(radians)
  const sinTheta = sin(radians)

  const rotatedPoint = position
    .mul(cosTheta)
    .add(cross(axis, position).mul(sinTheta))
    .add(axis.mul(dot(axis, position).mul(cosTheta.oneMinus())))

  return rotatedPoint
})

// @ts-ignore
const Sphere = Fn(([position, radius]) => {
  return length(position).sub(radius)
})

// @ts-ignore
const Box = Fn(([position, dimensions]) => {
  const distance = abs(position).sub(dimensions)
  return length(max(distance, 0.0)).add(
    min(max(distance.x, max(distance.y, distance.z)), 0.0)
  )
})

// @ts-ignore
const IntersectedSphereBox = Fn(([position, radius]) => {
  const circle = length(position).sub(radius.add(0.33))
  const box = Box(position, vec3(radius))
  return max(circle, box)
})

// @ts-ignore
const SubtractedSphereBox = Fn(([position, radius]) => {
  const circle = length(position).sub(radius.add(0.33))
  const box = Box(position, vec3(radius))
  return max(negate(circle), box)
})

// @ts-ignore
const sdfScene = Fn(([position]) => {
  const t = 0 // time.mul(0.5)

  const sphere = Sphere(position.sub(vec3(1.5, 1, 1.5)), 1)

  const box = Box(
    rotateAroundAxis(position.sub(vec3(1.5, 1, -1.5)), vec3(1, 1, 0), t),
    vec3(1)
  )

  const intersectedSphereBox = IntersectedSphereBox(
    rotateAroundAxis(position.sub(vec3(-1.5, 1, -1.5)), vec3(0, 1, 0), t),
    1
  )
  const subtractedSphereBox = SubtractedSphereBox(
    rotateAroundAxis(position.sub(vec3(-1.5, 1, 1.5)), vec3(1, 0, 0), t),
    1
  )

  const distance = sphere.toVar()
  distance.assign(min(distance, box))
  distance.assign(min(distance, intersectedSphereBox))
  distance.assign(min(distance, subtractedSphereBox))

  return distance
})

// @ts-ignore
const getNormal = Fn(([position, distance]) => {
  const offset = vec2(0.025, 0)

  return normalize(
    distance.sub(
      vec3(
        sdfScene(position.sub(offset.xyy)),
        sdfScene(position.sub(offset.yxy)),
        sdfScene(position.sub(offset.yyx))
      )
    )
  )
})

// @ts-ignore
const main = Fn(() => {
  const p = positionLocal

  const rayOrigin = camPos
  const lookAt = camTarget

  const forward = normalize(lookAt.sub(rayOrigin))
  const rayDirection = normalize(p.add(forward.mul(zoom)))

  const accumulatedDistance = float(cameraNear).toVar()
  const distance = float(0).toVar()
  const position = vec3(0).toVar()

  // @ts-ignore
  Loop({ start: 0, end: maxSteps }, () => {
    position.assign(rayOrigin.add(rayDirection.mul(accumulatedDistance)))
    distance.assign(sdfScene(position))

    If(
      abs(distance)
        .lessThan(surfaceDistance)
        .or(accumulatedDistance.greaterThan(cameraFar)),
      () => {
        Break()
      }
    )

    accumulatedDistance.addAssign(distance)
  })

  const finalColour = getNormal(position, distance)

  return finalColour
})

scene.backgroundNode = main()

const gui = new GUI()
// gui
//   .add(options, 'ambientStrength', 0, 0.2, 0.01)
//   .name('Ambient Strength')
//   .onChange((v) => {
//     ambientStrength.value = v
//   })

// gui
//   .add(options, 'shininess', 0, 100, 0.1)
//   .name('Shininess')
//   .onChange((v) => {
//     shininess.value = v
//   })

// gui
//   .add(options, 'specularStrength', 0, 1, 0.01)
//   .name('SpecularStrength')
//   .onChange((v) => {
//     specularStrength.value = v
//   })
// gui.addColor(options, 'diffuseColour')
// gui.addColor(options, 'specularColour')
// gui.addColor(options, 'ambientColour')

function animate() {
  controls.update()

  camPos.value.copy(camera.position)
  camTarget.value.copy(controls.target)

  renderer.render(scene, camera)
}

Final Script

./src/main.ts

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import './style.css'
import * as THREE from 'three/webgpu'
import {
  positionLocal,
  Fn,
  If,
  Loop,
  Break,
  float,
  vec2,
  vec3,
  min,
  max,
  length,
  normalize,
  cross,
  dot,
  time,
  sin,
  cos,
  abs,
  negate,
  uniform,
  pow,
  reflect,
  mix,
  color,
  clamp,
} from 'three/tsl'
import { OrbitControls } from 'three/addons/controls/OrbitControls.js'
import { GUI } from 'three/addons/libs/lil-gui.module.min.js'

const scene = new THREE.Scene()

const camera = new THREE.PerspectiveCamera(
  53,
  window.innerWidth / window.innerHeight,
  0.1,
  1000
)
camera.position.set(-5, 5, 4)

const renderer = new THREE.WebGPURenderer()
renderer.setSize(window.innerWidth, window.innerHeight)
document.body.appendChild(renderer.domElement)
renderer.setAnimationLoop(animate)

window.addEventListener('resize', function () {
  camera.aspect = window.innerWidth / window.innerHeight
  camera.updateProjectionMatrix()
  renderer.setSize(window.innerWidth, window.innerHeight)
})

const controls = new OrbitControls(camera, renderer.domElement)
controls.enableDamping = true
controls.target.y = 0.25

const options = {
  zoom: 0,
  maxSteps: 256,
  surfaceDistance: 0.0001,
  cameraNear: 0.1,
  cameraFar: 128.0,
  ambientStrength: 0.01,
  shininess: 32,
  specularStrength: 0.5,
  diffuseColour: new THREE.Color(0.1, 0.4, 1.0),
  specularColour: new THREE.Color(1.0, 0.05, 0.3),
  ambientColour: new THREE.Color(0.2, 1, 0.2),
}

const camPos = uniform(new THREE.Vector3())
const camTarget = uniform(new THREE.Vector3())
const zoom = uniform(options.zoom)
const maxSteps = uniform(options.maxSteps)
const surfaceDistance = uniform(options.surfaceDistance)
const cameraNear = uniform(options.cameraNear)
const cameraFar = uniform(options.cameraFar)
const ambientStrength = uniform(options.ambientStrength)
const shininess = uniform(options.shininess)
const specularStrength = uniform(options.specularStrength)
const diffuseColour = uniform(options.diffuseColour)
const specularColour = uniform(options.specularColour)
const ambientColour = uniform(options.ambientColour)

// @ts-ignore
const rotateAroundAxis = Fn(([position, axis, radians]) => {
  axis = normalize(axis)

  const cosTheta = cos(radians)
  const sinTheta = sin(radians)

  const rotatedPoint = position
    .mul(cosTheta)
    .add(cross(axis, position).mul(sinTheta))
    .add(axis.mul(dot(axis, position).mul(cosTheta.oneMinus())))

  return rotatedPoint
})

// @ts-ignore
const Sphere = Fn(([position, radius]) => {
  return length(position).sub(radius)
})

// @ts-ignore
const Box = Fn(([position, dimensions]) => {
  const distance = abs(position).sub(dimensions)
  return length(max(distance, 0.0)).add(
    min(max(distance.x, max(distance.y, distance.z)), 0.0)
  )
})

// @ts-ignore
const IntersectedSphereBox = Fn(([position, radius]) => {
  const circle = length(position).sub(radius.add(0.33))
  const box = Box(position, vec3(radius))
  return max(circle, box)
})

// @ts-ignore
const SubtractedSphereBox = Fn(([position, radius]) => {
  const circle = length(position).sub(radius.add(0.33))
  const box = Box(position, vec3(radius))
  return max(negate(circle), box)
})

// @ts-ignore
const sdfScene = Fn(([position]) => {
  const t = time.mul(0.5)

  const sphere = Sphere(position.sub(vec3(1.5, 1, 1.5)), 1)

  const box = Box(
    rotateAroundAxis(position.sub(vec3(1.5, 1, -1.5)), vec3(1, 1, 0), t),
    vec3(1)
  )

  const intersectedSphereBox = IntersectedSphereBox(
    rotateAroundAxis(position.sub(vec3(-1.5, 1, -1.5)), vec3(0, 1, 0), t),
    1
  )
  const subtractedSphereBox = SubtractedSphereBox(
    rotateAroundAxis(position.sub(vec3(-1.5, 1, 1.5)), vec3(1, 0, 0), t),
    1
  )

  const distance = sphere.toVar()
  distance.assign(min(distance, box))
  distance.assign(min(distance, intersectedSphereBox))
  distance.assign(min(distance, subtractedSphereBox))

  return distance
})

// @ts-ignore
const getNormal = Fn(([position, distance]) => {
  const offset = vec2(0.025, 0)

  return normalize(
    distance.sub(
      vec3(
        sdfScene(position.sub(offset.xyy)),
        sdfScene(position.sub(offset.yxy)),
        sdfScene(position.sub(offset.yyx))
      )
    )
  )
})

// @ts-ignore
const main = Fn(() => {
  const p = positionLocal

  const rayOrigin = camPos
  const lookAt = camTarget

  const forward = normalize(lookAt.sub(rayOrigin))
  const rayDirection = normalize(p.add(forward.mul(zoom)))

  const accumulatedDistance = float(cameraNear).toVar()
  const distance = float(0).toVar()
  const position = vec3(0).toVar()

  // @ts-ignore
  Loop({ start: 0, end: maxSteps }, () => {
    position.assign(rayOrigin.add(rayDirection.mul(accumulatedDistance)))
    distance.assign(sdfScene(position))

    If(
      abs(distance)
        .lessThan(surfaceDistance)
        .or(accumulatedDistance.greaterThan(cameraFar)),
      () => {
        Break()
      }
    )

    accumulatedDistance.addAssign(distance)
  })

  const finalColour = vec3(0).toVar()

  If(accumulatedDistance.lessThan(cameraFar), () => {
    const normal = getNormal(position, distance)

    const lightPosition = vec3(5, 5, 5) // Position the light in the 3D scene
    const lightDirection = normalize(lightPosition.sub(position)) // Normalize the direction to the light source
    const diffuse = clamp(dot(normal, lightDirection), 0, 1) // Get the dot product of the normal and lightDirection. The closer these two values are together, the brighter the color to return.

    const ambient = vec3(1).mul(ambientStrength)

    const viewDirection = normalize(rayOrigin.sub(position)) // Camera direction // ray origin
    const shineDirection = reflect(lightDirection.negate(), normal) // Reflect light about the normal

    const specularIntensity = pow(
      clamp(dot(viewDirection, shineDirection), 0.0, 1.0),
      shininess
    ).mul(specularStrength)
    const specularComponent = specularColour.mul(specularIntensity) // Apply color tint

    finalColour.assign(
      ambientColour
        .mul(ambient)
        .add(diffuseColour.mul(diffuse))
        .add(specularComponent)
    )
  })

  return finalColour
})

scene.backgroundNode = main()

const gui = new GUI()
gui
  .add(options, 'ambientStrength', 0, 0.2, 0.01)
  .name('Ambient Strength')
  .onChange((v) => {
    ambientStrength.value = v
  })

gui
  .add(options, 'shininess', 0, 100, 0.1)
  .name('Shininess')
  .onChange((v) => {
    shininess.value = v
  })

gui
  .add(options, 'specularStrength', 0, 1, 0.01)
  .name('SpecularStrength')
  .onChange((v) => {
    specularStrength.value = v
  })
gui.addColor(options, 'diffuseColour')
gui.addColor(options, 'specularColour')
gui.addColor(options, 'ambientColour')

function animate() {
  controls.update()

  camPos.value.copy(camera.position)
  camTarget.value.copy(controls.target)

  renderer.render(scene, camera)
}