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SDF Shadows

Video Lecture

Section Video Links
SDF Shadows SDF Shadows SDF Shadows

Description

We will implement hard and soft edged shadows.

After the diffuse has been calculated for a position, we can cast a shadow ray from that position towards the light source.

const shadow = shadowMarcher(position.add(normal.mul(surfaceDistance)), vec3(lightDirection))

To start off, set the shadow value to 1. This will later be multiplied to the diffuse.

const shadow = float(1).toVar()

March along the shadow ray and check the distance to objects.

Loop({ start: 0, end: maxSteps }, () => {
    const distance = sdfScene(rayOrigin.add(rayDirection.mul(accumulatedDistance)))
    // ...

If the distance hits an object, we can set the shadow to 0 and exit the loop.

The 0 will be multiplied to the diffuse and cause it to become black.

    If(abs(distance).lessThan(surfaceDistance), () => {
        shadow.assign(0)
        Break()
    }).Else(() => {
    // ...

For a hard shadow, we iterate through the loop add add the distance to the accumulatedDistance.

We continue until we hit a surface and set the shadow to 0.

    accumulatedDistance.addAssign(distance)

Or for a soft shadow, if the ray is close to an object, we darken the pixel proportionally based on how obstructed it is.

The calculation is based on how far away the obstacle is and the current accumulated distance.

    shadow.assign(min(shadow, shadowSoftness.mul(distance).div(accumulatedDistance)))
    accumulatedDistance.addAssign(clamp(distance, surfaceDistance, 0.025))

If when marching we go outside the camera far, then we break the loop with the shadow value unchanged at 1.

With the final shadow value for this position calculated, we can multiply it to the already calculated diffuse.

diffuse.mulAssign(shadow)

Working Example

<>

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,
  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),
  // shadowSoftness: 20,
  // shadowIntensity: 0.1
  // shadowMaxSteps: 256,
  // shadowFar: 128
}

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)
// const shadowSoftness = uniform(options.shadowSoftness)
// const shadowIntensity = uniform(options.shadowIntensity)
//const shadowMaxSteps = uniform(options.shadowMaxSteps)
//const shadowFar = uniform(options.shadowFar)

// @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 floor = position.y

  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 = floor.toVar()
  distance.assign(min(distance, sphere))
  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 shadowMarcher = Fn(([rayOrigin, rayDirection]) => {
//   const shadow = float(1).toVar()
//   const accumulatedDistance = float(cameraNear).toVar()

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

//     If(abs(distance).lessThan(surfaceDistance), () => {
//       shadow.assign(0)
//       Break()
//     }).Else(() => {
//       shadow.assign(min(shadow, shadowSoftness.mul(distance).div(accumulatedDistance))) //softens shadow
//       accumulatedDistance.addAssign(clamp(distance, surfaceDistance, 0.025)) // works better for soft shadows
//       //accumulatedDistance.addAssign(distance) // works better for hard shadows

//       If(accumulatedDistance.greaterThan(cameraFar), () => {
//         Break()
//       })
//     })
//   })

//   return shadow
// })

// @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)
    const lightPosition = vec3(sin(time).mul(5), 3, cos(time).mul(5))
    const lightDirection = normalize(lightPosition.sub(position))
    const diffuse = clamp(dot(normal, lightDirection), 0, 1).toVar()

    //const shadow = shadowMarcher(position.add(normal.mul(surfaceDistance)), vec3(lightDirection))
    //shadow.assign(max(shadowIntensity, shadow))

    //diffuse.mulAssign(shadow)

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

    const viewDirection = normalize(rayOrigin.sub(position))
    const shineDirection = reflect(lightDirection.negate(), normal)

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

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

  return finalColour
})

scene.backgroundNode = main()

const gui = new GUI()

const raymarchFolder = gui.addFolder('Raymarching')
raymarchFolder
  .add(options, 'zoom', 0, 10, 0.001)
  .name('Zoom')
  .onChange((v) => {
    zoom.value = v
  })
raymarchFolder
  .add(options, 'maxSteps', 1, 512, 1)
  .name('Raymarch Max Steps')
  .onChange((v) => {
    maxSteps.value = v
  })
raymarchFolder
  .add(options, 'surfaceDistance', 0, 0.001, 0.0001)
  .name('Surface Distance')
  .onChange((v) => {
    surfaceDistance.value = v
  })
raymarchFolder
  .add(options, 'cameraNear', 0.0001, 10, 0.1)
  .name('Camera Near')
  .onChange((v) => {
    cameraNear.value = v
  })
raymarchFolder
  .add(options, 'cameraFar', 1, 512, 0.1)
  .name('Camera Far')
  .onChange((v) => {
    cameraFar.value = v
  })
raymarchFolder.close()

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

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

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

const shadowFolder = gui.addFolder('Shadows')
// shadowFolder
//   .add(options, 'shadowSoftness', 0, 100, 0.01)
//   .name('Shadow Softness')
//   .onChange((v) => {
//     shadowSoftness.value = v
//   })
// shadowFolder
//   .add(options, 'shadowIntensity', 0, 1, 0.01)
//   .name('Shadow Intensity')
//   .onChange((v) => {
//     shadowIntensity.value = v
//   })
// shadowFolder
//   .add(options, 'shadowMaxSteps', 1, 512, 1)
//   .name('Shadow Max Steps')
//   .onChange((v) => {
//     shadowMaxSteps.value = v
//   })
// shadowFolder
//   .add(options, 'shadowFar', 1, 512, 0.1)
//   .name('Shadow Far')
//   .onChange((v) => {
//     shadowFar.value = v
//   })
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,
  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),
  shadowSoftness: 20,
  shadowIntensity: 0.1,
  shadowMaxSteps: 256,
  shadowFar: 128,
}

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)
const shadowSoftness = uniform(options.shadowSoftness)
const shadowIntensity = uniform(options.shadowIntensity)
const shadowMaxSteps = uniform(options.shadowMaxSteps)
const shadowFar = uniform(options.shadowFar)

// @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 floor = position.y

  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 = floor.toVar()
  distance.assign(min(distance, sphere))
  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 shadowMarcher = Fn(([rayOrigin, rayDirection]) => {
  const shadow = float(1).toVar()
  const accumulatedDistance = float(cameraNear).toVar()

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

    If(abs(distance).lessThan(surfaceDistance), () => {
      shadow.assign(0)
      Break()
    }).Else(() => {
      shadow.assign(
        min(shadow, shadowSoftness.mul(distance).div(accumulatedDistance))
      ) //softens shadow
      accumulatedDistance.addAssign(clamp(distance, surfaceDistance, 0.025)) // works better for soft shadows
      //accumulatedDistance.addAssign(distance) // works better for hard shadows

      If(accumulatedDistance.greaterThan(shadowFar), () => {
        Break()
      })
    })
  })

  return shadow
})

// @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)
    const lightPosition = vec3(sin(time).mul(5), 3, cos(time).mul(5))
    const lightDirection = normalize(lightPosition.sub(position))
    const diffuse = clamp(dot(normal, lightDirection), 0, 1).toVar()

    const shadow = shadowMarcher(
      position.add(normal.mul(surfaceDistance)),
      vec3(lightDirection)
    )
    shadow.assign(max(shadowIntensity, shadow))

    diffuse.mulAssign(shadow)

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

    const viewDirection = normalize(rayOrigin.sub(position))
    const shineDirection = reflect(lightDirection.negate(), normal)

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

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

  return finalColour
})

scene.backgroundNode = main()

const gui = new GUI()

const raymarchFolder = gui.addFolder('Raymarching')
raymarchFolder
  .add(options, 'zoom', 0, 10, 0.001)
  .name('Zoom')
  .onChange((v) => {
    zoom.value = v
  })
raymarchFolder
  .add(options, 'maxSteps', 1, 512, 1)
  .name('Raymarch Max Steps')
  .onChange((v) => {
    maxSteps.value = v
  })
raymarchFolder
  .add(options, 'surfaceDistance', 0, 0.001, 0.0001)
  .name('Surface Distance')
  .onChange((v) => {
    surfaceDistance.value = v
  })
raymarchFolder
  .add(options, 'cameraNear', 0.0001, 10, 0.1)
  .name('Camera Near')
  .onChange((v) => {
    cameraNear.value = v
  })
raymarchFolder
  .add(options, 'cameraFar', 1, 512, 0.1)
  .name('Camera Far')
  .onChange((v) => {
    cameraFar.value = v
  })
raymarchFolder.close()

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

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

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

const shadowFolder = gui.addFolder('Shadows')
shadowFolder
  .add(options, 'shadowSoftness', 0, 100, 0.01)
  .name('Shadow Softness')
  .onChange((v) => {
    shadowSoftness.value = v
  })
shadowFolder
  .add(options, 'shadowIntensity', 0, 1, 0.01)
  .name('Shadow Intensity')
  .onChange((v) => {
    shadowIntensity.value = v
  })
shadowFolder
  .add(options, 'shadowMaxSteps', 1, 512, 1)
  .name('Shadow Max Steps')
  .onChange((v) => {
    shadowMaxSteps.value = v
  })
shadowFolder
  .add(options, 'shadowFar', 1, 512, 0.1)
  .name('Shadow Far')
  .onChange((v) => {
    shadowFar.value = v
  })
function animate() {
  controls.update()

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

  renderer.render(scene, camera)
}