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Distance Lines

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Description

We can take colouring SDF scenes in different directions.

In this lesson, we will experiment with,

  • creating distance lines using different functions,
  • colouring them,
  • creating some more shapes,
  • more examples of union, subtraction and intersection.

Working Example

<>

Start Script

./src/main.ts

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import './style.css'
import * as THREE from 'three/webgpu'
import {
  positionLocal,
  length,
  vec2,
  abs,
  Fn,
  vec3,
  min,
  max,
  rotateUV,
  time,
  negate,
  select,
  sin,
  uniform,
  add,
  mul,
  cos,
  atan,
  ShaderNodeObject,
} 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(
  75,
  window.innerWidth / window.innerHeight,
  0.1,
  10
)
camera.position.z = 1.5

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

const Circle = Fn(
  ([position, radius]: [ShaderNodeObject<THREE.Node>, number]) => {
    return length(position).sub(radius)
  }
)

const Ellipse = Fn(
  ([position, radius, scale, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const scaledPosition = angledPosition.mul(scale)
    return length(scaledPosition).sub(radius)
  }
)

const Box = Fn(
  ([position, dimensions, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const distance = abs(angledPosition).sub(dimensions)
    return length(max(distance, 0.0)).add(
      min(max(distance.x, distance.y), 0.0)
    )
  }
)

const Flower = Fn(
  ([position, radius, frequency, amplitude, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const circleAngle = atan(angledPosition.y, angledPosition.x) // Get the angle around the circle
    const bumps = cos(circleAngle.mul(frequency)).mul(amplitude)
    return length(position).sub(radius).add(bumps)
  }
)

const Butterfly = Fn(
  ([position, radius, frequency, amplitude]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circleAngle = atan(position.y, position.x)
    const bumps = cos(circleAngle.mul(frequency)).mul(
      amplitude.mul(negate(position.y).mul(1.5).oneMinus())
    )
    return length(position).sub(radius).add(bumps)
  }
)

const Moon = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const innerCircle = length(
      angledPosition.div(0.8).sub(vec2(0.15, 0.0))
    ).sub(radius)
    const outerCircle = length(position).sub(radius)
    return max(negate(innerCircle), outerCircle) // subtraction
  }
)

const IntersectedCircleBox = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circle = length(position).sub(radius)
    const angledPosition = rotateUV(position, angle, vec2())
    const box = Box(
      angledPosition,
      vec2(radius.sub(0.025), radius.sub(0.025)),
      0
    )
    return max(circle, box)
  }
)

const UnionedCircleBox = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circle = length(position).sub(radius)
    const angledPosition = rotateUV(position, angle, vec2())
    const box = Box(
      angledPosition,
      vec2(radius.sub(0.025), radius.sub(0.025)),
      0
    )
    return min(circle, box)
  }
)

const options = {
  radius: 0.25,
  //fade: 12
}

const radius = uniform(options.radius)
//const fade = uniform(options.fade)

const main = Fn(() => {
  const p = positionLocal.xy
  const t = 0 //time.div(2)

  const circle = Circle(p.sub(vec2(-0.66, 0.66)), radius)

  const intersectedCircleBox = IntersectedCircleBox(
    p.sub(vec2(0, 0.66)),
    radius,
    t
  )

  const ellipse = Ellipse(p.sub(vec2(0.66, 0.66)), radius, vec2(1, 2), t)

  const flower = Flower(p.sub(vec2(-0.66, 0)), radius, 8, 0.1, t)

  const butterfly = Butterfly(p, radius, 4, 0.1)
  // const butterfly = Butterfly(vec2(p.x.div(sin(time.mul(2))), p.y), radius, 4, 0.1)

  const moon = Moon(p.sub(vec2(0.66, 0)), radius, t)

  const box = Box(p.sub(vec2(-0.66, -0.66)), vec2(radius, 0.25), negate(t))

  const unionedCircleBox = UnionedCircleBox(p.sub(vec2(0, -0.66)), radius, t)

  const torus = Circle(p.sub(vec2(0.66, -0.66)), radius)
    .abs()
    .sub(0.05)
  // const torus = Ellipse(p.sub(vec2(0.5, -0.5)), radius, vec2(1, 2), time).abs().sub(0.05)
  // const torus = Box(p.sub(vec2(0.66, -0.66)), vec2(radius, 0.25), t).abs().sub(0.05)

  const sdfScene = min(circle, intersectedCircleBox)
  sdfScene.assign(min(sdfScene, ellipse))
  sdfScene.assign(min(sdfScene, flower))
  sdfScene.assign(min(sdfScene, butterfly))
  sdfScene.assign(min(sdfScene, moon))
  sdfScene.assign(min(sdfScene, box))
  sdfScene.assign(min(sdfScene, unionedCircleBox))
  sdfScene.assign(min(sdfScene, torus))

  // const colour = vec3(1)

  // const finalColour = colour.mul(sdfScene)

  // return finalColour

  return sdfScene
})

const material = new THREE.NodeMaterial()
material.fragmentNode = main()

const mesh = new THREE.Mesh(new THREE.PlaneGeometry(2, 2), material)
scene.add(mesh)

const gui = new GUI()
gui.add(options, 'radius', 0, 1, 0.01).onChange((v) => {
  radius.value = v
})
// gui.add(options, 'fade', 0, 100, 0.01).onChange((v) => {
//   fade.value = v
// })

function animate() {
  controls.update()

  renderer.render(scene, camera)
}

Final Script

./src/main.ts

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import './style.css'
import * as THREE from 'three/webgpu'
import {
  positionLocal,
  length,
  vec2,
  abs,
  Fn,
  vec3,
  min,
  max,
  rotateUV,
  time,
  negate,
  select,
  sin,
  uniform,
  add,
  mul,
  cos,
  atan,
  ShaderNodeObject,
} 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(
  75,
  window.innerWidth / window.innerHeight,
  0.1,
  10
)
camera.position.z = 1.5

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

const Circle = Fn(
  ([position, radius]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    return length(position).sub(radius)
  }
)

const Ellipse = Fn(
  ([position, radius, scale, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const scaledPosition = angledPosition.mul(scale)
    return length(scaledPosition).sub(radius)
  }
)

const Box = Fn(
  ([position, dimensions, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const distance = abs(angledPosition).sub(dimensions)
    return length(max(distance, 0.0)).add(
      min(max(distance.x, distance.y), 0.0)
    )
  }
)

const Flower = Fn(
  ([position, radius, frequency, amplitude, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const circleAngle = atan(angledPosition.y, angledPosition.x) // Get the angle around the circle
    const bumps = cos(circleAngle.mul(frequency)).mul(amplitude)
    return length(position).sub(radius).add(bumps)
  }
)

const Butterfly = Fn(
  ([position, radius, frequency, amplitude]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circleAngle = atan(position.y, position.x)
    const bumps = cos(circleAngle.mul(frequency)).mul(
      amplitude.mul(negate(position.y).mul(1.5).oneMinus())
    )
    return length(position).sub(radius).add(bumps)
  }
)

const Moon = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const angledPosition = rotateUV(position, angle, vec2())
    const innerCircle = length(
      angledPosition.div(0.8).sub(vec2(0.15, 0.0))
    ).sub(radius)
    const outerCircle = length(position).sub(radius)
    return max(negate(innerCircle), outerCircle) // subtraction
  }
)

const IntersectedCircleBox = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circle = length(position).sub(radius)
    const angledPosition = rotateUV(position, angle, vec2())
    const box = Box(
      angledPosition,
      vec2(radius.sub(0.025), radius.sub(0.025)),
      0
    )
    return max(circle, box)
  }
)

const UnionedCircleBox = Fn(
  ([position, radius, angle]: [
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>,
    ShaderNodeObject<THREE.Node>
  ]) => {
    const circle = length(position).sub(radius)
    const angledPosition = rotateUV(position, angle, vec2())
    const box = Box(
      angledPosition,
      vec2(radius.sub(0.025), radius.sub(0.025)),
      0
    )
    return min(circle, box)
  }
)

const options = {
  radius: 0.25,
  fade: 12,
}

const radius = uniform(options.radius)
const fade = uniform(options.fade)

const main = Fn(() => {
  const p = positionLocal.xy
  const t = time.div(2)

  const circle = Circle(p.sub(vec2(-0.66, 0.66)), radius)

  const intersectedCircleBox = IntersectedCircleBox(
    p.sub(vec2(0, 0.66)),
    radius,
    t
  )

  const ellipse = Ellipse(p.sub(vec2(0.66, 0.66)), radius, vec2(1, 2), t)

  const flower = Flower(p.sub(vec2(-0.66, 0)), radius, 8, 0.1, t)

  //const butterfly = Butterfly(p, radius, 4, 0.1)
  const butterfly = Butterfly(
    vec2(p.x.div(sin(time.mul(2))), p.y),
    radius,
    4,
    0.1
  )

  const moon = Moon(p.sub(vec2(0.66, 0)), radius, t)

  const box = Box(p.sub(vec2(-0.66, -0.66)), vec2(radius, 0.25), negate(t))

  const unionedCircleBox = UnionedCircleBox(p.sub(vec2(0, -0.66)), radius, t)

  const torus = Circle(p.sub(vec2(0.66, -0.66)), radius)
    .abs()
    .sub(0.05)
  // const torus = Ellipse(p.sub(vec2(0.5, -0.5)), radius, vec2(1, 2), time).abs().sub(0.05)
  // const torus = Box(p.sub(vec2(0.66, -0.66)), vec2(radius, 0.25), t).abs().sub(0.05)

  const sdfScene = min(circle, intersectedCircleBox)
  sdfScene.assign(min(sdfScene, ellipse))
  sdfScene.assign(min(sdfScene, flower))
  sdfScene.assign(min(sdfScene, butterfly))
  sdfScene.assign(min(sdfScene, moon))
  sdfScene.assign(min(sdfScene, box))
  sdfScene.assign(min(sdfScene, unionedCircleBox))
  sdfScene.assign(min(sdfScene, torus))

  // const colour = select(
  //   sdfScene.greaterThan(0),
  //   vec3(1.0, 0.05, 0.3).mul(sdfScene.mul(fade).oneMinus()),
  //   vec3(0.1, 0.2, 0.8).mul(sdfScene.mul(fade).add(1))
  // )

  const colour = select(
    sdfScene.lessThan(0),
    vec3(add(0.5, mul(0.5, cos(time.add(p).add(vec3(0, 2, 4)))))).mul(
      sdfScene.mul(fade).oneMinus()
    ),
    vec3(add(0.5, mul(0.5, cos(time.add(p).add(vec3(4, 2, 0)))))).mul(
      abs(sdfScene.mul(fade)).oneMinus()
    )
  )

  const finalColour = colour.mul(sdfScene.mul(75).add(time).sin().abs())

  return finalColour
})

const material = new THREE.NodeMaterial()
material.fragmentNode = main()

const mesh = new THREE.Mesh(new THREE.PlaneGeometry(2, 2), material)
scene.add(mesh)

const gui = new GUI()
gui.add(options, 'radius', 0, 1, 0.01).onChange((v) => {
  radius.value = v
})
gui.add(options, 'fade', 0, 100, 0.01).onChange((v) => {
  fade.value = v
})

function animate() {
  controls.update()

  renderer.render(scene, camera)
}

2D Distance Functions