feature: IBL??

src/entities/CameraEntity.ts

@@ -17,6 +17,8 @@ export interface CameraEntityOptions {
   root: Entity;
   target: RenderTarget;
   lights: LightEntity[];
+  textureIBLLUT: GLCatTexture<WebGL2RenderingContext>;
+  textureEnv: GLCatTexture<WebGL2RenderingContext>;
   textureRandom: GLCatTexture<WebGL2RenderingContext>;
 }
 
@@ -185,6 +187,8 @@ export class CameraEntity {
       shadingMaterial.blend = [ gl.ONE, gl.ONE ];
       shadingMaterial.addUniformTexture( 'samplerAo', aoTarget.texture );
       shadingMaterial.addUniformTexture( 'samplerShadow', light.shadowMap.texture );
+      shadingMaterial.addUniformTexture( 'samplerIBLLUT', options.textureIBLLUT );
+      shadingMaterial.addUniformTexture( 'samplerEnv', options.textureEnv );
       shadingMaterial.addUniformTexture( 'samplerRandom', options.textureRandom );
 
       const shadingQuad = new Quad( {

src/entities/EnvironmentMap.ts

@@ -0,0 +1,81 @@
+import { Entity } from '../heck/Entity';
+import { GLCatTexture } from '@fms-cat/glcat-ts';
+import { Material } from '../heck/Material';
+import { Quad } from '../heck/components/Quad';
+import environmentMapFrag from '../shaders/environment-map.frag';
+import quadVert from '../shaders/quad.vert';
+import { BufferRenderTarget } from '../heck/BufferRenderTarget';
+import { Swap, Xorshift } from '@fms-cat/experimental';
+import { Lambda } from '../heck/components/Lambda';
+
+const WIDTH = 1024;
+const HEIGHT = 512;
+
+export class EnvironmentMap {
+  public entity: Entity;
+
+  public swap: Swap<BufferRenderTarget>;
+
+  public get texture(): GLCatTexture<WebGL2RenderingContext> {
+    return this.swap.o.texture;
+  }
+
+  public constructor() {
+    this.entity = new Entity();
+    this.entity.visible = false;
+
+    const rng = new Xorshift( 114514 );
+
+    // -- swap -------------------------------------------------------------------------------------
+    this.swap = new Swap(
+      new BufferRenderTarget( {
+        width: WIDTH,
+        height: HEIGHT,
+        name: process.env.DEV && 'EnvironmentMap/swap0',
+      } ),
+      new BufferRenderTarget( {
+        width: WIDTH,
+        height: HEIGHT,
+        name: process.env.DEV && 'EnvironmentMap/swap1',
+      } ),
+    );
+
+    // -- post -------------------------------------------------------------------------------------
+    const material = new Material(
+      quadVert,
+      environmentMapFrag,
+    );
+    material.addUniform( 'uniformSeed', '4f', rng.gen(), rng.gen(), rng.gen(), rng.gen() );
+    material.addUniformTexture( 'sampler0', this.swap.i.texture );
+
+    if ( process.env.DEV ) {
+      if ( module.hot ) {
+        module.hot.accept( '../shaders/environment-map.frag', () => {
+          material.replaceShader( quadVert, environmentMapFrag );
+        } );
+      }
+    }
+
+    const quad = new Quad( {
+      target: this.swap.o,
+      material,
+      name: process.env.DEV && 'EnvironmentMap/quad',
+    } );
+
+    // -- swapper ----------------------------------------------------------------------------------
+    this.entity.components.push( new Lambda( {
+      onUpdate: () => {
+        this.swap.swap();
+
+        material.addUniform( 'uniformSeed', '4f', rng.gen(), rng.gen(), rng.gen(), rng.gen() );
+        material.addUniformTexture( 'sampler0', this.swap.i.texture );
+
+        quad.target = this.swap.o;
+      },
+      visible: false,
+      name: process.env.DEV && 'EnvironmentMap/swapper',
+    } ) );
+
+    this.entity.components.push( quad );
+  }
+}

src/entities/IBLLUT.ts

@@ -0,0 +1,80 @@
+import { Entity } from '../heck/Entity';
+import { GLCatTexture } from '@fms-cat/glcat-ts';
+import { Material } from '../heck/Material';
+import { Quad } from '../heck/components/Quad';
+import iblLutFrag from '../shaders/ibl-lut.frag';
+import quadVert from '../shaders/quad.vert';
+import { BufferRenderTarget } from '../heck/BufferRenderTarget';
+import { Swap } from '@fms-cat/experimental';
+import { Lambda } from '../heck/components/Lambda';
+import { vdc } from '../utils/vdc';
+
+const IBL_SIZE = 256;
+
+export class IBLLUT {
+  public entity: Entity;
+
+  public swap: Swap<BufferRenderTarget>;
+
+  public get texture(): GLCatTexture<WebGL2RenderingContext> {
+    return this.swap.o.texture;
+  }
+
+  public constructor() {
+    this.entity = new Entity();
+    this.entity.visible = false;
+
+    // -- swap -------------------------------------------------------------------------------------
+    this.swap = new Swap(
+      new BufferRenderTarget( {
+        width: IBL_SIZE,
+        height: IBL_SIZE,
+        name: process.env.DEV && 'IBLLUT/swap0',
+      } ),
+      new BufferRenderTarget( {
+        width: IBL_SIZE,
+        height: IBL_SIZE,
+        name: process.env.DEV && 'IBLLUT/swap1',
+      } ),
+    );
+
+    // -- post -------------------------------------------------------------------------------------
+    let samples = 0.0;
+
+    const material = new Material(
+      quadVert,
+      iblLutFrag,
+    );
+    material.addUniform( 'samples', '1f', samples );
+    material.addUniform( 'vdc', '1f', vdc( samples, 2.0 ) );
+    material.addUniformTexture( 'sampler0', this.swap.i.texture );
+
+    const quad = new Quad( {
+      target: this.swap.o,
+      material,
+      name: process.env.DEV && 'IBLLUT/quad',
+    } );
+
+    // -- swapper ----------------------------------------------------------------------------------
+    this.entity.components.push( new Lambda( {
+      onUpdate: () => {
+        samples ++;
+        this.swap.swap();
+
+        if ( samples > 1024 ) {
+          this.entity.active = false;
+        } else {
+          material.addUniform( 'samples', '1f', samples );
+          material.addUniform( 'vdc', '1f', vdc( samples, 2.0 ) );
+          material.addUniformTexture( 'sampler0', this.swap.i.texture );
+
+          quad.target = this.swap.o;
+        }
+      },
+      visible: false,
+      name: process.env.DEV && 'IBLLUT/swapper',
+    } ) );
+
+    this.entity.components.push( quad );
+  }
+}

src/main.ts

@@ -24,6 +24,8 @@ import { RTInspector } from './entities/RTInspector';
 import { Component } from './heck/components/Component';
 import { FlickyParticles } from './entities/FlickyParticles';
 import { PixelSorter } from './entities/PixelSorter';
+import { IBLLUT } from './entities/IBLLUT';
+import { EnvironmentMap } from './entities/EnvironmentMap';
 
 // == music ========================================================================================
 const audio = new AudioContext();
@@ -193,6 +195,13 @@ dog.root.components.push( new Lambda( {
   name: process.env.DEV && 'main/update',
 } ) );
 
+// -- bake -----------------------------------------------------------------------------------------
+const ibllut = new IBLLUT();
+dog.root.children.push( ibllut.entity );
+
+const environmentMap = new EnvironmentMap();
+dog.root.children.push( environmentMap.entity );
+
 // -- "objects" ------------------------------------------------------------------------------------
 const sphereParticles = new SphereParticles( {
   particlesSqrt: 256,
@@ -201,13 +210,13 @@ const sphereParticles = new SphereParticles( {
 } );
 dog.root.children.push( sphereParticles.entity );
 
-const trails = new Trails( {
-  trails: 4096,
-  trailLength: 64,
-  textureRandom: randomTexture.texture,
-  textureRandomStatic: randomTextureStatic.texture
-} );
-dog.root.children.push( trails.entity );
+// const trails = new Trails( {
+//   trails: 4096,
+//   trailLength: 64,
+//   textureRandom: randomTexture.texture,
+//   textureRandomStatic: randomTextureStatic.texture
+// } );
+// dog.root.children.push( trails.entity );
 
 const rings = new Rings();
 dog.root.children.push( rings.entity );
@@ -219,11 +228,11 @@ const flickyParticles = new FlickyParticles( {
 } );
 dog.root.children.push( flickyParticles.entity );
 
-const raymarcher = new Raymarcher( {
-  textureRandom: randomTexture.texture,
-  textureRandomStatic: randomTextureStatic.texture
-} );
-dog.root.children.push( raymarcher.entity );
+// const raymarcher = new Raymarcher( {
+//   textureRandom: randomTexture.texture,
+//   textureRandomStatic: randomTextureStatic.texture
+// } );
+// dog.root.children.push( raymarcher.entity );
 
 // -- things that is not an "object" ---------------------------------------------------------------
 const swapOptions = {
@@ -249,7 +258,7 @@ const light = new LightEntity( {
   shadowMapFar: 20.0,
   namePrefix: process.env.DEV && 'light1',
 } );
-light.color = [ 60.0, 60.0, 60.0 ];
+light.color = [ 40.0, 40.0, 40.0 ];
 light.entity.transform.lookAt( new Vector3( [ -1.0, 2.0, 8.0 ] ) );
 dog.root.children.push( light.entity );
 
@@ -271,6 +280,8 @@ const camera = new CameraEntity( {
     light,
     // light2
   ],
+  textureIBLLUT: ibllut.texture,
+  textureEnv: environmentMap.texture,
   textureRandom: randomTexture.texture
 } );
 camera.camera.clear = [ 0.0, 0.0, 0.0, 0.0 ];

src/shaders/bloom-post.frag

@@ -9,12 +9,16 @@ out vec4 fragColor;
 uniform sampler2D samplerDry;
 uniform sampler2D samplerWet;
 
+vec4 sampleLOD( vec2 uv, float lv ) {
+  float p = pow( 0.5, float( lv ) );
+  vec2 uvt = mix( vec2( 1.0 - p ), vec2( 1.0 - 0.5 * p ), uv );
+  return texture( samplerWet, uvt );
+}
+
 void main() {
   fragColor = texture( samplerDry, vUv );
   for ( int i = 0; i < 5; i ++ ) {
-    float fuck = pow( 0.5, float( i ) );
-    vec2 suv = mix( vec2( 1.0 - fuck ), vec2( 1.0 - 0.5 * fuck ), vUv );
-    fragColor += texture( samplerWet, suv );
+    fragColor += sampleLOD( vUv, float( i ) );
   }
   fragColor.xyz = max( vec3( 0.0 ), fragColor.xyz );
 }

src/shaders/environment-map.frag

@@ -0,0 +1,119 @@
+#version 300 es
+
+// https://learnopengl.com/PBR/IBL/Specular-IBL
+
+precision highp float;
+
+#define saturate(x) clamp(x,0.,1.)
+#define linearstep(a,b,x) saturate(((x)-(a))/((b)-(a)))
+
+#pragma glslify: prng = require( ./-prng );
+
+const int SAMPLES = 16;
+const float UV_MARGIN = 0.9;
+const float PI = 3.14159265;
+const float TAU = 6.283185307;
+
+in vec2 vUv;
+
+out vec4 fragColor;
+
+uniform float head;
+uniform vec2 resolution;
+uniform vec4 uniformSeed;
+uniform sampler2D sampler0;
+
+vec4 seed;
+
+float vdc( float i, float base ) {
+  float r = 0.0;
+  float denom = 1.0;
+
+  for ( int j = 0; j < 32; j ++ ) {
+    denom *= base;
+    r += mod( i, base ) / denom;
+    i = floor( i / base );
+
+    if ( i <= 0.0 ) { break; }
+  }
+
+  return r;
+}
+
+vec3 ImportanceSampleGGX( vec2 Xi, float roughness, vec3 N ) {
+  float a = roughness * roughness;
+
+  float phi = TAU * Xi.x;
+  float cosTheta = roughness < 0.0 // negative roughness to usa lambert ???
+    ? asin( sqrt( Xi.y ) )
+    : sqrt( ( 1.0 - Xi.y ) / ( 1.0 + ( a * a - 1.0 ) * Xi.y ) );
+  float sinTheta = sqrt( 1.0 - cosTheta * cosTheta );
+
+  // from spherical coordinates to cartesian coordinates
+  vec3 H = vec3(
+    cos( phi ) * sinTheta,
+    sin( phi ) * sinTheta,
+    cosTheta
+  );
+
+  // from tangent-space vector to world-space sample vector
+  vec3 up = abs( N.y ) < 0.999 ? vec3( 0.0, 1.0, 0.0 ) : vec3( 1.0, 0.0, 0.0 );
+  vec3 tangent = normalize( cross( up, N ) );
+  vec3 bitangent = cross( N, tangent );
+
+  vec3 sampleVec = tangent * H.x + bitangent * H.y + N * H.z;
+  return normalize( sampleVec );
+}
+
+vec3 haha( vec3 L ) {
+  bool circ = dot( L, normalize( vec3( 1.0, 3.0, 3.0 ) ) ) > 0.9;
+  vec3 c = circ ? 0.01 * vec3( 0.1, 0.1, 1.0 ) : vec3( 0.0 );
+
+  bool ring = abs( dot( L, vec3( 0.0, 1.0, 0.0 ) ) ) < 0.1;
+  c += ring ? 10.0 * vec3( 0.1, 1.0, 0.3 ) : vec3( 0.0 );
+
+  return c;
+  // return 0.5 + 0.5 * L;
+}
+
+void main() {
+  vec2 halfTexel = 1.0 / resolution; // * 0.5;
+
+  float lv = ceil( -log( 1.0 - min( vUv.x, vUv.y ) ) / log( 2.0 ) );
+  float p = pow( 0.5, lv );
+  vec2 uv00 = floor( vUv / p ) * p;
+  vec2 uv11 = uv00 + p;
+  vec2 uv = clamp( vUv, uv00 + halfTexel, uv11 - halfTexel );
+  uv = linearstep( uv00, uv11, uv );
+  uv = ( uv - 0.5 ) / UV_MARGIN + 0.5;
+
+  vec3 tex = texture( sampler0, vUv ).xyz;
+  float roughness = lv * 0.2;
+
+  float a = TAU * uv.x;
+  float b = PI * ( uv.y - 0.5 );
+  vec3 N = vec3( sin( a ) * cos( b ), -sin( b ), -cos( a ) * cos( b ) );
+  vec3 R = N;
+  vec3 V = R;
+
+  seed = uniformSeed + N.xyzx;
+
+  vec4 col = vec4( 0.0 );
+  for ( int i = 0; i < SAMPLES; i ++ ) {
+    vec2 Xi = vec2( prng( seed ), prng( seed ) );
+    vec3 H = ImportanceSampleGGX( Xi, roughness, N );
+    vec3 L = normalize( 2.0 * dot( V, H ) * H - V );
+
+    float NoL = dot( N, L );
+
+    if ( NoL > 0.0 ) {
+      col += vec4( haha( L ), 1.0 ) * NoL;
+    }
+  }
+
+  col.xyz = col.w <= 0.001 ? vec3( 0.0 ) : ( col.xyz / col.w );
+
+  tex.xyz = mix( tex.xyz, col.xyz, 1.0 / 16.0 );
+
+  fragColor = vec4( tex, 1.0 );
+}

src/shaders/ibl-lut.frag

@@ -0,0 +1,90 @@
+#version 300 es
+
+precision highp float;
+
+const float TAU = 6.283185307;
+
+in vec2 vUv;
+
+out vec4 fragColor;
+
+uniform float samples;
+uniform float vdc;
+uniform sampler2D sampler0;
+
+vec3 ImportanceSampleGGX( vec2 Xi, float roughness, vec3 N ) {
+  float a = roughness * roughness;
+
+  float phi = TAU * Xi.x;
+  float cosTheta = sqrt( ( 1.0 - Xi.y ) / ( 1.0 + ( a * a - 1.0 ) * Xi.y ) );
+  float sinTheta = sqrt( 1.0 - cosTheta * cosTheta );
+
+  // from spherical coordinates to cartesian coordinates
+  vec3 H = vec3(
+    cos( phi ) * sinTheta,
+    sin( phi ) * sinTheta,
+    cosTheta
+  );
+
+  // from tangent-space vector to world-space sample vector
+  vec3 up = abs( N.y ) < 0.999 ? vec3( 0.0, 1.0, 0.0 ) : vec3( 1.0, 0.0, 0.0 );
+  vec3 tangent = normalize( cross( up, N ) );
+  vec3 bitangent = cross( N, tangent );
+
+  vec3 sampleVec = tangent * H.x + bitangent * H.y + N * H.z;
+  return normalize( sampleVec );
+}
+
+float GeometrySchlickGGX( float NdotV, float roughness ) {
+  float a = roughness;
+  float k = ( a * a ) / 2.0;
+
+  float nom = NdotV;
+  float denom = NdotV * ( 1.0 - k ) + k;
+
+  return nom / denom;
+}
+
+float GeometrySmith( float roughness, float NoV, float NoL ) {
+  float ggx2 = GeometrySchlickGGX( NoV, roughness );
+  float ggx1 = GeometrySchlickGGX( NoL, roughness );
+
+  return ggx1 * ggx2;
+}
+
+// https://github.com/HectorMF/BRDFGenerator/blob/master/BRDFGenerator/BRDFGenerator.cpp
+vec2 IntegrateBRDF( float NdotV, float roughness ) {
+  vec3 V = vec3( sqrt( 1.0 - NdotV * NdotV ), 0.0, NdotV );
+  vec3 N = vec3( 0.0, 0.0, 1.0 );
+
+  vec2 Xi = vec2( samples / 1024.0, vdc );
+  vec3 H = ImportanceSampleGGX( Xi, roughness, N );
+  vec3 L = normalize( 2.0 * dot( V, H ) * H - V );
+
+  float NoL = max( L.z, 0.0 );
+  float NoH = max( H.z, 0.0 );
+  float VoH = max( dot( V, H ), 0.0 );
+  float NoV = max( dot( N, V ), 0.0 );
+
+  if ( NoL > 0.0 ) {
+    float G = GeometrySmith( roughness, NoV, NoL );
+
+    float G_Vis = ( G * VoH ) / ( NoH * NoV );
+    float Fc = pow( 1.0 - VoH, 5.0 );
+
+    return vec2( ( 1.0 - Fc ) * G_Vis, Fc * G_Vis );
+  }
+
+  return vec2( 0.0 );
+}
+
+void main() {
+  vec2 tex = texture( sampler0, vUv ).xy;
+
+  float NdotV = vUv.y;
+  float roughness = vUv.x;
+
+  tex = mix( tex, IntegrateBRDF( NdotV, roughness ), 1.0 / samples );
+
+  fragColor = vec4( tex, 0.0, 1.0 );
+}

src/shaders/raymarcher.frag

@@ -70,7 +70,7 @@ void main() {
   }
 
   vec3 normal = normalFunc( rayPos, 1E-4 );
-  vec4 color = vec4( 0.1, 0.2, 0.4, 1.0 );
+  vec4 color = vec4( 0.4, 0.7, 0.9, 1.0 );
 
   vec4 projPos = projectionMatrix * viewMatrix * vec4( rayPos, 1.0 ); // terrible
   float depth = projPos.z / projPos.w;
@@ -79,5 +79,5 @@ void main() {
   fragPosition = vec4( rayPos, depth );
   fragNormal = vec4( normal, 1.0 );
   fragColor = color;
-  fragWTF = vec4( vec3( 2.0, 0.9, 0.9 ), MTL_IRIDESCENT );
+  fragWTF = vec4( vec3( 0.8, 0.8, 0.0 ), MTL_PBR );
 }

src/shaders/shading.frag

@@ -8,6 +8,7 @@ const int MTL_PBR = 2;
 const int MTL_GRADIENT = 3;
 const int MTL_IRIDESCENT = 4;
 const int AO_ITER = 8;
+const float ENV_UV_MARGIN = 0.9;
 const float AO_BIAS = 0.0;
 const float AO_RADIUS = 0.5;
 const float PI = 3.14159265359;
@@ -36,7 +37,7 @@ uniform sampler2D sampler1; // normal.xyz (yes, this is not good)
 uniform sampler2D sampler2; // color.rgba (what is a though????)
 uniform sampler2D sampler3; // materialParams.xyz, materialId
 uniform sampler2D samplerShadow;
-uniform sampler2D samplerBRDFLUT;
+uniform sampler2D samplerIBLLUT;
 uniform sampler2D samplerEnv;
 uniform sampler2D samplerAo;
 uniform sampler2D samplerRandom;
@@ -86,6 +87,21 @@ vec3 blurpleGradient( float t ) {
   );
 }
 
+vec4 sampleEnvNearest( vec2 uv, float lv ) {
+  float p = pow( 0.5, float( lv ) );
+  vec2 uvt = ENV_UV_MARGIN * ( uv - 0.5 ) + 0.5;
+  uvt = mix( vec2( 1.0 - p ), vec2( 1.0 - 0.5 * p ), uvt );
+  return texture( samplerEnv, uvt );
+}
+
+vec4 sampleEnvLinear( vec2 uv, float lv ) {
+  return mix(
+    sampleEnvNearest( uv, floor( lv ) ),
+    sampleEnvNearest( uv, floor( lv + 1.0 ) ),
+    fract( lv )
+  );
+}
+
 // == structs ======================================================================================
 struct Isect {
   vec2 screenUv;
@@ -188,16 +204,18 @@ vec3 shadePBR( Isect isect, AngularInfo aI ) {
   vec3 color = shade;
 
 #ifdef IS_FIRST_LIGHT
-//   vec3 refl = reflect( aI.V, isect.normal );
-//   vec2 envCoord = vec2(
-//     0.5 + atan( refl.z, refl.x ) / TAU,
-//     0.5 + atan( refl.y, length( refl.zx ) ) / PI
-//   );
-//   vec2 brdf = texture( samplerBRDFLUT, vec2( aI.dotNV, 1.0 - roughness ) ).xy;
+  vec3 refl = reflect( aI.V, isect.normal );
+  vec2 envUv = vec2(
+    0.5 + atan( refl.x, -refl.z ) / TAU,
+    0.5 + atan( refl.y, length( refl.zx ) ) / PI
+  );
 
-//   vec3 texEnv = 0.2 * pow( texture( samplerEnv, envCoord ).rgb, vec3( 2.2 ) );
-//   color += PI * texEnv * ( brdf.x * F0 + brdf.y );
+  // reflective ibl
+  vec2 brdf = texture( samplerIBLLUT, vec2( aI.dotNV, 1.0 - roughness ) ).xy;
+  vec3 texEnv = 0.2 * sampleEnvLinear( envUv, 5.0 * roughness ).rgb;
+  color += PI * ao * texEnv * ( brdf.x * F0 + brdf.y );
 
+  // emissive
   color += emissive * aI.dotNV * isect.albedo;
 #endif // IS_FIRST_LIGHT
 

src/shaders/sphere-particles-render.frag

@@ -38,5 +38,5 @@ void main() {
   fragPosition = vPosition;
   fragNormal = vec4( vNormal, 1.0 );
   fragColor = vec4( vColor.xyz, 1.0 );
-  fragWTF = vec4( vec3( 0.8, 0.8, 0.0 ), MTL_PBR );
+  fragWTF = vec4( vec3( 0.4, 0.4, 0.0 ), MTL_PBR );
 }

src/shaders/sphere-particles-render.vert

@@ -83,15 +83,15 @@ void main() {
   size *= sin( PI * saturate( vLife ) );
 
   vec3 shape = position * size;
-  shape.yz = rotate2D( 7.0 * vPosition.x ) * shape.yz;
-  shape.zx = rotate2D( 7.0 * vPosition.y ) * shape.zx;
+  shape.yz = rotate2D( 7.0 * ( vPosition.x + vDice.z ) ) * shape.yz;
+  shape.zx = rotate2D( 7.0 * ( vPosition.y + vDice.w ) ) * shape.zx;
 
   vPosition.xyz += shape;
 
   // == compute normals ============================================================================
   vNormal = ( normalMatrix * vec4( normal, 1.0 ) ).xyz;
-  vNormal.yz = rotate2D( 7.0 * vPosition.x ) * vNormal.yz;
-  vNormal.zx = rotate2D( 7.0 * vPosition.y ) * vNormal.zx;
+  vNormal.yz = rotate2D( 7.0 * ( vPosition.x + vDice.z ) ) * vNormal.yz;
+  vNormal.zx = rotate2D( 7.0 * ( vPosition.y + vDice.w ) ) * vNormal.zx;
 
   // == send the vertex position ===================================================================
   vPosition = modelMatrix * vPosition;

src/utils/vdc.ts

@@ -0,0 +1,18 @@
+/**
+ * Generate a number using Van der Corput sequence.
+ * e.g. vdc(i, 2) = 1/2, 1/4, 3/4, 1/8, 5/8, 3/8, 7/8, 1/16, ...
+ * @param i Index of the sequence
+ * @param base Base of the sequence
+ */
+export function vdc( i: number, base: number ) {
+  let r = 0;
+  let denom = 1;
+
+  while ( 0 < i ) {
+    denom *= base;
+    r += ( i % base ) / denom;
+    i = Math.floor( i / base );
+  }
+
+  return r;
+}