support for tiling FBMs

Author: tayloraswift

sources/noise/compounds.swift

@@ -108,6 +108,45 @@ struct FBM<Source>:Noise where Source:Noise
     }
 }
 
+extension FBM where Source:TilingNoise
+{
+    public
+    init(tiling source:Source, octaves:Int, persistence:Double = 0.5)
+    {
+        print("tiling fbm")
+        // calculate maximum range
+        let range_inverse:Double
+        if persistence == 0.5
+        {
+            range_inverse = Double(1 << (octaves - 1)) / Double(1 << octaves - 1)
+        }
+        else
+        {
+            var accumulation:Double = 1,
+                contribution:Double = persistence
+            for _ in (0 ..< octaves - 1)
+            {
+                accumulation += contribution
+                contribution *= persistence
+            }
+
+            range_inverse = 1 / accumulation
+        }
+
+        var generators:[Source] = [source.amplitude_scaled(by: range_inverse)]
+            generators.reserveCapacity(octaves)
+        for i in (0 ..< octaves - 1)
+        {
+            generators.append( generators[i].amplitude_scaled(by: persistence)
+                                            .frequency_scaled(by: 2)
+                                            .transposed(octaves: 1)
+                                            .reseeded())
+        }
+
+        self.generators  = generators
+    }
+}
+
 // UNDOCUMENTED
 public
 struct DistortedNoise<Source, Displacement>:Noise where Source:Noise, Displacement:Noise

sources/noise/hash.swift

@@ -38,7 +38,13 @@ extension HashedNoise
     }
 }
 
-protocol HashedTilingNoise:Noise
+public
+protocol TilingNoise:Noise
+{
+    func transposed(octaves:Int) -> Self
+}
+
+protocol HashedTilingNoise:TilingNoise
 {
     associatedtype IntV
 
@@ -75,10 +81,9 @@ extension HashedTilingNoise
     }
 
     public
-    func transposed(octaves:Int) -> Self
+    func transposed(octaves:Int = 1) -> Self
     {
-        let frequency_factor:Double = octaves >= 0 ? Double(1 << octaves) : 1 / Double(1 << -octaves)
-        return Self(amplitude: self.amplitude, frequency: self.frequency * frequency_factor,
+        return Self(amplitude: self.amplitude, frequency: self.frequency,
                     permutation_table: self.permutation_table,
                     wavelengths: self._transpose_wavelengths(self.wavelengths, octaves: octaves))
     }

tests/LinuxMain.swift

@@ -35,8 +35,25 @@ try png_encode(path: "tests/disk2d.png", raw_data: pixbuf, properties: png_prope
 
 benchmark(noise: CellNoise2D(amplitude: 255, frequency: 0.01), name: "cell2d")
 benchmark(noise: CellNoise3D(amplitude: 255, frequency: 0.01), name: "cell3d")
-benchmark(noise: TilingCellNoise3D(amplitude: 255, frequency: 16 / Double(viewer_size), wavelengths: 16), name: "cell_tiling3d")
-benchmark(noise: FBM<ClassicNoise3D>(ClassicNoise3D(amplitude: 255, frequency: 0.001), octaves: 10, persistence: 0.62), name: "classic3d", offset: 127.5)
-benchmark(noise: TilingClassicNoise3D(amplitude: 255, frequency: 16 / Double(viewer_size), wavelengths: 16), name: "classic_tiling3d", offset: 127.5)
-benchmark(noise: FBM<GradientNoise2D>(GradientNoise2D(amplitude: 180, frequency: 0.001), octaves: 10, persistence: 0.62), name: "gradient2d", offset: 127.5)
-benchmark(noise: FBM<GradientNoise3D>(GradientNoise3D(amplitude: 180, frequency: 0.001), octaves: 10, persistence: 0.62), name: "gradient3d", offset: 127.5)
+benchmark(  noise: TilingCellNoise3D(   amplitude: 255, frequency: 16 / Double(viewer_size),
+                                        wavelengths: 16),
+            name: "cell_tiling3d")
+benchmark(  noise: FBM<TilingClassicNoise3D>(tiling: TilingClassicNoise3D(  amplitude: 255,
+                                                                            frequency: 16 / Double(viewer_size),
+                                                                            wavelengths: 16),
+                                                octaves: 10, persistence: 0.62),
+            name: "classic_tiling_fbm3d",
+            offset: 127.5)
+benchmark(  noise: FBM<ClassicNoise3D>( ClassicNoise3D(amplitude: 255, frequency: 0.001),
+                                        octaves: 10, persistence: 0.62),
+            name: "classic3d",
+            offset: 127.5)
+benchmark(  noise: TilingClassicNoise3D(amplitude: 255, frequency: 16 / Double(viewer_size), wavelengths: 16),
+            name: "classic_tiling3d",
+            offset: 127.5)
+benchmark(noise: FBM<GradientNoise2D>(GradientNoise2D(amplitude: 180, frequency: 0.001), octaves: 10, persistence: 0.62),
+            name: "gradient2d",
+            offset: 127.5)
+benchmark(noise: FBM<GradientNoise3D>(GradientNoise3D(amplitude: 180, frequency: 0.001), octaves: 10, persistence: 0.62),
+            name: "gradient3d",
+            offset: 127.5)