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Cory Leach
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NoiseSample and Value Derivative Calculation
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‎Runtime/Utility/NoiseSample.cs

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using UnityEngine;
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namespace Gameframe.Procgen
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{
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/// <summary>
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/// A sampling of noise including the value of the noise and the derivative at the same position
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/// </summary>
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public struct NoiseSample
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{
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public float value;
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public Vector3 derivative;
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public static NoiseSample operator +(NoiseSample a, NoiseSample b)
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{
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a.value += b.value;
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a.derivative += b.derivative;
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return a;
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}
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public static NoiseSample operator +(NoiseSample a, float b)
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{
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a.value += b;
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return a;
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}
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public static NoiseSample operator +(float a, NoiseSample b)
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{
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b.value += a;
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return b;
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}
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public static NoiseSample operator -(NoiseSample a, float b)
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{
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a.value -= b;
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return a;
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}
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public static NoiseSample operator -(float a, NoiseSample b)
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{
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b.value = a - b.value;
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b.derivative = -b.derivative;
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return b;
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}
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public static NoiseSample operator -(NoiseSample a, NoiseSample b)
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{
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a.value -= b.value;
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a.derivative -= b.derivative;
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return a;
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}
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public static NoiseSample operator *(NoiseSample a, float b)
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{
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a.value *= b;
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a.derivative *= b;
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return a;
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}
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public static NoiseSample operator *(float a, NoiseSample b)
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{
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b.value *= a;
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b.derivative *= a;
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return b;
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}
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public static NoiseSample operator *(NoiseSample a, NoiseSample b)
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{
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a.derivative = a.derivative * b.value + b.derivative * a.value;
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a.value *= b.value;
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return a;
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}
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}
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}

‎Runtime/Utility/NoiseSample.cs.meta

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‎Runtime/Utility/PerlinGradientNoise.cs

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@@ -197,6 +197,44 @@ public static float Noise1D(float x, uint seed)
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return v * 0.5f + 0.5f; //Remap from -1 to 1, to 0 to 1
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}
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public static NoiseSample Sample1D(float x, uint seed, float frequency = 1)
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{
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var x0 = Mathf.FloorToInt(x * frequency);
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var x1 = x0 + 1;
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var t0 = x - x0;
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var t1 = t0 - 1f;
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var g0 = HashToGradient1D(Hash1D(x0, seed));
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var g1 = HashToGradient1D(Hash1D(x1, seed));
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var v0 = g0 * t0;
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var v1 = g1 * t1;
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var t = Smooth(t0);
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var dt = SmoothDerivative(t0);
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var a = v0;
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var b = v1 - v0;
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var v = a + b * t;
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var dv = b * t;
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var sample = new NoiseSample
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{
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value = v * 2f,
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};
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sample.derivative.x = dv;
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sample.derivative.y = 0;
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sample.derivative.z = 0;
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sample.derivative *= frequency;
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return sample;
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}
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/// <summary>
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/// 2 dimensional perlin noise
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/// </summary>
@@ -237,6 +275,52 @@ public static float Noise2D(float x, float y, uint seed)
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return v * 0.5f + 0.5f; //Remap from -1 to 1, to 0 to 1
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}
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public static NoiseSample Sample2D(float x, float y, uint seed, float frequency = 1f)
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{
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x *= frequency;
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y *= frequency;
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var x0 = Mathf.FloorToInt(x);
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var x1 = x0 + 1;
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var y0 = Mathf.FloorToInt(y);
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var y1 = y0 + 1;
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var tx0 = x - x0;
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var tx1 = tx0 - 1f;
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var ty0 = y - y0;
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var ty1 = ty0 - 1f;
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var g00 = HashToGradient2D(Hash2D(x0, y0, seed));
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var g10 = HashToGradient2D(Hash2D(x1, y0, seed));
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var g01 = HashToGradient2D(Hash2D(x0, y1, seed));
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var g11 = HashToGradient2D(Hash2D(x1, y1, seed));
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var v00 = Dot2D(g00, tx0, ty0);
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var v10 = Dot2D(g10, tx1, ty0);
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var v01 = Dot2D(g01, tx0, ty1);
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var v11 = Dot2D(g11, tx1, ty1);
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var tx = Smooth(tx0);
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var ty = Smooth(ty0);
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var a = v00;
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var b = v10 - v00;
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var v0 = Mathf.Lerp(v00, v10, tx);
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var v1 = Mathf.Lerp(v01, v11, tx);
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var v = Mathf.Lerp(v0, v1, ty) * Sqr2;
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var sample = new NoiseSample
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{
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};
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return sample;
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}
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/// <summary>
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/// 2 dimensional perlin noise
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/// </summary>
@@ -377,9 +461,21 @@ private static float Smooth(float t)
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{
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return SmoothStep.Degree5(t);
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}
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private static float SmoothDerivative(float t)
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{
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return SmoothStep.Degree5Derivative(t);
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}
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}
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public static class SimplexGradientNoise
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{
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public static float Noise1D(float x, uint seed)
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{
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var x0 = Mathf.FloorToInt(x);
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var x1 = x - x0;
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return 0;
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}
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}
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}

‎Runtime/Utility/SmoothStep.cs

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@@ -28,5 +28,10 @@ public static float Degree5(float t)
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{
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return t * t * t * (t * (t * 6f - 15f) + 10f);
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}
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public static float Degree5Derivative(float t)
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{
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return 30f * t * t * (t * (t - 2f) + 1f);
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}
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}
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}

‎Runtime/Utility/ValueNoise.cs

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@@ -143,6 +143,36 @@ public static float Noise1D(float x, uint seed)
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return Mathf.Lerp(v0, v1, t);
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}
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public static NoiseSample Sample1D(float x, uint seed, float frequency = 1)
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{
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var x0 = Mathf.FloorToInt(x * frequency);
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var x1 = x0 + 1;
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var t = Smooth(x - x0);
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var dt = SmoothDerivative(x - x0);
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var v0 = SquirrelEiserloh.Get1dNoiseZeroToOne(x0, seed);
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var v1 = SquirrelEiserloh.Get1dNoiseZeroToOne(x1, seed);
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var a = v0;
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var b = v1 - v0;
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var v = a + b * t; //Lerp
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var dv = b * dt; //Lerp Derivative
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var sample = new NoiseSample
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{
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value = v,
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};
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sample.derivative.x = dv;
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sample.derivative.y = 0;
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sample.derivative.z = 0;
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sample.derivative *= frequency;
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return sample;
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}
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public static float Noise2D(float x, float y, uint seed)
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{
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var x0 = Mathf.FloorToInt(x);
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return Mathf.Lerp(edge1, edge2, ty);
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}
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public static NoiseSample Sample2D(float x, float y, uint seed, float frequency = 1f)
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{
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x *= frequency;
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y *= frequency;
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var x0 = Mathf.FloorToInt(x);
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var y0 = Mathf.FloorToInt(y);
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var x1 = x0 + 1;
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var y1 = y0 + 1;
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var tx = Smooth(x - x0);
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var ty = Smooth(y - y0);
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var dtx = SmoothDerivative(x - x0);
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var dty = SmoothDerivative(y - y0);
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var v00 = SquirrelEiserloh.Get2dNoiseZeroToOne(x0, y0, seed);
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var v01 = SquirrelEiserloh.Get2dNoiseZeroToOne(x0, y1, seed);
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var v10 = SquirrelEiserloh.Get2dNoiseZeroToOne(x1, y0, seed);
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var v11 = SquirrelEiserloh.Get2dNoiseZeroToOne(x1, y1, seed);
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var a = v00;
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var b = v10 - v00;
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var c = v01 - v00;
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var d = v11 - v01 - v10 + v00;
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var v = a + b * tx + (c + d * tx) * ty;
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var sample = new NoiseSample
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{
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value = v
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};
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sample.derivative.x = (b + d * ty) * dtx;
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sample.derivative.y = (c + d * tx) * dty;
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sample.derivative.z = 0;
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sample.derivative *= frequency;
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return sample;
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}
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public static float Noise2D(Vector2 v, uint seed)
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{
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return Noise2D(v.x, v.y, seed);
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{
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return SmoothStep.Degree5(t);
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}
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private static float SmoothDerivative(float t)
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{
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return SmoothStep.Degree5Derivative(t);
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}
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}
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}

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