Assets/X-PostProcessing/Shaders/XNoiseLibrary.hlsl

﻿//----------------------------------------------------------------------------------------------------------
// X-PostProcessing Library
// https://github.com/QianMo/X-PostProcessing-Library
// Copyright (C) 2020 QianMo. All rights reserved.
// Licensed under the MIT License
// You may not use this file except in compliance with the License.You may obtain a copy of the License at
// http://opensource.org/licenses/MIT
//----------------------------------------------------------------------------------------------------------

//----------------------------------------------------------------------------------------------------------
//  XNoiseLibrary.hlsl
// A Collection of  2D/3D/4D Simplex Noise 、 2D/3D textureless classic Noise 、Re-oriented 4 / 8-Point BCC Noise
//
// Reference 1: Webgl Noise -  https://github.com/ashima/webgl-noise
// Reference 2: KdotJPG New Simplex Style Gradient Noise - https://github.com/KdotJPG/New-Simplex-Style-Gradient-Noise
// Reference 3: Noise Shader Library for Unity - https://github.com/keijiro/NoiseShader
// Reference 4: noiseSimplex.cginc - https://forum.unity.com/threads/2d-3d-4d-optimised-perlin-noise-cg-hlsl-library-cginc.218372/
// ----------------------------------------------------------------------------------------------------------


#ifndef X_NOISE_LIBRARY
#define X_NOISE_LIBRARY


//==================================================================================================================================
// 0. Comon
//==================================================================================================================================
// 1 / 289
#define NOISE_SIMPLEX_1_DIV_289 0.00346020761245674740484429065744f

float mod289(float x)
{
	return x - floor(x * NOISE_SIMPLEX_1_DIV_289) * 289.0;
}

float2 mod289(float2 x)
{
	return x - floor(x * NOISE_SIMPLEX_1_DIV_289) * 289.0;
}

float3 mod289(float3 x)
{
	return x - floor(x * NOISE_SIMPLEX_1_DIV_289) * 289.0;
}

float4 mod289(float4 x)
{
	return x - floor(x * NOISE_SIMPLEX_1_DIV_289) * 289.0;
}

float4 mod(float4 x, float4 y)
{
	return x - y * floor(x / y);
}

float3 mod(float3 x, float3 y)
{
	return x - y * floor(x / y);
}

// ( x*34.0 + 1.0 )*x =x*x*34.0 + x
float permute(float x)
{
	return mod289(x * x * 34.0 + x);
}

float3 permute(float3 x)
{
	return mod289(x * x * 34.0 + x);
}

float4 permute(float4 x)
{
	return mod289(x * x * 34.0 + x);
}

float3 taylorInvSqrt(float3 r)
{
	return 1.79284291400159 - 0.85373472095314 * r;
}

float4 taylorInvSqrt(float4 r)
{
	return 1.79284291400159 - r * 0.85373472095314;
}
	
float2 fade(float2 t)
{
	return t * t * t * (t * (t * 6.0 - 15.0) + 10.0);
}


float3 fade(float3 t)
{
	return t * t * t * (t * (t * 6.0 - 15.0) + 10.0);
}

//==================================================================================================================================
// 1. Simplex Noise
//==================================================================================================================================
// 
// This shader is based on the webgl-noise GLSL shader. For further details
// of the original shader, please see the following description from the
// original source code.
//
//
// Description : Array and textureless GLSL 2D/3D/4D simplex
//               noise functions.
//      Author : Ian McEwan, Ashima Arts.
//  Maintainer : ijm
//     Lastmod : 20110822 (ijm)
//     License : Copyright (C) 2011 Ashima Arts. All rights reserved.
//               Distributed under the MIT License. See LICENSE file.
//               https://github.com/ashima/webgl-noise
//
//
// Usage:
//		float ns = snoise(v);
//		v is any of: float2, float3, float4
// Return type is float.
// To generate 2 or more components of noise(colorful noise),
// call these functions several times with different
// constant offsets for the arguments.
// E.g.:

// float3 colorNs = float3(
//	snoise(v),
//	snoise(v + 17.0),
//	snoise(v - 43.0),
//	);


//----------------------------------------------------[1.1]  2D Simplex Noise ----------------------------------------------------


float snoise(float2 v)
{
	const float4 C = float4(0.211324865405187, // (3.0-sqrt(3.0))/6.0
	0.366025403784439, // 0.5*(sqrt(3.0)-1.0)
	- 0.577350269189626, // -1.0 + 2.0 * C.x
	0.024390243902439); // 1.0 / 41.0
	// First corner
	float2 i = floor(v + dot(v, C.yy));
	float2 x0 = v - i + dot(i, C.xx);
	
	// Other corners
	float2 i1;
	i1.x = step(x0.y, x0.x);
	i1.y = 1.0 - i1.x;
	
	// x1 = x0 - i1  + 1.0 * C.xx;
	// x2 = x0 - 1.0 + 2.0 * C.xx;
	float2 x1 = x0 + C.xx - i1;
	float2 x2 = x0 + C.zz;
	
	// Permutations
	i = mod289(i); // Avoid truncation effects in permutation
	float3 p = permute(permute(i.y + float3(0.0, i1.y, 1.0))
	+ i.x + float3(0.0, i1.x, 1.0));
	
	float3 m = max(0.5 - float3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), 0.0);
	m = m * m;
	m = m * m;
	
	// Gradients: 41 points uniformly over a line, mapped onto a diamond.
	// The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
	float3 x = 2.0 * frac(p * C.www) - 1.0;
	float3 h = abs(x) - 0.5;
	float3 ox = floor(x + 0.5);
	float3 a0 = x - ox;
	
	// Normalise gradients implicitly by scaling m
	m *= taylorInvSqrt(a0 * a0 + h * h);
	
	// Compute final noise value at P
	float3 g;
	g.x = a0.x * x0.x + h.x * x0.y;
	g.y = a0.y * x1.x + h.y * x1.y;
	g.z = a0.z * x2.x + h.z * x2.y;
	return 130.0 * dot(m, g);
}

float3 snoise_grad(float2 v)
{
	const float4 C = float4(0.211324865405187, // (3.0-sqrt(3.0))/6.0
	0.366025403784439, // 0.5*(sqrt(3.0)-1.0)
	- 0.577350269189626, // -1.0 + 2.0 * C.x
	0.024390243902439); // 1.0 / 41.0
	// First corner
	float2 i = floor(v + dot(v, C.yy));
	float2 x0 = v - i + dot(i, C.xx);
	
	// Other corners
	float2 i1;
	i1.x = step(x0.y, x0.x);
	i1.y = 1.0 - i1.x;
	
	// x1 = x0 - i1  + 1.0 * C.xx;
	// x2 = x0 - 1.0 + 2.0 * C.xx;
	float2 x1 = x0 + C.xx - i1;
	float2 x2 = x0 + C.zz;
	
	// Permutations
	i = mod289(i); // Avoid truncation effects in permutation
	float3 p = permute(permute(i.y + float3(0.0, i1.y, 1.0))
	+ i.x + float3(0.0, i1.x, 1.0));
	
	float3 m = max(0.5 - float3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), 0.0);
	float3 m2 = m * m;
	float3 m3 = m2 * m;
	float3 m4 = m2 * m2;
	
	// Gradients: 41 points uniformly over a line, mapped onto a diamond.
	// The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
	float3 x = 2.0 * frac(p * C.www) - 1.0;
	float3 h = abs(x) - 0.5;
	float3 ox = floor(x + 0.5);
	float3 a0 = x - ox;
	
	// Normalise gradients
	float3 norm = taylorInvSqrt(a0 * a0 + h * h);
	float2 g0 = float2(a0.x, h.x) * norm.x;
	float2 g1 = float2(a0.y, h.y) * norm.y;
	float2 g2 = float2(a0.z, h.z) * norm.z;
	
	// Compute noise and gradient at P
	float2 grad = -6.0 * m3.x * x0 * dot(x0, g0) + m4.x * g0 +
	- 6.0 * m3.y * x1 * dot(x1, g1) + m4.y * g1 +
	- 6.0 * m3.z * x2 * dot(x2, g2) + m4.z * g2;
	float3 px = float3(dot(x0, g0), dot(x1, g1), dot(x2, g2));
	return 130.0 * float3(grad, dot(m4, px));
}


//---------------------------------------------------[1.2] 3D Simplex Noise ---------------------------------------------

float snoise(float3 v)
{
	const float2 C = float2(1.0 / 6.0, 1.0 / 3.0);
	
	// First corner
	float3 i = floor(v + dot(v, C.yyy));
	float3 x0 = v - i + dot(i, C.xxx);
	
	// Other corners
	float3 g = step(x0.yzx, x0.xyz);
	float3 l = 1.0 - g;
	float3 i1 = min(g.xyz, l.zxy);
	float3 i2 = max(g.xyz, l.zxy);
	
	// x1 = x0 - i1  + 1.0 * C.xxx;
	// x2 = x0 - i2  + 2.0 * C.xxx;
	// x3 = x0 - 1.0 + 3.0 * C.xxx;
	float3 x1 = x0 - i1 + C.xxx;
	float3 x2 = x0 - i2 + C.yyy;
	float3 x3 = x0 - 0.5;
	
	// Permutations
	i = mod289(i); // Avoid truncation effects in permutation
	float4 p = permute(permute(permute(i.z + float4(0.0, i1.z, i2.z, 1.0))
	+ i.y + float4(0.0, i1.y, i2.y, 1.0))
	+ i.x + float4(0.0, i1.x, i2.x, 1.0));
	
	// Gradients: 7x7 points over a square, mapped onto an octahedron.
	// The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294)
	float4 j = p - 49.0 * floor(p / 49.0);  // mod(p,7*7)
	
	float4 x_ = floor(j / 7.0);
	float4 y_ = floor(j - 7.0 * x_);  // mod(j,N)
	
	float4 x = (x_ * 2.0 + 0.5) / 7.0 - 1.0;
	float4 y = (y_ * 2.0 + 0.5) / 7.0 - 1.0;
	
	float4 h = 1.0 - abs(x) - abs(y);
	
	float4 b0 = float4(x.xy, y.xy);
	float4 b1 = float4(x.zw, y.zw);
	
	//float4 s0 = float4(lessThan(b0, 0.0)) * 2.0 - 1.0;
	//float4 s1 = float4(lessThan(b1, 0.0)) * 2.0 - 1.0;
	float4 s0 = floor(b0) * 2.0 + 1.0;
	float4 s1 = floor(b1) * 2.0 + 1.0;
	float4 sh = -step(h, 0.0);
	
	float4 a0 = b0.xzyw + s0.xzyw * sh.xxyy;
	float4 a1 = b1.xzyw + s1.xzyw * sh.zzww;
	
	float3 g0 = float3(a0.xy, h.x);
	float3 g1 = float3(a0.zw, h.y);
	float3 g2 = float3(a1.xy, h.z);
	float3 g3 = float3(a1.zw, h.w);
	
	// Normalise gradients
	float4 norm = taylorInvSqrt(float4(dot(g0, g0), dot(g1, g1), dot(g2, g2), dot(g3, g3)));
	g0 *= norm.x;
	g1 *= norm.y;
	g2 *= norm.z;
	g3 *= norm.w;
	
	// Mix final noise value
	float4 m = max(0.6 - float4(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), 0.0);
	m = m * m;
	m = m * m;
	
	float4 px = float4(dot(x0, g0), dot(x1, g1), dot(x2, g2), dot(x3, g3));
	return 42.0 * dot(m, px);
}

float4 snoise_grad(float3 v)
{
	const float2 C = float2(1.0 / 6.0, 1.0 / 3.0);
	
	// First corner
	float3 i = floor(v + dot(v, C.yyy));
	float3 x0 = v - i + dot(i, C.xxx);
	
	// Other corners
	float3 g = step(x0.yzx, x0.xyz);
	float3 l = 1.0 - g;
	float3 i1 = min(g.xyz, l.zxy);
	float3 i2 = max(g.xyz, l.zxy);
	
	// x1 = x0 - i1  + 1.0 * C.xxx;
	// x2 = x0 - i2  + 2.0 * C.xxx;
	// x3 = x0 - 1.0 + 3.0 * C.xxx;
	float3 x1 = x0 - i1 + C.xxx;
	float3 x2 = x0 - i2 + C.yyy;
	float3 x3 = x0 - 0.5;
	
	// Permutations
	i = mod289(i); // Avoid truncation effects in permutation
	float4 p = permute(permute(permute(i.z + float4(0.0, i1.z, i2.z, 1.0))
	+ i.y + float4(0.0, i1.y, i2.y, 1.0))
	+ i.x + float4(0.0, i1.x, i2.x, 1.0));
	
	// Gradients: 7x7 points over a square, mapped onto an octahedron.
	// The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294)
	float4 j = p - 49.0 * floor(p / 49.0);  // mod(p,7*7)
	
	float4 x_ = floor(j / 7.0);
	float4 y_ = floor(j - 7.0 * x_);  // mod(j,N)
	
	float4 x = (x_ * 2.0 + 0.5) / 7.0 - 1.0;
	float4 y = (y_ * 2.0 + 0.5) / 7.0 - 1.0;
	
	float4 h = 1.0 - abs(x) - abs(y);
	
	float4 b0 = float4(x.xy, y.xy);
	float4 b1 = float4(x.zw, y.zw);
	
	//float4 s0 = float4(lessThan(b0, 0.0)) * 2.0 - 1.0;
	//float4 s1 = float4(lessThan(b1, 0.0)) * 2.0 - 1.0;
	float4 s0 = floor(b0) * 2.0 + 1.0;
	float4 s1 = floor(b1) * 2.0 + 1.0;
	float4 sh = -step(h, 0.0);
	
	float4 a0 = b0.xzyw + s0.xzyw * sh.xxyy;
	float4 a1 = b1.xzyw + s1.xzyw * sh.zzww;
	
	float3 g0 = float3(a0.xy, h.x);
	float3 g1 = float3(a0.zw, h.y);
	float3 g2 = float3(a1.xy, h.z);
	float3 g3 = float3(a1.zw, h.w);
	
	// Normalise gradients
	float4 norm = taylorInvSqrt(float4(dot(g0, g0), dot(g1, g1), dot(g2, g2), dot(g3, g3)));
	g0 *= norm.x;
	g1 *= norm.y;
	g2 *= norm.z;
	g3 *= norm.w;
	
	// Compute noise and gradient at P
	float4 m = max(0.6 - float4(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), 0.0);
	float4 m2 = m * m;
	float4 m3 = m2 * m;
	float4 m4 = m2 * m2;
	float3 grad = -6.0 * m3.x * x0 * dot(x0, g0) + m4.x * g0 +
	- 6.0 * m3.y * x1 * dot(x1, g1) + m4.y * g1 +
	- 6.0 * m3.z * x2 * dot(x2, g2) + m4.z * g2 +
	- 6.0 * m3.w * x3 * dot(x3, g3) + m4.w * g3;
	float4 px = float4(dot(x0, g0), dot(x1, g1), dot(x2, g2), dot(x3, g3));
	return 42.0 * float4(grad, dot(m4, px));
}


//----------------------------------------------------[1.3]  4D Simplex Noise ----------------------------------------------------

float4 grad4(float j, float4 ip)
{
	const float4 ones = float4(1.0, 1.0, 1.0, -1.0);
	float4 p, s;
	p.xyz = floor(frac(j * ip.xyz) * 7.0) * ip.z - 1.0;
	p.w = 1.5 - dot(abs(p.xyz), ones.xyz);

	// GLSL: lessThan(x, y) = x < y
	// HLSL: 1 - step(y, x) = x < y
	p.xyz -= sign(p.xyz) * (p.w < 0);

	return p;
}

float snoise(float4 v)
{
	const float4 C = float4(
		0.138196601125011, // (5 - sqrt(5))/20 G4
		0.276393202250021, // 2 * G4
		0.414589803375032, // 3 * G4
		-0.447213595499958  // -1 + 4 * G4
		);

	// First corner
	float4 i = floor(v +dot(v,0.309016994374947451)); // (sqrt(5) - 1) / 4
	float4 x0 = v - i + dot(i, C.xxxx);

	// Other corners

	// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
	float4 i0;
	float3 isX = step(x0.yzw, x0.xxx);
	float3 isYZ = step(x0.zww, x0.yyz);
	i0.x = isX.x + isX.y + isX.z;
	i0.yzw = 1.0 - isX;
	i0.y += isYZ.x + isYZ.y;
	i0.zw += 1.0 - isYZ.xy;
	i0.z += isYZ.z;
	i0.w += 1.0 - isYZ.z;

	// i0 now contains the unique values 0,1,2,3 in each channel
	float4 i3 = saturate(i0);
	float4 i2 = saturate(i0 - 1.0);
	float4 i1 = saturate(i0 - 2.0);

	//    x0 = x0 - 0.0 + 0.0 * C.xxxx
	//    x1 = x0 - i1  + 1.0 * C.xxxx
	//    x2 = x0 - i2  + 2.0 * C.xxxx
	//    x3 = x0 - i3  + 3.0 * C.xxxx
	//    x4 = x0 - 1.0 + 4.0 * C.xxxx
	float4 x1 = x0 - i1 + C.xxxx;
	float4 x2 = x0 - i2 + C.yyyy;
	float4 x3 = x0 - i3 + C.zzzz;
	float4 x4 = x0 + C.wwww;

	// Permutations
	i = mod289(i);
	float j0 = permute(permute(permute(permute(i.w) + i.z) + i.y) + i.x);
	float4 j1 = permute(permute(permute(permute(i.w + float4(i1.w, i2.w, i3.w, 1.0)) + i.z + float4(i1.z, i2.z, i3.z, 1.0)) + i.y + float4(i1.y, i2.y, i3.y, 1.0)) + i.x + float4(i1.x, i2.x, i3.x, 1.0));

	// Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope
	// 7*7*6 = 294, which is close to the ring size 17*17 = 289.
	const float4 ip = float4(0.003401360544217687075, // 1/294
		0.020408163265306122449, // 1/49
		0.142857142857142857143, // 1/7
		0.0);

	float4 p0 = grad4(j0, ip);
	float4 p1 = grad4(j1.x, ip);
	float4 p2 = grad4(j1.y, ip);
	float4 p3 = grad4(j1.z, ip);
	float4 p4 = grad4(j1.w, ip);

	// Normalise gradients
	float4 norm = rsqrt(float4(dot(p0, p0),dot(p1, p1),dot(p2, p2),dot(p3, p3)));
	p0 *= norm.x;
	p1 *= norm.y;
	p2 *= norm.z;
	p3 *= norm.w;
	p4 *= rsqrt(dot(p4, p4));

	// Mix contributions from the five corners
	float3 m0 = max(0.6 - float3(dot(x0, x0),dot(x1, x1),dot(x2, x2)),0.0);
	float2 m1 = max(0.6 - float2(dot(x3, x3),dot(x4, x4)),0.0);
	m0 = m0 * m0;
	m1 = m1 * m1;

	return 49.0 * (dot(m0*m0,float3(dot(p0, x0),dot(p1, x1),dot(p2, x2))) + dot(m1*m1,float2(dot(p3, x3),dot(p4, x4))));
}


//==================================================================================================================================
// 2. Classic Noise
//==================================================================================================================================
//
// GLSL textureless classic 2D noise "cnoise",
// with an RSL-style periodic variant "pnoise".
// Author:  Stefan Gustavson (stefan.gustavson@liu.se)
// Version: 2011-08-22
//
// Many thanks to Ian McEwan of Ashima Arts for the
// ideas for permutation and gradient selection.
//
// Copyright (c) 2011 Stefan Gustavson. All rights reserved.
// Distributed under the MIT license. See LICENSE file.
// https://github.com/ashima/webgl-noise


//-------------------------------------------------------[2.1] 2D  Classic Noise---------------------------------------------
// Classic Perlin noise
float cnoise(float2 P)
{
	float4 Pi = floor(P.xyxy) + float4(0.0, 0.0, 1.0, 1.0);
	float4 Pf = frac(P.xyxy) - float4(0.0, 0.0, 1.0, 1.0);
	Pi = mod289(Pi); // To avoid truncation effects in permutation
	float4 ix = Pi.xzxz;
	float4 iy = Pi.yyww;
	float4 fx = Pf.xzxz;
	float4 fy = Pf.yyww;
	
	float4 i = permute(permute(ix) + iy);
	
	float4 gx = frac(i / 41.0) * 2.0 - 1.0;
	float4 gy = abs(gx) - 0.5;
	float4 tx = floor(gx + 0.5);
	gx = gx - tx;
	
	float2 g00 = float2(gx.x, gy.x);
	float2 g10 = float2(gx.y, gy.y);
	float2 g01 = float2(gx.z, gy.z);
	float2 g11 = float2(gx.w, gy.w);
	
	float4 norm = taylorInvSqrt(float4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
	g00 *= norm.x;
	g01 *= norm.y;
	g10 *= norm.z;
	g11 *= norm.w;
	
	float n00 = dot(g00, float2(fx.x, fy.x));
	float n10 = dot(g10, float2(fx.y, fy.y));
	float n01 = dot(g01, float2(fx.z, fy.z));
	float n11 = dot(g11, float2(fx.w, fy.w));
	
	float2 fade_xy = fade(Pf.xy);
	float2 n_x = lerp(float2(n00, n01), float2(n10, n11), fade_xy.x);
	float n_xy = lerp(n_x.x, n_x.y, fade_xy.y);
	return 2.3 * n_xy;
}

// Classic Perlin noise, periodic variant
float pnoise(float2 P, float2 rep)
{
	float4 Pi = floor(P.xyxy) + float4(0.0, 0.0, 1.0, 1.0);
	float4 Pf = frac(P.xyxy) - float4(0.0, 0.0, 1.0, 1.0);
	Pi = mod(Pi, rep.xyxy); // To create noise with explicit period
	Pi = mod289(Pi);        // To avoid truncation effects in permutation
	float4 ix = Pi.xzxz;
	float4 iy = Pi.yyww;
	float4 fx = Pf.xzxz;
	float4 fy = Pf.yyww;
	
	float4 i = permute(permute(ix) + iy);
	
	float4 gx = frac(i / 41.0) * 2.0 - 1.0;
	float4 gy = abs(gx) - 0.5;
	float4 tx = floor(gx + 0.5);
	gx = gx - tx;
	
	float2 g00 = float2(gx.x, gy.x);
	float2 g10 = float2(gx.y, gy.y);
	float2 g01 = float2(gx.z, gy.z);
	float2 g11 = float2(gx.w, gy.w);
	
	float4 norm = taylorInvSqrt(float4(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11)));
	g00 *= norm.x;
	g01 *= norm.y;
	g10 *= norm.z;
	g11 *= norm.w;
	
	float n00 = dot(g00, float2(fx.x, fy.x));
	float n10 = dot(g10, float2(fx.y, fy.y));
	float n01 = dot(g01, float2(fx.z, fy.z));
	float n11 = dot(g11, float2(fx.w, fy.w));
	
	float2 fade_xy = fade(Pf.xy);
	float2 n_x = lerp(float2(n00, n01), float2(n10, n11), fade_xy.x);
	float n_xy = lerp(n_x.x, n_x.y, fade_xy.y);
	return 2.3 * n_xy;
}


//----------------------------------------------------[2.2] 3D  Classic Noise--------------------------------------------------
// Classic Perlin noise
float cnoise(float3 P)
{
	float3 Pi0 = floor(P); // Integer part for indexing
	float3 Pi1 = Pi0 + (float3)1.0; // Integer part + 1
	Pi0 = mod289(Pi0);
	Pi1 = mod289(Pi1);
	float3 Pf0 = frac(P); // Fractional part for interpolation
	float3 Pf1 = Pf0 - (float3)1.0; // Fractional part - 1.0
	float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
	float4 iy = float4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
	float4 iz0 = (float4)Pi0.z;
	float4 iz1 = (float4)Pi1.z;
	
	float4 ixy = permute(permute(ix) + iy);
	float4 ixy0 = permute(ixy + iz0);
	float4 ixy1 = permute(ixy + iz1);
	
	float4 gx0 = ixy0 / 7.0;
	float4 gy0 = frac(floor(gx0) / 7.0) - 0.5;
	gx0 = frac(gx0);
	float4 gz0 = (float4)0.5 - abs(gx0) - abs(gy0);
	float4 sz0 = step(gz0, (float4)0.0);
	gx0 -= sz0 * (step((float4)0.0, gx0) - 0.5);
	gy0 -= sz0 * (step((float4)0.0, gy0) - 0.5);
	
	float4 gx1 = ixy1 / 7.0;
	float4 gy1 = frac(floor(gx1) / 7.0) - 0.5;
	gx1 = frac(gx1);
	float4 gz1 = (float4)0.5 - abs(gx1) - abs(gy1);
	float4 sz1 = step(gz1, (float4)0.0);
	gx1 -= sz1 * (step((float4)0.0, gx1) - 0.5);
	gy1 -= sz1 * (step((float4)0.0, gy1) - 0.5);
	
	float3 g000 = float3(gx0.x, gy0.x, gz0.x);
	float3 g100 = float3(gx0.y, gy0.y, gz0.y);
	float3 g010 = float3(gx0.z, gy0.z, gz0.z);
	float3 g110 = float3(gx0.w, gy0.w, gz0.w);
	float3 g001 = float3(gx1.x, gy1.x, gz1.x);
	float3 g101 = float3(gx1.y, gy1.y, gz1.y);
	float3 g011 = float3(gx1.z, gy1.z, gz1.z);
	float3 g111 = float3(gx1.w, gy1.w, gz1.w);
	
	float4 norm0 = taylorInvSqrt(float4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
	g000 *= norm0.x;
	g010 *= norm0.y;
	g100 *= norm0.z;
	g110 *= norm0.w;
	
	float4 norm1 = taylorInvSqrt(float4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
	g001 *= norm1.x;
	g011 *= norm1.y;
	g101 *= norm1.z;
	g111 *= norm1.w;
	
	float n000 = dot(g000, Pf0);
	float n100 = dot(g100, float3(Pf1.x, Pf0.y, Pf0.z));
	float n010 = dot(g010, float3(Pf0.x, Pf1.y, Pf0.z));
	float n110 = dot(g110, float3(Pf1.x, Pf1.y, Pf0.z));
	float n001 = dot(g001, float3(Pf0.x, Pf0.y, Pf1.z));
	float n101 = dot(g101, float3(Pf1.x, Pf0.y, Pf1.z));
	float n011 = dot(g011, float3(Pf0.x, Pf1.y, Pf1.z));
	float n111 = dot(g111, Pf1);
	
	float3 fade_xyz = fade(Pf0);
	float4 n_z = lerp(float4(n000, n100, n010, n110), float4(n001, n101, n011, n111), fade_xyz.z);
	float2 n_yz = lerp(n_z.xy, n_z.zw, fade_xyz.y);
	float n_xyz = lerp(n_yz.x, n_yz.y, fade_xyz.x);
	return 2.2 * n_xyz;
}

// Classic Perlin noise, periodic variant
float pnoise(float3 P, float3 rep)
{
	float3 Pi0 = mod(floor(P), rep); // Integer part, modulo period
	float3 Pi1 = mod(Pi0 + (float3)1.0, rep); // Integer part + 1, mod period
	Pi0 = mod289(Pi0);
	Pi1 = mod289(Pi1);
	float3 Pf0 = frac(P); // Fractional part for interpolation
	float3 Pf1 = Pf0 - (float3)1.0; // Fractional part - 1.0
	float4 ix = float4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
	float4 iy = float4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
	float4 iz0 = (float4)Pi0.z;
	float4 iz1 = (float4)Pi1.z;
	
	float4 ixy = permute(permute(ix) + iy);
	float4 ixy0 = permute(ixy + iz0);
	float4 ixy1 = permute(ixy + iz1);
	
	float4 gx0 = ixy0 / 7.0;
	float4 gy0 = frac(floor(gx0) / 7.0) - 0.5;
	gx0 = frac(gx0);
	float4 gz0 = (float4)0.5 - abs(gx0) - abs(gy0);
	float4 sz0 = step(gz0, (float4)0.0);
	gx0 -= sz0 * (step((float4)0.0, gx0) - 0.5);
	gy0 -= sz0 * (step((float4)0.0, gy0) - 0.5);
	
	float4 gx1 = ixy1 / 7.0;
	float4 gy1 = frac(floor(gx1) / 7.0) - 0.5;
	gx1 = frac(gx1);
	float4 gz1 = (float4)0.5 - abs(gx1) - abs(gy1);
	float4 sz1 = step(gz1, (float4)0.0);
	gx1 -= sz1 * (step((float4)0.0, gx1) - 0.5);
	gy1 -= sz1 * (step((float4)0.0, gy1) - 0.5);
	
	float3 g000 = float3(gx0.x, gy0.x, gz0.x);
	float3 g100 = float3(gx0.y, gy0.y, gz0.y);
	float3 g010 = float3(gx0.z, gy0.z, gz0.z);
	float3 g110 = float3(gx0.w, gy0.w, gz0.w);
	float3 g001 = float3(gx1.x, gy1.x, gz1.x);
	float3 g101 = float3(gx1.y, gy1.y, gz1.y);
	float3 g011 = float3(gx1.z, gy1.z, gz1.z);
	float3 g111 = float3(gx1.w, gy1.w, gz1.w);
	
	float4 norm0 = taylorInvSqrt(float4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
	g000 *= norm0.x;
	g010 *= norm0.y;
	g100 *= norm0.z;
	g110 *= norm0.w;
	float4 norm1 = taylorInvSqrt(float4(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111)));
	g001 *= norm1.x;
	g011 *= norm1.y;
	g101 *= norm1.z;
	g111 *= norm1.w;
	
	float n000 = dot(g000, Pf0);
	float n100 = dot(g100, float3(Pf1.x, Pf0.y, Pf0.z));
	float n010 = dot(g010, float3(Pf0.x, Pf1.y, Pf0.z));
	float n110 = dot(g110, float3(Pf1.x, Pf1.y, Pf0.z));
	float n001 = dot(g001, float3(Pf0.x, Pf0.y, Pf1.z));
	float n101 = dot(g101, float3(Pf1.x, Pf0.y, Pf1.z));
	float n011 = dot(g011, float3(Pf0.x, Pf1.y, Pf1.z));
	float n111 = dot(g111, Pf1);
	
	float3 fade_xyz = fade(Pf0);
	float4 n_z = lerp(float4(n000, n100, n010, n110), float4(n001, n101, n011, n111), fade_xyz.z);
	float2 n_yz = lerp(n_z.xy, n_z.zw, fade_xyz.y);
	float n_xyz = lerp(n_yz.x, n_yz.y, fade_xyz.x);
	return 2.2 * n_xyz;
}


//==================================================================================================================================
// 3. Simplex-like Re-oriented BBC Noise
//==================================================================================================================================

//
// The original shader was created by KdotJPG and released into the public
// domain (Unlicense). Refer to the following GitHub repository for the details
// of the original work.
//
// https://github.com/KdotJPG/New-Simplex-Style-Gradient-Noise
//


float4 bcc4_mod(float4 x, float4 y)
{
	return x - y * floor(x / y);
}

// Inspired by Stefan Gustavson's noise
float4 bcc4_permute(float4 t)
{
	return t * (t * 34.0 + 133.0);
}


//--------------------------------------------------[3.1] 4-Point BCC Noise-----------------------------------------------
// K.jpg's Smooth Re-oriented 8-Point BCC Noise
// Output: float4(dF/dx, dF/dy, dF/dz, value)


// Gradient set is a normalized expanded rhombic dodecahedron
float3 bcc4_grad(float hash)
{
	
	// Random vertex of a cube, +/- 1 each
	float3 cube = frac(floor(hash / float3(1, 2, 4)) * 0.5) * 4 - 1;
	
	// Random edge of the three edges connected to that vertex
	// Also a cuboctahedral vertex
	// And corresponds to the face of its dual, the rhombic dodecahedron
	float3 cuboct = cube;
	cuboct *= int3(0, 1, 2) != (int) (hash / 16);
	
	// In a funky way, pick one of the four points on the rhombic face
	float type = frac(floor(hash / 8) * 0.5) * 2;
	float3 rhomb = (1.0 - type) * cube + type * (cuboct + cross(cube, cuboct));
	
	// Expand it so that the new edges are the same length
	// as the existing ones
	float3 grad = cuboct * 1.22474487139 + rhomb;
	
	// To make all gradients the same length, we only need to shorten the
	// second type of vector. We also put in the whole noise scale constant.
	// The compiler should reduce it into the existing floats. I think.
	grad *= (1.0 - 0.042942436724648037 * type) * 32.80201376986577;
	
	return grad;
}

// BCC lattice split up into 2 cube lattices
float4 Bcc4NoiseBase(float3 X)
{
	
	// First half-lattice, closest edge
	float3 v1 = round(X);
	float3 d1 = X - v1;
	float3 score1 = abs(d1);
	float3 dir1 = max(score1.yzx, score1.zxy) < score1;
	float3 v2 = v1 + dir1 * (d1 < 0 ? - 1: 1);
	float3 d2 = X - v2;
	
	// Second half-lattice, closest edge
	float3 X2 = X + 144.5;
	float3 v3 = round(X2);
	float3 d3 = X2 - v3;
	float3 score2 = abs(d3);
	float3 dir2 = max(score2.yzx, score2.zxy) < score2;
	float3 v4 = v3 + dir2 * (d3 < 0 ? - 1: 1);
	float3 d4 = X2 - v4;
	
	// Gradient hashes for the four points, two from each half-lattice
	float4 hashes = bcc4_permute(bcc4_mod(float4(v1.x, v2.x, v3.x, v4.x), 289.0));
	hashes = bcc4_permute(bcc4_mod(hashes + float4(v1.y, v2.y, v3.y, v4.y), 289.0));
	hashes = bcc4_mod(bcc4_permute(bcc4_mod(hashes + float4(v1.z, v2.z, v3.z, v4.z), 289.0)), 48.0);
	
	// Gradient extrapolations & kernel function
	float4 a = max(0.5 - float4(dot(d1, d1), dot(d2, d2), dot(d3, d3), dot(d4, d4)), 0.0);
	float4 aa = a * a; float4 aaaa = aa * aa;
	float3 g1 = bcc4_grad(hashes.x); float3 g2 = bcc4_grad(hashes.y);
	float3 g3 = bcc4_grad(hashes.z); float3 g4 = bcc4_grad(hashes.w);
	float4 extrapolations = float4(dot(d1, g1), dot(d2, g2), dot(d3, g3), dot(d4, g4));
	
	// Derivatives of the noise
	float3 derivative = -8.0 * mul(aa * a * extrapolations, float4x3(d1, d2, d3, d4))
	+ mul(aaaa, float4x3(g1, g2, g3, g4));
	
	// Return it all as a float4
	return float4(derivative, dot(aaaa, extrapolations));
}

// Use this if you don't want Z to look different from X and Y
float4 Bcc4NoiseClassic(float3 X)
{
	
	// Rotate around the main diagonal. Not a skew transform.
	float4 result = Bcc4NoiseBase(dot(X, 2.0 / 3.0) - X);
	return float4(dot(result.xyz, 2.0 / 3.0) - result.xyz, result.w);
}

// Use this if you want to show X and Y in a plane, and use Z for time, etc.
float4 Bcc4NoisePlaneFirst(float3 X)
{
	
	// Rotate so Z points down the main diagonal. Not a skew transform.
	float3x3 orthonormalMap = float3x3
	(
		0.788675134594813, -0.211324865405187, -0.577350269189626,
		- 0.211324865405187, 0.788675134594813, -0.577350269189626,
		0.577350269189626, 0.577350269189626, 0.577350269189626);
		
	float4 result = Bcc4NoiseBase(mul(X, orthonormalMap));
	return float4(mul(orthonormalMap, result.xyz), result.w);
}
		
		
//------------------------------------------------[3.2] 8-Point BCC Noise------------------------------------------------------
// K.jpg's Smooth Re-oriented 8-Point BCC Noise
// Output: float4(dF/dx, dF/dy, dF/dz, value)


float4 bcc8_mod(float4 x, float4 y)
{
	return x - y * floor(x / y);
}

// Borrowed from Stefan Gustavson's noise code
float4 bcc8_permute(float4 t)
{
	return t * (t * 34.0 + 133.0);
}

// Gradient set is a normalized expanded rhombic dodecahedron
float3 bcc8_grad(float hash)
{
	
	// Random vertex of a cube, +/- 1 each
	float3 cube = frac(floor(hash / float3(1, 2, 4)) * 0.5) * 4 - 1;
	
	// Random edge of the three edges connected to that vertex
	// Also a cuboctahedral vertex
	// And corresponds to the face of its dual, the rhombic dodecahedron
	float3 cuboct = cube;
	cuboct *= int3(0, 1, 2) != (int) (hash / 16);
	
	// In a funky way, pick one of the four points on the rhombic face
	float type = frac(floor(hash / 8) * 0.5) * 2;
	float3 rhomb = (1.0 - type) * cube + type * (cuboct + cross(cube, cuboct));
	
	// Expand it so that the new edges are the same length
	// as the existing ones
	float3 grad = cuboct * 1.22474487139 + rhomb;
	
	// To make all gradients the same length, we only need to shorten the
	// second type of vector. We also put in the whole noise scale constant.
	// The compiler should reduce it into the existing floats. I think.
	grad *= (1.0 - 0.042942436724648037 * type) * 3.5946317686139184;
	
	return grad;
}

// BCC lattice split up into 2 cube lattices
float4 Bcc8NoiseBase(float3 X)
{
	float3 b = floor(X);
	float4 i4 = float4(X - b, 2.5);
	
	// Pick between each pair of oppposite corners in the cube.
	float3 v1 = b + floor(dot(i4, .25));
	float3 v2 = b + float3(1, 0, 0) + float3(-1, 1, 1) * floor(dot(i4, float4( - .25, .25, .25, .35)));
	float3 v3 = b + float3(0, 1, 0) + float3(1, -1, 1) * floor(dot(i4, float4(.25, - .25, .25, .35)));
	float3 v4 = b + float3(0, 0, 1) + float3(1, 1, -1) * floor(dot(i4, float4(.25, .25, - .25, .35)));
	
	// Gradient hashes for the four vertices in this half-lattice.
	float4 hashes = bcc8_permute(bcc8_mod(float4(v1.x, v2.x, v3.x, v4.x), 289.0));
	hashes = bcc8_permute(bcc8_mod(hashes + float4(v1.y, v2.y, v3.y, v4.y), 289.0));
	hashes = bcc8_mod(bcc8_permute(bcc8_mod(hashes + float4(v1.z, v2.z, v3.z, v4.z), 289.0)), 48.0);
	
	// Gradient extrapolations & kernel function
	float3 d1 = X - v1; float3 d2 = X - v2; float3 d3 = X - v3; float3 d4 = X - v4;
	float4 a = max(0.75 - float4(dot(d1, d1), dot(d2, d2), dot(d3, d3), dot(d4, d4)), 0.0);
	float4 aa = a * a; float4 aaaa = aa * aa;
	float3 g1 = bcc8_grad(hashes.x); float3 g2 = bcc8_grad(hashes.y);
	float3 g3 = bcc8_grad(hashes.z); float3 g4 = bcc8_grad(hashes.w);
	float4 extrapolations = float4(dot(d1, g1), dot(d2, g2), dot(d3, g3), dot(d4, g4));
	
	// Derivatives of the noise
	float3 derivative = -8.0 * mul(aa * a * extrapolations, float4x3(d1, d2, d3, d4))
	+ mul(aaaa, float4x3(g1, g2, g3, g4));
	
	// Return it all as a float4
	return float4(derivative, dot(aaaa, extrapolations));
}

// Rotates domain, but preserve shape. Hides grid better in cardinal slices.
// Good for texturing 3D objects with lots of flat parts along cardinal planes.
float4 Bcc8NoiseClassic(float3 X)
{
	X = dot(X, 2.0 / 3.0) - X;
	
	float4 result = Bcc8NoiseBase(X) + Bcc8NoiseBase(X + 144.5);
	
	return float4(dot(result.xyz, 2.0 / 3.0) - result.xyz, result.w);
}

// Gives X and Y a triangular alignment, and lets Z move up the main diagonal.
// Might be good for terrain, or a time varying X/Y plane. Z repeats.
float4 Bcc8NoisePlaneFirst(float3 X)
{
	
	// Not a skew transform.
	float3x3 orthonormalMap = float3x3(
		0.788675134594813, -0.211324865405187, -0.577350269189626,
		- 0.211324865405187, 0.788675134594813, -0.577350269189626,
		0.577350269189626, 0.577350269189626, 0.577350269189626);
		
	X = mul(X, orthonormalMap);
	float4 result = Bcc8NoiseBase(X) + Bcc8NoiseBase(X + 144.5);
	
	return float4(mul(orthonormalMap, result.xyz), result.w);
}
				
				
#endif