// ref: https://github.com/stegu/webgl-noise/blob/master/src/classicnoise3D.glsl

/*
	GLSL textureless classic 3D noise "cnoise".
	Author:  Stefan Gustavson (stefan.gustavson@liu.se)
	Version: 2011-10-11

	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/stegu/webgl-noise

	Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
	The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/

float cnoise(vec3 P) {
	vec3 Pi0 = floor(P);
	vec3 Pi1 = Pi0+vec3(1.0);
	Pi0 = mod289(Pi0);
	Pi1 = mod289(Pi1);
	vec3 Pf0 = fract(P);
	vec3 Pf1 = Pf0-vec3(1.0);
	vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
	vec4 iy = vec4(Pi0.yy, Pi1.yy);
	vec4 iz0 = Pi0.zzzz;
	vec4 iz1 = Pi1.zzzz;

	vec4 ixy = permute(permute(ix)+iy);
	vec4 ixy0 = permute(ixy+iz0);
	vec4 ixy1 = permute(ixy+iz1);

	vec4 gx0 = ixy0*(1.0/7.0);
	vec4 gy0 = fract(floor(gx0)*(1.0/7.0))-0.5;
	gx0 = fract(gx0);
	vec4 gz0 = vec4(0.5)-abs(gx0)-abs(gy0);
	vec4 sz0 = step(gz0, vec4(0.0));
	gx0 -= sz0*(step(0.0, gx0)-0.5);
	gy0 -= sz0*(step(0.0, gy0)-0.5);

	vec4 gx1 = ixy1*(1.0/7.0);
	vec4 gy1 = fract(floor(gx1)*(1.0/7.0))-0.5;
	gx1 = fract(gx1);
	vec4 gz1 = vec4(0.5)-abs(gx1)-abs(gy1);
	vec4 sz1 = step(gz1, vec4(0.0));
	gx1 -= sz1*(step(0.0, gx1)-0.5);
	gy1 -= sz1*(step(0.0, gy1)-0.5);

	vec3 g000 = vec3(gx0.x, gy0.x, gz0.x);
	vec3 g100 = vec3(gx0.y, gy0.y, gz0.y);
	vec3 g010 = vec3(gx0.z, gy0.z, gz0.z);
	vec3 g110 = vec3(gx0.w, gy0.w, gz0.w);
	vec3 g001 = vec3(gx1.x, gy1.x, gz1.x);
	vec3 g101 = vec3(gx1.y, gy1.y, gz1.y);
	vec3 g011 = vec3(gx1.z, gy1.z, gz1.z);
	vec3 g111 = vec3(gx1.w, gy1.w, gz1.w);

	vec4 norm0 = taylorInvSqrt(vec4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
	g000 *= norm0.x;
	g010 *= norm0.y;
	g100 *= norm0.z;
	g110 *= norm0.w;
	vec4 norm1 = taylorInvSqrt(vec4(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, vec3(Pf1.x, Pf0.yz));
	float n010 = dot(g010, vec3(Pf0.x, Pf1.y, Pf0.z));
	float n110 = dot(g110, vec3(Pf1.xy, Pf0.z));
	float n001 = dot(g001, vec3(Pf0.xy, Pf1.z));
	float n101 = dot(g101, vec3(Pf1.x, Pf0.y, Pf1.z));
	float n011 = dot(g011, vec3(Pf0.x, Pf1.yz));
	float n111 = dot(g111, Pf1);

	vec3 fade_xyz = fade(Pf0);
	vec4 n_z = mix(vec4(n000, n100, n010, n110), vec4(n001, n101, n011, n111), fade_xyz.z);
	vec2 n_yz = mix(n_z.xy, n_z.zw, fade_xyz.y);
	float n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x);
	return 2.2*n_xyz;
}

float pnoise(vec3 P, vec3 rep) {
	vec3 Pi0 = mod(floor(P), rep);
	vec3 Pi1 = mod(Pi0+vec3(1.0), rep);
	Pi0 = mod289(Pi0);
	Pi1 = mod289(Pi1);
	vec3 Pf0 = fract(P);
	vec3 Pf1 = Pf0-vec3(1.0);
	vec4 ix = vec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
	vec4 iy = vec4(Pi0.yy, Pi1.yy);
	vec4 iz0 = Pi0.zzzz;
	vec4 iz1 = Pi1.zzzz;

	vec4 ixy = permute(permute(ix)+iy);
	vec4 ixy0 = permute(ixy+iz0);
	vec4 ixy1 = permute(ixy+iz1);

	vec4 gx0 = ixy0*(1.0/7.0);
	vec4 gy0 = fract(floor(gx0)*(1.0/7.0))-0.5;
	gx0 = fract(gx0);
	vec4 gz0 = vec4(0.5)-abs(gx0)-abs(gy0);
	vec4 sz0 = step(gz0, vec4(0.0));
	gx0 -= sz0*(step(0.0, gx0)-0.5);
	gy0 -= sz0*(step(0.0, gy0)-0.5);

	vec4 gx1 = ixy1*(1.0/7.0);
	vec4 gy1 = fract(floor(gx1)*(1.0/7.0))-0.5;
	gx1 = fract(gx1);
	vec4 gz1 = vec4(0.5)-abs(gx1)-abs(gy1);
	vec4 sz1 = step(gz1, vec4(0.0));
	gx1 -= sz1*(step(0.0, gx1)-0.5);
	gy1 -= sz1*(step(0.0, gy1)-0.5);

	vec3 g000 = vec3(gx0.x, gy0.x, gz0.x);
	vec3 g100 = vec3(gx0.y, gy0.y, gz0.y);
	vec3 g010 = vec3(gx0.z, gy0.z, gz0.z);
	vec3 g110 = vec3(gx0.w, gy0.w, gz0.w);
	vec3 g001 = vec3(gx1.x, gy1.x, gz1.x);
	vec3 g101 = vec3(gx1.y, gy1.y, gz1.y);
	vec3 g011 = vec3(gx1.z, gy1.z, gz1.z);
	vec3 g111 = vec3(gx1.w, gy1.w, gz1.w);

	vec4 norm0 = taylorInvSqrt(vec4(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110)));
	g000 *= norm0.x;
	g010 *= norm0.y;
	g100 *= norm0.z;
	g110 *= norm0.w;
	vec4 norm1 = taylorInvSqrt(vec4(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, vec3(Pf1.x, Pf0.yz));
	float n010 = dot(g010, vec3(Pf0.x, Pf1.y, Pf0.z));
	float n110 = dot(g110, vec3(Pf1.xy, Pf0.z));
	float n001 = dot(g001, vec3(Pf0.xy, Pf1.z));
	float n101 = dot(g101, vec3(Pf1.x, Pf0.y, Pf1.z));
	float n011 = dot(g011, vec3(Pf0.x, Pf1.yz));
	float n111 = dot(g111, Pf1);

	vec3 fade_xyz = fade(Pf0);
	vec4 n_z = mix(vec4(n000, n100, n010, n110), vec4(n001, n101, n011, n111), fade_xyz.z);
	vec2 n_yz = mix(n_z.xy, n_z.zw, fade_xyz.y);
	float n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x);
	return 2.2*n_xyz;
}