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FastNoiseLite.h
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FastNoiseLite.h
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// MIT License
//
// Copyright(c) 2020 Jordan Peck (jordan.me2@gmail.com)
// Copyright(c) 2020 Contributors
//
// 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.
//
// .'',;:cldxkO00KKXXNNWWWNNXKOkxdollcc::::::;:::ccllloooolllllllllooollc:,'... ...........',;cldxkO000Okxdlc::;;;,,;;;::cclllllll
// ..',;:ldxO0KXXNNNNNNNNXXK0kxdolcc::::::;;;,,,,,,;;;;;;;;;;:::cclllllc:;'.... ...........',;:ldxO0KXXXK0Okxdolc::;;;;::cllodddddo
// ...',:loxO0KXNNNNNXXKK0Okxdolc::;::::::::;;;,,'''''.....''',;:clllllc:;,'............''''''''',;:loxO0KXNNNNNXK0Okxdollccccllodxxxxxxd
// ....';:ldkO0KXXXKK00Okxdolcc:;;;;;::cclllcc:;;,''..... ....',;clooddolcc:;;;;,,;;;;;::::;;;;;;:cloxk0KXNWWWWWWNXKK0Okxddoooddxxkkkkkxx
// .....';:ldxkOOOOOkxxdolcc:;;;,,,;;:cllooooolcc:;'... ..,:codxkkkxddooollloooooooollcc:::::clodkO0KXNWWWWWWNNXK00Okxxxxxxxxkkkkxxx
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// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo
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// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c
// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc
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// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd
// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk
// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000
// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX
//
// VERSION: 1.0.1
// https://github.com/Auburn/FastNoise
// In *one* C or C++ file, use #define FNL_IMPL to generate implementation
#ifndef FASTNOISELITE_H
#define FASTNOISELITE_H
// Switch between using floats or doubles for input position
typedef float FNLfloat;
//typedef double FNLfloat;
#if defined(__cplusplus)
extern "C" {
#endif
#include <math.h>
#include <stdint.h>
#include <stdbool.h>
#include <float.h>
// Enums
typedef enum
{
FNL_NOISE_OPENSIMPLEX2,
FNL_NOISE_OPENSIMPLEX2S,
FNL_NOISE_CELLULAR,
FNL_NOISE_PERLIN,
FNL_NOISE_VALUE_CUBIC,
FNL_NOISE_VALUE
} fnl_noise_type;
typedef enum
{
FNL_ROTATION_NONE,
FNL_ROTATION_IMPROVE_XY_PLANES,
FNL_ROTATION_IMPROVE_XZ_PLANES
} fnl_rotation_type_3d;
typedef enum
{
FNL_FRACTAL_NONE,
FNL_FRACTAL_FBM,
FNL_FRACTAL_RIDGED,
FNL_FRACTAL_PINGPONG,
FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE,
FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT
} fnl_fractal_type;
typedef enum
{
FNL_CELLULAR_DISTANCE_EUCLIDEAN,
FNL_CELLULAR_DISTANCE_EUCLIDEANSQ,
FNL_CELLULAR_DISTANCE_MANHATTAN,
FNL_CELLULAR_DISTANCE_HYBRID
} fnl_cellular_distance_func;
typedef enum
{
FNL_CELLULAR_RETURN_VALUE_CELLVALUE,
FNL_CELLULAR_RETURN_VALUE_DISTANCE,
FNL_CELLULAR_RETURN_VALUE_DISTANCE2,
FNL_CELLULAR_RETURN_VALUE_DISTANCE2ADD,
FNL_CELLULAR_RETURN_VALUE_DISTANCE2SUB,
FNL_CELLULAR_RETURN_VALUE_DISTANCE2MUL,
FNL_CELLULAR_RETURN_VALUE_DISTANCE2DIV,
} fnl_cellular_return_type;
typedef enum
{
FNL_DOMAIN_WARP_OPENSIMPLEX2,
FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED,
FNL_DOMAIN_WARP_BASICGRID
} fnl_domain_warp_type;
/**
* Structure containing entire noise system state.
* @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set.
*/
typedef struct fnl_state
{
/**
* Seed used for all noise types.
* @remark Default: 1337
*/
int seed;
/**
* The frequency for all noise types.
* @remark Default: 0.01
*/
float frequency;
/**
* The noise algorithm to be used by GetNoise(...).
* @remark Default: FNL_NOISE_OPENSIMPLEX2
*/
fnl_noise_type noise_type;
/**
* Sets noise rotation type for 3D.
* @remark Default: FNL_ROTATION_NONE
*/
fnl_rotation_type_3d rotation_type_3d;
/**
* The method used for combining octaves for all fractal noise types.
* @remark Default: None
* @remark FNL_FRACTAL_DOMAIN_WARP_... only effects fnlDomainWarp...
*/
fnl_fractal_type fractal_type;
/**
* The octave count for all fractal noise types.
* @remark Default: 3
*/
int octaves;
/**
* The octave lacunarity for all fractal noise types.
* @remark Default: 2.0
*/
float lacunarity;
/**
* The octave gain for all fractal noise types.
* @remark Default: 0.5
*/
float gain;
/**
* The octave weighting for all none Domaain Warp fractal types.
* @remark Default: 0.0
* @remark
*/
float weighted_strength;
/**
* The strength of the fractal ping pong effect.
* @remark Default: 2.0
*/
float ping_pong_strength;
/**
* The distance function used in cellular noise calculations.
* @remark Default: FNL_CELLULAR_FUNC_DISTANCE
*/
fnl_cellular_distance_func cellular_distance_func;
/**
* The cellular return type from cellular noise calculations.
* @remark Default: FNL_CELLULAR_RETURN_VALUE_EUCLIEANSQ
*/
fnl_cellular_return_type cellular_return_type;
/**
* The maximum distance a cellular point can move from it's grid position.
* @remark Default: 1.0
* @note Setting this higher than 1 will cause artifacts.
*/
float cellular_jitter_mod;
/**
* The warp algorithm when using fnlDomainWarp...
* @remark Default: OpenSimplex2
*/
fnl_domain_warp_type domain_warp_type;
/**
* The maximum warp distance from original position when using fnlDomainWarp...
* @remark Default: 1.0
*/
float domain_warp_amp;
} fnl_state;
/**
* Creates a noise state with default values.
* @param seed Optionally set the state seed.
*/
fnl_state fnlCreateState();
/**
* 2D noise at given position using the state settings
* @returns Noise output bounded between -1 and 1.
*/
float fnlGetNoise2D(fnl_state *state, FNLfloat x, FNLfloat y);
/**
* 3D noise at given position using the state settings
* @returns Noise output bounded between -1 and 1.
*/
float fnlGetNoise3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z);
/**
* 2D warps the input position using current domain warp settings.
*
* Example usage with fnlGetNoise2D:
* ```
* fnlDomainWarp2D(&state, &x, &y);
* noise = fnlGetNoise2D(&state, x, y);
* ```
*/
void fnlDomainWarp2D(fnl_state *state, FNLfloat *x, FNLfloat *y);
/**
* 3D warps the input position using current domain warp settings.
*
* Example usage with fnlGetNoise3D:
* ```
* fnlDomainWarp3D(&state, &x, &y, &z);
* noise = fnlGetNoise3D(&state, x, y, z);
* ```
*/
void fnlDomainWarp3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z);
// ====================
// Below this line is the implementation
// ====================
#if defined(FNL_IMPL)
// Constants
static const float GRADIENTS_2D[] =
{
0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,
0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,
0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,
-0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,
-0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,
0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,
0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,
0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,
-0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,
-0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,
0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,
0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,
0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,
-0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,
-0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,
0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,
0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,
0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,
-0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,
-0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,
0.130526192220052f, 0.99144486137381f, 0.38268343236509f, 0.923879532511287f, 0.608761429008721f, 0.793353340291235f, 0.793353340291235f, 0.608761429008721f,
0.923879532511287f, 0.38268343236509f, 0.99144486137381f, 0.130526192220051f, 0.99144486137381f, -0.130526192220051f, 0.923879532511287f, -0.38268343236509f,
0.793353340291235f, -0.60876142900872f, 0.608761429008721f, -0.793353340291235f, 0.38268343236509f, -0.923879532511287f, 0.130526192220052f, -0.99144486137381f,
-0.130526192220052f, -0.99144486137381f, -0.38268343236509f, -0.923879532511287f, -0.608761429008721f, -0.793353340291235f, -0.793353340291235f, -0.608761429008721f,
-0.923879532511287f, -0.38268343236509f, -0.99144486137381f, -0.130526192220052f, -0.99144486137381f, 0.130526192220051f, -0.923879532511287f, 0.38268343236509f,
-0.793353340291235f, 0.608761429008721f, -0.608761429008721f, 0.793353340291235f, -0.38268343236509f, 0.923879532511287f, -0.130526192220052f, 0.99144486137381f,
0.38268343236509f, 0.923879532511287f, 0.923879532511287f, 0.38268343236509f, 0.923879532511287f, -0.38268343236509f, 0.38268343236509f, -0.923879532511287f,
-0.38268343236509f, -0.923879532511287f, -0.923879532511287f, -0.38268343236509f, -0.923879532511287f, 0.38268343236509f, -0.38268343236509f, 0.923879532511287f,
};
static const float RAND_VECS_2D[] =
{
-0.2700222198f, -0.9628540911f, 0.3863092627f, -0.9223693152f, 0.04444859006f, -0.999011673f, -0.5992523158f, -0.8005602176f, -0.7819280288f, 0.6233687174f, 0.9464672271f, 0.3227999196f, -0.6514146797f, -0.7587218957f, 0.9378472289f, 0.347048376f,
-0.8497875957f, -0.5271252623f, -0.879042592f, 0.4767432447f, -0.892300288f, -0.4514423508f, -0.379844434f, -0.9250503802f, -0.9951650832f, 0.0982163789f, 0.7724397808f, -0.6350880136f, 0.7573283322f, -0.6530343002f, -0.9928004525f, -0.119780055f,
-0.0532665713f, 0.9985803285f, 0.9754253726f, -0.2203300762f, -0.7665018163f, 0.6422421394f, 0.991636706f, 0.1290606184f, -0.994696838f, 0.1028503788f, -0.5379205513f, -0.84299554f, 0.5022815471f, -0.8647041387f, 0.4559821461f, -0.8899889226f,
-0.8659131224f, -0.5001944266f, 0.0879458407f, -0.9961252577f, -0.5051684983f, 0.8630207346f, 0.7753185226f, -0.6315704146f, -0.6921944612f, 0.7217110418f, -0.5191659449f, -0.8546734591f, 0.8978622882f, -0.4402764035f, -0.1706774107f, 0.9853269617f,
-0.9353430106f, -0.3537420705f, -0.9992404798f, 0.03896746794f, -0.2882064021f, -0.9575683108f, -0.9663811329f, 0.2571137995f, -0.8759714238f, -0.4823630009f, -0.8303123018f, -0.5572983775f, 0.05110133755f, -0.9986934731f, -0.8558373281f, -0.5172450752f,
0.09887025282f, 0.9951003332f, 0.9189016087f, 0.3944867976f, -0.2439375892f, -0.9697909324f, -0.8121409387f, -0.5834613061f, -0.9910431363f, 0.1335421355f, 0.8492423985f, -0.5280031709f, -0.9717838994f, -0.2358729591f, 0.9949457207f, 0.1004142068f,
0.6241065508f, -0.7813392434f, 0.662910307f, 0.7486988212f, -0.7197418176f, 0.6942418282f, -0.8143370775f, -0.5803922158f, 0.104521054f, -0.9945226741f, -0.1065926113f, -0.9943027784f, 0.445799684f, -0.8951327509f, 0.105547406f, 0.9944142724f,
-0.992790267f, 0.1198644477f, -0.8334366408f, 0.552615025f, 0.9115561563f, -0.4111755999f, 0.8285544909f, -0.5599084351f, 0.7217097654f, -0.6921957921f, 0.4940492677f, -0.8694339084f, -0.3652321272f, -0.9309164803f, -0.9696606758f, 0.2444548501f,
0.08925509731f, -0.996008799f, 0.5354071276f, -0.8445941083f, -0.1053576186f, 0.9944343981f, -0.9890284586f, 0.1477251101f, 0.004856104961f, 0.9999882091f, 0.9885598478f, 0.1508291331f, 0.9286129562f, -0.3710498316f, -0.5832393863f, -0.8123003252f,
0.3015207509f, 0.9534596146f, -0.9575110528f, 0.2883965738f, 0.9715802154f, -0.2367105511f, 0.229981792f, 0.9731949318f, 0.955763816f, -0.2941352207f, 0.740956116f, 0.6715534485f, -0.9971513787f, -0.07542630764f, 0.6905710663f, -0.7232645452f,
-0.290713703f, -0.9568100872f, 0.5912777791f, -0.8064679708f, -0.9454592212f, -0.325740481f, 0.6664455681f, 0.74555369f, 0.6236134912f, 0.7817328275f, 0.9126993851f, -0.4086316587f, -0.8191762011f, 0.5735419353f, -0.8812745759f, -0.4726046147f,
0.9953313627f, 0.09651672651f, 0.9855650846f, -0.1692969699f, -0.8495980887f, 0.5274306472f, 0.6174853946f, -0.7865823463f, 0.8508156371f, 0.52546432f, 0.9985032451f, -0.05469249926f, 0.1971371563f, -0.9803759185f, 0.6607855748f, -0.7505747292f,
-0.03097494063f, 0.9995201614f, -0.6731660801f, 0.739491331f, -0.7195018362f, -0.6944905383f, 0.9727511689f, 0.2318515979f, 0.9997059088f, -0.0242506907f, 0.4421787429f, -0.8969269532f, 0.9981350961f, -0.061043673f, -0.9173660799f, -0.3980445648f,
-0.8150056635f, -0.5794529907f, -0.8789331304f, 0.4769450202f, 0.0158605829f, 0.999874213f, -0.8095464474f, 0.5870558317f, -0.9165898907f, -0.3998286786f, -0.8023542565f, 0.5968480938f, -0.5176737917f, 0.8555780767f, -0.8154407307f, -0.5788405779f,
0.4022010347f, -0.9155513791f, -0.9052556868f, -0.4248672045f, 0.7317445619f, 0.6815789728f, -0.5647632201f, -0.8252529947f, -0.8403276335f, -0.5420788397f, -0.9314281527f, 0.363925262f, 0.5238198472f, 0.8518290719f, 0.7432803869f, -0.6689800195f,
-0.985371561f, -0.1704197369f, 0.4601468731f, 0.88784281f, 0.825855404f, 0.5638819483f, 0.6182366099f, 0.7859920446f, 0.8331502863f, -0.553046653f, 0.1500307506f, 0.9886813308f, -0.662330369f, -0.7492119075f, -0.668598664f, 0.743623444f,
0.7025606278f, 0.7116238924f, -0.5419389763f, -0.8404178401f, -0.3388616456f, 0.9408362159f, 0.8331530315f, 0.5530425174f, -0.2989720662f, -0.9542618632f, 0.2638522993f, 0.9645630949f, 0.124108739f, -0.9922686234f, -0.7282649308f, -0.6852956957f,
0.6962500149f, 0.7177993569f, -0.9183535368f, 0.3957610156f, -0.6326102274f, -0.7744703352f, -0.9331891859f, -0.359385508f, -0.1153779357f, -0.9933216659f, 0.9514974788f, -0.3076565421f, -0.08987977445f, -0.9959526224f, 0.6678496916f, 0.7442961705f,
0.7952400393f, -0.6062947138f, -0.6462007402f, -0.7631674805f, -0.2733598753f, 0.9619118351f, 0.9669590226f, -0.254931851f, -0.9792894595f, 0.2024651934f, -0.5369502995f, -0.8436138784f, -0.270036471f, -0.9628500944f, -0.6400277131f, 0.7683518247f,
-0.7854537493f, -0.6189203566f, 0.06005905383f, -0.9981948257f, -0.02455770378f, 0.9996984141f, -0.65983623f, 0.751409442f, -0.6253894466f, -0.7803127835f, -0.6210408851f, -0.7837781695f, 0.8348888491f, 0.5504185768f, -0.1592275245f, 0.9872419133f,
0.8367622488f, 0.5475663786f, -0.8675753916f, -0.4973056806f, -0.2022662628f, -0.9793305667f, 0.9399189937f, 0.3413975472f, 0.9877404807f, -0.1561049093f, -0.9034455656f, 0.4287028224f, 0.1269804218f, -0.9919052235f, -0.3819600854f, 0.924178821f,
0.9754625894f, 0.2201652486f, -0.3204015856f, -0.9472818081f, -0.9874760884f, 0.1577687387f, 0.02535348474f, -0.9996785487f, 0.4835130794f, -0.8753371362f, -0.2850799925f, -0.9585037287f, -0.06805516006f, -0.99768156f, -0.7885244045f, -0.6150034663f,
0.3185392127f, -0.9479096845f, 0.8880043089f, 0.4598351306f, 0.6476921488f, -0.7619021462f, 0.9820241299f, 0.1887554194f, 0.9357275128f, -0.3527237187f, -0.8894895414f, 0.4569555293f, 0.7922791302f, 0.6101588153f, 0.7483818261f, 0.6632681526f,
-0.7288929755f, -0.6846276581f, 0.8729032783f, -0.4878932944f, 0.8288345784f, 0.5594937369f, 0.08074567077f, 0.9967347374f, 0.9799148216f, -0.1994165048f, -0.580730673f, -0.8140957471f, -0.4700049791f, -0.8826637636f, 0.2409492979f, 0.9705377045f,
0.9437816757f, -0.3305694308f, -0.8927998638f, -0.4504535528f, -0.8069622304f, 0.5906030467f, 0.06258973166f, 0.9980393407f, -0.9312597469f, 0.3643559849f, 0.5777449785f, 0.8162173362f, -0.3360095855f, -0.941858566f, 0.697932075f, -0.7161639607f,
-0.002008157227f, -0.9999979837f, -0.1827294312f, -0.9831632392f, -0.6523911722f, 0.7578824173f, -0.4302626911f, -0.9027037258f, -0.9985126289f, -0.05452091251f, -0.01028102172f, -0.9999471489f, -0.4946071129f, 0.8691166802f, -0.2999350194f, 0.9539596344f,
0.8165471961f, 0.5772786819f, 0.2697460475f, 0.962931498f, -0.7306287391f, -0.6827749597f, -0.7590952064f, -0.6509796216f, -0.907053853f, 0.4210146171f, -0.5104861064f, -0.8598860013f, 0.8613350597f, 0.5080373165f, 0.5007881595f, -0.8655698812f,
-0.654158152f, 0.7563577938f, -0.8382755311f, -0.545246856f, 0.6940070834f, 0.7199681717f, 0.06950936031f, 0.9975812994f, 0.1702942185f, -0.9853932612f, 0.2695973274f, 0.9629731466f, 0.5519612192f, -0.8338697815f, 0.225657487f, -0.9742067022f,
0.4215262855f, -0.9068161835f, 0.4881873305f, -0.8727388672f, -0.3683854996f, -0.9296731273f, -0.9825390578f, 0.1860564427f, 0.81256471f, 0.5828709909f, 0.3196460933f, -0.9475370046f, 0.9570913859f, 0.2897862643f, -0.6876655497f, -0.7260276109f,
-0.9988770922f, -0.047376731f, -0.1250179027f, 0.992154486f, -0.8280133617f, 0.560708367f, 0.9324863769f, -0.3612051451f, 0.6394653183f, 0.7688199442f, -0.01623847064f, -0.9998681473f, -0.9955014666f, -0.09474613458f, -0.81453315f, 0.580117012f,
0.4037327978f, -0.9148769469f, 0.9944263371f, 0.1054336766f, -0.1624711654f, 0.9867132919f, -0.9949487814f, -0.100383875f, -0.6995302564f, 0.7146029809f, 0.5263414922f, -0.85027327f, -0.5395221479f, 0.841971408f, 0.6579370318f, 0.7530729462f,
0.01426758847f, -0.9998982128f, -0.6734383991f, 0.7392433447f, 0.639412098f, -0.7688642071f, 0.9211571421f, 0.3891908523f, -0.146637214f, -0.9891903394f, -0.782318098f, 0.6228791163f, -0.5039610839f, -0.8637263605f, -0.7743120191f, -0.6328039957f,
};
static const float GRADIENTS_3D[] =
{
0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0,
1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0,
1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0,
0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0,
1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0,
1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0,
0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0,
1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0,
1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0,
0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0,
1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0,
1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0,
0, 1, 1, 0, 0,-1, 1, 0, 0, 1,-1, 0, 0,-1,-1, 0,
1, 0, 1, 0, -1, 0, 1, 0, 1, 0,-1, 0, -1, 0,-1, 0,
1, 1, 0, 0, -1, 1, 0, 0, 1,-1, 0, 0, -1,-1, 0, 0,
1, 1, 0, 0, 0,-1, 1, 0, -1, 1, 0, 0, 0,-1,-1, 0
};
static const float RAND_VECS_3D[] =
{
-0.7292736885f, -0.6618439697f, 0.1735581948f, 0, 0.790292081f, -0.5480887466f, -0.2739291014f, 0, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0, 0.565683137f, -0.8208298145f, -0.0790000257f, 0, 0.760049034f, -0.5555979497f, -0.3370999617f, 0, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0, -0.1277062463f, -0.4254438999f, -0.8959289049f, 0, -0.2881560924f, -0.5815838982f, 0.7607405838f, 0,
0.5849561111f, -0.662820239f, -0.4674352136f, 0, 0.3307171178f, 0.0391653737f, 0.94291689f, 0, 0.8712121778f, -0.4113374369f, -0.2679381538f, 0, 0.580981015f, 0.7021915846f, 0.4115677815f, 0, 0.503756873f, 0.6330056931f, -0.5878203852f, 0, 0.4493712205f, 0.601390195f, 0.6606022552f, 0, -0.6878403724f, 0.09018890807f, -0.7202371714f, 0, -0.5958956522f, -0.6469350577f, 0.475797649f, 0,
-0.5127052122f, 0.1946921978f, -0.8361987284f, 0, -0.9911507142f, -0.05410276466f, -0.1212153153f, 0, -0.2149721042f, 0.9720882117f, -0.09397607749f, 0, -0.7518650936f, -0.5428057603f, 0.3742469607f, 0, 0.5237068895f, 0.8516377189f, -0.02107817834f, 0, 0.6333504779f, 0.1926167129f, -0.7495104896f, 0, -0.06788241606f, 0.3998305789f, 0.9140719259f, 0, -0.5538628599f, -0.4729896695f, -0.6852128902f, 0,
-0.7261455366f, -0.5911990757f, 0.3509933228f, 0, -0.9229274737f, -0.1782808786f, 0.3412049336f, 0, -0.6968815002f, 0.6511274338f, 0.3006480328f, 0, 0.9608044783f, -0.2098363234f, -0.1811724921f, 0, 0.06817146062f, -0.9743405129f, 0.2145069156f, 0, -0.3577285196f, -0.6697087264f, -0.6507845481f, 0, -0.1868621131f, 0.7648617052f, -0.6164974636f, 0, -0.6541697588f, 0.3967914832f, 0.6439087246f, 0,
0.6993340405f, -0.6164538506f, 0.3618239211f, 0, -0.1546665739f, 0.6291283928f, 0.7617583057f, 0, -0.6841612949f, -0.2580482182f, -0.6821542638f, 0, 0.5383980957f, 0.4258654885f, 0.7271630328f, 0, -0.5026987823f, -0.7939832935f, -0.3418836993f, 0, 0.3202971715f, 0.2834415347f, 0.9039195862f, 0, 0.8683227101f, -0.0003762656404f, -0.4959995258f, 0, 0.791120031f, -0.08511045745f, 0.6057105799f, 0,
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};
// Utilities
static inline float _fnlFastMin(float x, float y) { return x < y ? x : y; }
static inline float _fnlFastMax(float x, float y) { return x > y ? x : y; }
static inline float _fnlFastAbs(float f) { return f < 0 ? -f : f; }
static inline float _fnlCasti32Tof32(int i)
{
union
{
float f;
int32_t i;
} u;
u.i = i;
return u.f;
}
static inline int _fnlCastf32Toi32(float f)
{
union
{
float f;
int32_t i;
} u;
u.f = f;
return u.i;
}
static inline float _fnlInvSqrt(float a)
{
float xhalf = 0.5f * a;
a = _fnlCasti32Tof32(0x5f3759df - (_fnlCastf32Toi32(a) >> 1));
a = a * (1.5f - xhalf * a * a);
return a;
}
// NOTE: If your language does not support this method (seen above), then simply use the native sqrt function.
static inline float _fnlFastSqrt(float a) { return a * _fnlInvSqrt(a); }
static inline int _fnlFastFloor(FNLfloat f) { return (f >= 0 ? (int)f : (int)f - 1); }
static inline int _fnlFastRound(FNLfloat f) { return (f >= 0) ? (int)(f + 0.5f) : (int)(f - 0.5f); }
static inline float _fnlLerp(float a, float b, float t) { return a + t * (b - a); }
static inline float _fnlInterpHermite(float t) { return t * t * (3 - 2 * t); }
static inline float _fnlInterpQuintic(float t) { return t * t * t * (t * (t * 6 - 15) + 10); }
static inline float _fnlCubicLerp(float a, float b, float c, float d, float t)
{
float p = (d - c) - (a - b);
return t * t * t * p + t * t * ((a - b) - p) + t * (c - a) + b;
}
static inline float _fnlPingPong(float t)
{
t -= (int)(t * 0.5f) * 2;
return t < 1 ? t : 2 - t;
}
static float _fnlCalculateFractalBounding(fnl_state *state)
{
float gain = _fnlFastAbs(state->gain);
float amp = gain;
float ampFractal = 1.0f;
for (int i = 1; i < state->octaves; i++)
{
ampFractal += amp;
amp *= gain;
}
return 1.0f / ampFractal;
}
// Hashing
static const int PRIME_X = 501125321;
static const int PRIME_Y = 1136930381;
static const int PRIME_Z = 1720413743;
static inline int _fnlHash2D(int seed, int xPrimed, int yPrimed)
{
int hash = seed ^ xPrimed ^ yPrimed;
hash *= 0x27d4eb2d;
return hash;
}
static inline int _fnlHash3D(int seed, int xPrimed, int yPrimed, int zPrimed)
{
int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed;
hash *= 0x27d4eb2d;
return hash;
}
static inline float _fnlValCoord2D(int seed, int xPrimed, int yPrimed)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed);
hash *= hash;
hash ^= hash << 19;
return hash * (1 / 2147483648.0f);
}
static inline float _fnlValCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed)
{
int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
hash *= hash;
hash ^= hash << 19;
return hash * (1 / 2147483648.0f);
}
static inline float _fnlGradCoord2D(int seed, int xPrimed, int yPrimed, float xd, float yd)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed);
hash ^= hash >> 15;
hash &= 127 << 1;
return xd * GRADIENTS_2D[hash] + yd * GRADIENTS_2D[hash | 1];
}
static inline float _fnlGradCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd)
{
int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
hash ^= hash >> 15;
hash &= 63 << 2;
return xd * GRADIENTS_3D[hash] + yd * GRADIENTS_3D[hash | 1] + zd * GRADIENTS_3D[hash | 2];
}
static inline void _fnlGradCoordOut2D(int seed, int xPrimed, int yPrimed, float *xo, float *yo)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed) & (255 << 1);
*xo = RAND_VECS_2D[hash];
*yo = RAND_VECS_2D[hash | 1];
}
static inline void _fnlGradCoordOut3D(int seed, int xPrimed, int yPrimed, int zPrimed, float *xo, float *yo, float *zo)
{
int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed) & (255 << 2);
*xo = RAND_VECS_3D[hash];
*yo = RAND_VECS_3D[hash | 1];
*zo = RAND_VECS_3D[hash | 2];
}
static inline void _fnlGradCoordDual2D(int seed, int xPrimed, int yPrimed, float xd, float yd, float *xo, float *yo)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed);
int index1 = hash & (127 << 1);
int index2 = (hash >> 7) & (255 << 1);
float xg = GRADIENTS_2D[index1];
float yg = GRADIENTS_2D[index1 | 1];
float value = xd * xg + yd * yg;
float xgo = RAND_VECS_2D[index2];
float ygo = RAND_VECS_2D[index2 | 1];
*xo = value * xgo;
*yo = value * ygo;
}
static inline void _fnlGradCoordDual3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, float *xo, float *yo, float *zo)
{
int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
int index1 = hash & (63 << 2);
int index2 = (hash >> 6) & (255 << 2);
float xg = GRADIENTS_3D[index1];
float yg = GRADIENTS_3D[index1 | 1];
float zg = GRADIENTS_3D[index1 | 2];
float value = xd * xg + yd * yg + zd * zg;
float xgo = RAND_VECS_3D[index2];
float ygo = RAND_VECS_3D[index2 | 1];
float zgo = RAND_VECS_3D[index2 | 2];
*xo = value * xgo;
*yo = value * ygo;
*zo = value * zgo;
}
// Generic Noise Gen
static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y);
static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y);
static float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlSingleCellular2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y);
static float _fnlSingleCellular3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlSinglePerlin2D(int seed, FNLfloat x, FNLfloat y);
static float _fnlSinglePerlin3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlSingleValueCubic2D(int seed, FNLfloat x, FNLfloat y);
static float _fnlSingleValueCubic3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlSingleValue2D(int seed, FNLfloat x, FNLfloat y);
static float _fnlSingleValue3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z);
static float _fnlGenNoiseSingle2D(fnl_state *state, int seed, FNLfloat x, FNLfloat y)
{
switch (state->noise_type)
{
case FNL_NOISE_OPENSIMPLEX2:
return _fnlSingleSimplex2D(seed, x, y);
case FNL_NOISE_OPENSIMPLEX2S:
return _fnlSingleOpenSimplex2S2D(seed, x, y);
case FNL_NOISE_CELLULAR:
return _fnlSingleCellular2D(state, seed, x, y);
case FNL_NOISE_PERLIN:
return _fnlSinglePerlin2D(seed, x, y);
case FNL_NOISE_VALUE_CUBIC:
return _fnlSingleValueCubic2D(seed, x, y);
case FNL_NOISE_VALUE:
return _fnlSingleValue2D(seed, x, y);
default:
return 0;
}
}
static float _fnlGenNoiseSingle3D(fnl_state *state, int seed, FNLfloat x, FNLfloat y, FNLfloat z)
{
switch (state->noise_type)
{
case FNL_NOISE_OPENSIMPLEX2:
return _fnlSingleOpenSimplex23D(seed, x, y, z);
case FNL_NOISE_OPENSIMPLEX2S:
return _fnlSingleOpenSimplex2S3D(seed, x, y, z);
case FNL_NOISE_CELLULAR:
return _fnlSingleCellular3D(state, seed, x, y, z);
case FNL_NOISE_PERLIN:
return _fnlSinglePerlin3D(seed, x, y, z);
case FNL_NOISE_VALUE_CUBIC:
return _fnlSingleValueCubic3D(seed, x, y, z);
case FNL_NOISE_VALUE:
return _fnlSingleValue3D(seed, x, y, z);
default:
return 0;
}
}
// Noise Coordinate Transforms (frequency, and possible skew or rotation)
static void _fnlTransformNoiseCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
{
*x *= state->frequency;
*y *= state->frequency;
switch (state->noise_type)
{
case FNL_NOISE_OPENSIMPLEX2:
case FNL_NOISE_OPENSIMPLEX2S:
{
const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059;
const FNLfloat F2 = 0.5f * (SQRT3 - 1);
FNLfloat t = (*x + *y) * F2;
*x += t;
*y += t;
}
break;
default:
break;
}
}
static void _fnlTransformNoiseCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
{
*x *= state->frequency;
*y *= state->frequency;
*z *= state->frequency;
switch (state->rotation_type_3d)
{
case FNL_ROTATION_IMPROVE_XY_PLANES:
{
FNLfloat xy = *x + *y;
FNLfloat s2 = xy * -(FNLfloat)0.211324865405187;
*z *= (FNLfloat)0.577350269189626;
*x += s2 - *z;
*y = *y + s2 - *z;
*z += xy * (FNLfloat)0.577350269189626;
}
break;
case FNL_ROTATION_IMPROVE_XZ_PLANES:
{
FNLfloat xz = *x + *z;
FNLfloat s2 = xz * -(FNLfloat)0.211324865405187;
*y *= (FNLfloat)0.577350269189626;
*x += s2 - *y;
*z += s2 - *y;
*y += xz * (FNLfloat)0.577350269189626;
}
break;
default:
switch (state->noise_type)
{
case FNL_NOISE_OPENSIMPLEX2:
case FNL_NOISE_OPENSIMPLEX2S:
{
const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew
*x = r - *x;
*y = r - *y;
*z = r - *z;
}
break;
default:
break;
}
}
}
// Domain Warp Coordinate Transforms
static void _fnlTransformDomainWarpCoordinate2D(fnl_state *state, FNLfloat *x, FNLfloat *y)
{
switch (state->domain_warp_type)
{
case FNL_DOMAIN_WARP_OPENSIMPLEX2:
case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
{
const FNLfloat SQRT3 = (FNLfloat)1.7320508075688772935274463415059;
const FNLfloat F2 = 0.5f * (SQRT3 - 1);
FNLfloat t = (*x + *y) * F2;
*x += t;
*y += t;
}
break;
default:
break;
}
}
static void _fnlTransformDomainWarpCoordinate3D(fnl_state *state, FNLfloat *x, FNLfloat *y, FNLfloat *z)
{
switch (state->rotation_type_3d)
{
case FNL_ROTATION_IMPROVE_XY_PLANES:
{
FNLfloat xy = *x + *y;
FNLfloat s2 = xy * -(FNLfloat)0.211324865405187;
*z *= (FNLfloat)0.577350269189626;
*x += s2 - *z;
*y = *y + s2 - *z;
*z += xy * (FNLfloat)0.577350269189626;
}
break;
case FNL_ROTATION_IMPROVE_XZ_PLANES:
{
FNLfloat xz = *x + *z;
FNLfloat s2 = xz * -(FNLfloat)0.211324865405187;
*y *= (FNLfloat)0.577350269189626;
*x += s2 - *y;
*z += s2 - *y;
*y += xz * (FNLfloat)0.577350269189626;
}
break;
default:
switch (state->domain_warp_type)
{
case FNL_DOMAIN_WARP_OPENSIMPLEX2:
case FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED:
{
const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
FNLfloat r = (*x + *y + *z) * R3; // Rotation, not skew
*x = r - *x;
*y = r - *y;
*z = r - *z;
}
break;
default:
break;
}
}
}
// Fractal FBm
static float _fnlGenFractalFBM2D(fnl_state *state, FNLfloat x, FNLfloat y)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlGenNoiseSingle2D(state, seed++, x, y);
sum += noise * amp;
amp *= _fnlLerp(1.0f, _fnlFastMin(noise + 1, 2) * 0.5f, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
static float _fnlGenFractalFBM3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlGenNoiseSingle3D(state, seed++, x, y, z);
sum += noise * amp;
amp *= _fnlLerp(1.0f, (noise + 1) * 0.5f, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
z *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
// Fractal Ridged
static float _fnlGenFractalRidged2D(fnl_state *state, FNLfloat x, FNLfloat y)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlFastAbs(_fnlGenNoiseSingle2D(state, seed++, x, y));
sum += (noise * -2 + 1) * amp;
amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
static float _fnlGenFractalRidged3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlFastAbs(_fnlGenNoiseSingle3D(state, seed++, x, y, z));
sum += (noise * -2 + 1) * amp;
amp *= _fnlLerp(1.0f, 1 - noise, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
z *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
// Fractal PingPong
static float _fnlGenFractalPingPong2D(fnl_state *state, FNLfloat x, FNLfloat y)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlPingPong((_fnlGenNoiseSingle2D(state, seed++, x, y) + 1) * state->ping_pong_strength);
sum += (noise - 0.5f) * 2 * amp;
amp *= _fnlLerp(1.0f, noise, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
static float _fnlGenFractalPingPong3D(fnl_state *state, FNLfloat x, FNLfloat y, FNLfloat z)
{
int seed = state->seed;
float sum = 0;
float amp = _fnlCalculateFractalBounding(state);
for (int i = 0; i < state->octaves; i++)
{
float noise = _fnlPingPong((_fnlGenNoiseSingle3D(state, seed++, x, y, z) + 1) * state->ping_pong_strength);
sum += (noise - 0.5f) * 2 * amp;
amp *= _fnlLerp(1.0f, noise, state->weighted_strength);
x *= state->lacunarity;
y *= state->lacunarity;
z *= state->lacunarity;
amp *= state->gain;
}
return sum;
}
// Simplex/OpenSimplex2 Noise
static float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y)
{
// 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex.
const float SQRT3 = 1.7320508075688772935274463415059f;
const float G2 = (3 - SQRT3) / 6;
/*
* --- Skew moved to TransformNoiseCoordinate method ---
* const FNLfloat F2 = 0.5f * (SQRT3 - 1);
* FNLfloat s = (x + y) * F2;
* x += s; y += s;
*/
int i = _fnlFastFloor(x);
int j = _fnlFastFloor(y);
float xi = (float)(x - i);
float yi = (float)(y - j);
float t = (xi + yi) * G2;
float x0 = (float)(xi - t);
float y0 = (float)(yi - t);
i *= PRIME_X;
j *= PRIME_Y;
float n0, n1, n2;
float a = 0.5f - x0 * x0 - y0 * y0;
if (a <= 0)
n0 = 0;
else
{
n0 = (a * a) * (a * a) * _fnlGradCoord2D(seed, i, j, x0, y0);
}
float c = (float)(2 * (1 - 2 * G2) * (1 / G2 - 2)) * t + ((float)(-2 * (1 - 2 * G2) * (1 - 2 * G2)) + a);
if (c <= 0)
n2 = 0;
else
{
float x2 = x0 + (2 * (float)G2 - 1);
float y2 = y0 + (2 * (float)G2 - 1);
n2 = (c * c) * (c * c) * _fnlGradCoord2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2);
}
if (y0 > x0)
{
float x1 = x0 + (float)G2;
float y1 = y0 + ((float)G2 - 1);
float b = 0.5f - x1 * x1 - y1 * y1;
if (b <= 0)
n1 = 0;
else
{
n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x1, y1);
}
}
else
{
float x1 = x0 + ((float)G2 - 1);
float y1 = y0 + (float)G2;
float b = 0.5f - x1 * x1 - y1 * y1;
if (b <= 0)
n1 = 0;
else
{
n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i + PRIME_X, j, x1, y1);
}
}
return (n0 + n1 + n2) * 99.83685446303647f;
}
static float _fnlSingleOpenSimplex23D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
{
// 3D OpenSimplex2 case uses two offset rotated cube grids.
/*
* --- Rotation moved to TransformNoiseCoordinate method ---
* const FNLfloat R3 = (FNLfloat)(2.0 / 3.0);
* FNLfloat r = (x + y + z) * R3; // Rotation, not skew
* x = r - x; y = r - y; z = r - z;
*/
int i = _fnlFastRound(x);
int j = _fnlFastRound(y);
int k = _fnlFastRound(z);
float x0 = (float)(x - i);
float y0 = (float)(y - j);
float z0 = (float)(z - k);
int xNSign = (int)(-1.0f - x0) | 1;
int yNSign = (int)(-1.0f - y0) | 1;
int zNSign = (int)(-1.0f - z0) | 1;
float ax0 = xNSign * -x0;