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Copy pathFastNoiseLite.glsl
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FastNoiseLite.glsl
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// MIT License
//
// Copyright(c) 2023 Jordan Peck ([email protected])
// Copyright(c) 2023 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
// . ....';:cloddddo___________,,,,;;:clooddddoolc:,... ..,:ldx__00OOOkkk___kkkkkkxxdollc::::cclodkO0KXXNNNNNNXXK0OOkxxxxxxxxxxxxddd
// .......',;:cccc:| |,,,;;:cclooddddoll:;'.. ..';cox| \KKK000| |KK00OOkxdocc___;::clldxxkO0KKKKK00Okkxdddddddddddddddoo
// .......'',,,,,''| ________|',,;;::cclloooooolc:;'......___:ldk| \KK000| |XKKK0Okxolc| |;;::cclodxxkkkkxxdoolllcclllooodddooooo
// ''......''''....| | ....'',,,,;;;::cclloooollc:;,''.'| |oxk| \OOO0| |KKK00Oxdoll|___|;;;;;::ccllllllcc::;;,,;;;:cclloooooooo
// ;;,''.......... | |_____',,;;;____:___cllo________.___| |___| \xkk| |KK_______ool___:::;________;;;_______...'',;;:ccclllloo
// c:;,''......... | |:::/ ' |lo/ | | \dx| |0/ \d| |cc/ |'/ \......',,;;:ccllo
// ol:;,'..........| _____|ll/ __ |o/ ______|____ ___| | \o| |/ ___ \| |o/ ______|/ ___ \ .......'',;:clo
// dlc;,...........| |::clooo| / | |x\___ \KXKKK0| |dol| |\ \| | | | | |d\___ \..| | / / ....',:cl
// xoc;'... .....'| |llodddd| \__| |_____\ \KKK0O| |lc:| |'\ | |___| | |_____\ \.| |_/___/... ...',;:c
// dlc;'... ....',;| |oddddddo\ | |Okkx| |::;| |..\ |\ /| | | \ |... ....',;:c
// ol:,'.......',:c|___|xxxddollc\_____,___|_________/ddoll|___|,,,|___|...\_____|:\ ______/l|___|_________/...\________|'........',;::cc
// c:;'.......';:codxxkkkkxxolc::;::clodxkOO0OOkkxdollc::;;,,''''',,,,''''''''''',,'''''',;:loxkkOOkxol:;,'''',,;:ccllcc:;,'''''',;::ccll
// ;,'.......',:codxkOO0OOkxdlc:;,,;;:cldxxkkxxdolc:;;,,''.....'',;;:::;;,,,'''''........,;cldkO0KK0Okdoc::;;::cloodddoolc:;;;;;::ccllooo
// .........',;:lodxOO0000Okdoc:,,',,;:clloddoolc:;,''.......'',;:clooollc:;;,,''.......',:ldkOKXNNXX0Oxdolllloddxxxxxxdolccccccllooodddd
// . .....';:cldxkO0000Okxol:;,''',,;::cccc:;,,'.......'',;:cldxxkkxxdolc:;;,'.......';coxOKXNWWWNXKOkxddddxxkkkkkkxdoollllooddxxxxkkk
// ....',;:codxkO000OOxdoc:;,''',,,;;;;,''.......',,;:clodkO00000Okxolc::;,,''..',;:ldxOKXNWWWNNK0OkkkkkkkkkkkxxddooooodxxkOOOOO000
// ....',;;clodxkkOOOkkdolc:;,,,,,,,,'..........,;:clodxkO0KKXKK0Okxdolcc::;;,,,;;:codkO0XXNNNNXKK0OOOOOkkkkxxdoollloodxkO0KKKXXXXX
//
// VERSION: 1.1.1
// https://github.com/Auburn/FastNoiseLite
// Switch between using floats or doubles for input position
#define FNLfloat float
//#define FNLfloat double
// Noise Type
#define FNL_NOISE_OPENSIMPLEX2 0
#define FNL_NOISE_OPENSIMPLEX2S 1
#define FNL_NOISE_CELLULAR 2
#define FNL_NOISE_PERLIN 3
#define FNL_NOISE_VALUE_CUBIC 4
#define FNL_NOISE_VALUE 5
#define fnl_noise_type int
// Rotation types
#define FNL_ROTATION_NONE 0
#define FNL_ROTATION_IMPROVE_XY_PLANES 1
#define FNL_ROTATION_IMPROVE_XZ_PLANES 2
#define fnl_rotation_type_3d int
// Fractal types
#define FNL_FRACTAL_NONE 0
#define FNL_FRACTAL_FBM 1
#define FNL_FRACTAL_RIDGED 2
#define FNL_FRACTAL_PINGPONG 3
#define FNL_FRACTAL_DOMAIN_WARP_PROGRESSIVE 4
#define FNL_FRACTAL_DOMAIN_WARP_INDEPENDENT 5
#define fnl_fractal_type int
#define FNL_CELLULAR_DISTANCE_EUCLIDEAN 0
#define FNL_CELLULAR_DISTANCE_EUCLIDEANSQ 1
#define FNL_CELLULAR_DISTANCE_MANHATTAN 2
#define FNL_CELLULAR_DISTANCE_HYBRID 3
#define fnl_cellular_distance_func int
#define FNL_CELLULAR_RETURN_TYPE_CELLVALUE 0
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE 1
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2 2
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2ADD 3
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2SUB 4
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2MUL 5
#define FNL_CELLULAR_RETURN_TYPE_DISTANCE2DIV 6
#define fnl_cellular_return_type int
#define FNL_DOMAIN_WARP_OPENSIMPLEX2 0
#define FNL_DOMAIN_WARP_OPENSIMPLEX2_REDUCED 1
#define FNL_DOMAIN_WARP_BASICGRID 2
#define fnl_domain_warp_type int
// Structure containing entire noise system state.
// @note Must only be created using fnlCreateState(optional: seed). To ensure defaults are set.
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_DISTANCE_EUCLIDEANSQ
fnl_cellular_distance_func cellular_distance_func;
// The cellular return type from cellular noise calculations.
// @remark Default: FNL_CELLULAR_RETURN_TYPE_DISTANCE
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;
};
// From here on, this is private implementation
// Constants
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
};
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
};
const float GRADIENTS_3D[] =
{
0.f, 1.f, 1.f, 0.f, 0.f,-1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f,-1.f,-1.f, 0.f,
1.f, 0.f, 1.f, 0.f, -1.f, 0.f, 1.f, 0.f, 1.f, 0.f,-1.f, 0.f, -1.f, 0.f,-1.f, 0.f,
1.f, 1.f, 0.f, 0.f, -1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f, -1.f,-1.f, 0.f, 0.f,
0.f, 1.f, 1.f, 0.f, 0.f,-1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f,-1.f,-1.f, 0.f,
1.f, 0.f, 1.f, 0.f, -1.f, 0.f, 1.f, 0.f, 1.f, 0.f,-1.f, 0.f, -1.f, 0.f,-1.f, 0.f,
1.f, 1.f, 0.f, 0.f, -1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f, -1.f,-1.f, 0.f, 0.f,
0.f, 1.f, 1.f, 0.f, 0.f,-1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f,-1.f,-1.f, 0.f,
1.f, 0.f, 1.f, 0.f, -1.f, 0.f, 1.f, 0.f, 1.f, 0.f,-1.f, 0.f, -1.f, 0.f,-1.f, 0.f,
1.f, 1.f, 0.f, 0.f, -1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f, -1.f,-1.f, 0.f, 0.f,
0.f, 1.f, 1.f, 0.f, 0.f,-1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f,-1.f,-1.f, 0.f,
1.f, 0.f, 1.f, 0.f, -1.f, 0.f, 1.f, 0.f, 1.f, 0.f,-1.f, 0.f, -1.f, 0.f,-1.f, 0.f,
1.f, 1.f, 0.f, 0.f, -1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f, -1.f,-1.f, 0.f, 0.f,
0.f, 1.f, 1.f, 0.f, 0.f,-1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f,-1.f,-1.f, 0.f,
1.f, 0.f, 1.f, 0.f, -1.f, 0.f, 1.f, 0.f, 1.f, 0.f,-1.f, 0.f, -1.f, 0.f,-1.f, 0.f,
1.f, 1.f, 0.f, 0.f, -1.f, 1.f, 0.f, 0.f, 1.f,-1.f, 0.f, 0.f, -1.f,-1.f, 0.f, 0.f,
1.f, 1.f, 0.f, 0.f, 0.f,-1.f, 1.f, 0.f, -1.f, 1.f, 0.f, 0.f, 0.f,-1.f,-1.f, 0.f
};
const float RAND_VECS_3D[] =
{
-0.7292736885f, -0.6618439697f, 0.1735581948f, 0.f, 0.790292081f, -0.5480887466f, -0.2739291014f, 0.f, 0.7217578935f, 0.6226212466f, -0.3023380997f, 0.f, 0.565683137f, -0.8208298145f, -0.0790000257f, 0.f, 0.760049034f, -0.5555979497f, -0.3370999617f, 0.f, 0.3713945616f, 0.5011264475f, 0.7816254623f, 0.f, -0.1277062463f, -0.4254438999f, -0.8959289049f, 0.f, -0.2881560924f, -0.5815838982f, 0.7607405838f, 0.f,
0.5849561111f, -0.662820239f, -0.4674352136f, 0.f, 0.3307171178f, 0.0391653737f, 0.94291689f, 0.f, 0.8712121778f, -0.4113374369f, -0.2679381538f, 0.f, 0.580981015f, 0.7021915846f, 0.4115677815f, 0.f, 0.503756873f, 0.6330056931f, -0.5878203852f, 0.f, 0.4493712205f, 0.601390195f, 0.6606022552f, 0.f, -0.6878403724f, 0.09018890807f, -0.7202371714f, 0.f, -0.5958956522f, -0.6469350577f, 0.475797649f, 0.f,
-0.5127052122f, 0.1946921978f, -0.8361987284f, 0.f, -0.9911507142f, -0.05410276466f, -0.1212153153f, 0.f, -0.2149721042f, 0.9720882117f, -0.09397607749f, 0.f, -0.7518650936f, -0.5428057603f, 0.3742469607f, 0.f, 0.5237068895f, 0.8516377189f, -0.02107817834f, 0.f, 0.6333504779f, 0.1926167129f, -0.7495104896f, 0.f, -0.06788241606f, 0.3998305789f, 0.9140719259f, 0.f, -0.5538628599f, -0.4729896695f, -0.6852128902f, 0.f,
-0.7261455366f, -0.5911990757f, 0.3509933228f, 0.f, -0.9229274737f, -0.1782808786f, 0.3412049336f, 0.f, -0.6968815002f, 0.6511274338f, 0.3006480328f, 0.f, 0.9608044783f, -0.2098363234f, -0.1811724921f, 0.f, 0.06817146062f, -0.9743405129f, 0.2145069156f, 0.f, -0.3577285196f, -0.6697087264f, -0.6507845481f, 0.f, -0.1868621131f, 0.7648617052f, -0.6164974636f, 0.f, -0.6541697588f, 0.3967914832f, 0.6439087246f, 0.f,
0.6993340405f, -0.6164538506f, 0.3618239211f, 0.f, -0.1546665739f, 0.6291283928f, 0.7617583057f, 0.f, -0.6841612949f, -0.2580482182f, -0.6821542638f, 0.f, 0.5383980957f, 0.4258654885f, 0.7271630328f, 0.f, -0.5026987823f, -0.7939832935f, -0.3418836993f, 0.f, 0.3202971715f, 0.2834415347f, 0.9039195862f, 0.f, 0.8683227101f, -0.0003762656404f, -0.4959995258f, 0.f, 0.791120031f, -0.08511045745f, 0.6057105799f, 0.f,
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};
// Utilities
float _fnlFastMin(float x, float y) { return min(x, y); }
float _fnlFastMax(float x, float y) { return max(x, y); }
float _fnlFastAbs(float f) { return abs(f); }
float _fnlFastSqrt(float a) { return sqrt(a); }
int _fnlFastFloor(FNLfloat f) { return int(floor(f)); }
int _fnlFastRound(FNLfloat f) { return int(round(f)); }
float _fnlLerp(float a, float b, float t) { return mix(a, b, t); }
float _fnlInterpHermite(float t) { return t * t * (3.f - 2.f * t); }
float _fnlInterpQuintic(float t) { return t * t * t * (t * (t * 6.f - 15.f) + 10.f); }
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;
}
float _fnlPingPong(float t)
{
t -= float(int(t * 0.5f)) * 2.f;
return t < 1.f ? t : 2.f - t;
}
float _fnlCalculateFractalBounding(fnl_state state)
{
float gain = _fnlFastAbs(state.gain);
float amp = gain;
float ampFractal = 1.f;
for (int i = 1; i < state.octaves; i++)
{
ampFractal += amp;
amp *= gain;
}
return 1.f / ampFractal;
}
// Hashing
const int PRIME_X = 501125321;
const int PRIME_Y = 1136930381;
const int PRIME_Z = 1720413743;
int _fnlHash2D(int seed, int xPrimed, int yPrimed)
{
int hash = seed ^ xPrimed ^ yPrimed;
hash *= 0x27d4eb2d;
return hash;
}
int _fnlHash3D(int seed, int xPrimed, int yPrimed, int zPrimed)
{
int hash = seed ^ xPrimed ^ yPrimed ^ zPrimed;
hash *= 0x27d4eb2d;
return hash;
}
float _fnlValCoord2D(int seed, int xPrimed, int yPrimed)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed);
hash *= hash;
hash ^= hash << 19;
return float(hash) * (1.f / 2147483648.f);
}
float _fnlValCoord3D(int seed, int xPrimed, int yPrimed, int zPrimed)
{
int hash = _fnlHash3D(seed, xPrimed, yPrimed, zPrimed);
hash *= hash;
hash ^= hash << 19;
return float(hash) * (1.f / 2147483648.f);
}
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];
}
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];
}
void _fnlGradCoordOut2D(int seed, int xPrimed, int yPrimed, out float xo, out float yo)
{
int hash = _fnlHash2D(seed, xPrimed, yPrimed) & (255 << 1);
xo = RAND_VECS_2D[hash];
yo = RAND_VECS_2D[hash | 1];
}
void _fnlGradCoordOut3D(int seed, int xPrimed, int yPrimed, int zPrimed, out float xo, out float yo, out 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];
}
void _fnlGradCoordDual2D(int seed, int xPrimed, int yPrimed, float xd, float yd, out float xo, out 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;
}
void _fnlGradCoordDual3D(int seed, int xPrimed, int yPrimed, int zPrimed, float xd, float yd, float zd, out float xo, out float yo, out 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;
}
// Noise Coordinate Transforms (frequency, and possible skew or rotation)
void _fnlTransformNoiseCoordinate2D(fnl_state state, inout FNLfloat x, inout 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.f);
FNLfloat t = (x + y) * F2;
x += t;
y += t;
}
break;
default:
break;
}
}
void _fnlTransformNoiseCoordinate3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout 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.f / 3.f);
FNLfloat r = (x + y + z) * R3; // Rotation, not skew
x = r - x;
y = r - y;
z = r - z;
}
break;
default:
break;
}
break;
}
}
// Domain Warp Coordinate Transforms
void _fnlTransformDomainWarpCoordinate2D(fnl_state state, inout FNLfloat x, inout 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.f);
FNLfloat t = (x + y) * F2;
x += t;
y += t;
}
break;
default:
break;
}
}
void _fnlTransformDomainWarpCoordinate3D(fnl_state state, inout FNLfloat x, inout FNLfloat y, inout 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.f / 3.f);
FNLfloat r = (x + y + z) * R3; // Rotation, not skew
x = r - x;
y = r - y;
z = r - z;
}
break;
default:
break;
}
break;
}
}
// Simplex/OpenSimplex2 Noise
float _fnlSingleSimplex2D(int seed, FNLfloat x, FNLfloat y)
{
// 2D OpenSimplex2 case uses the same algorithm as ordinary Simplex.
const float SQRT3 = 1.7320508075688772935274463415059;
const float G2 = (3.f - SQRT3) / 6.f;
// --- 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 = x - float(i);
float yi = y - float(j);
float t = (xi + yi) * G2;
float x0 = xi - t;
float y0 = yi - t;
i *= PRIME_X;
j *= PRIME_Y;
float n0, n1, n2;
float a = 0.5f - x0 * x0 - y0 * y0;
if (a <= 0.f)
{
n0 = 0.f;
}
else
{
n0 = (a * a) * (a * a) * _fnlGradCoord2D(seed, i, j, x0, y0);
}
float c = (2.f * (1.f - 2.f * G2) * (1.f / G2 - 2.f)) * t + ((-2.f * (1.f - 2.f * G2) * (1.f - 2.f * G2)) + a);
if (c <= 0.f)
{
n2 = 0.f;
}
else
{
float x2 = x0 + (2.f * G2 - 1.f);
float y2 = y0 + (2.f * G2 - 1.f);
n2 = (c * c) * (c * c) * _fnlGradCoord2D(seed, i + PRIME_X, j + PRIME_Y, x2, y2);
}
if (y0 > x0)
{
float x1 = x0 + G2;
float y1 = y0 + G2 - 1.f;
float b = 0.5f - x1 * x1 - y1 * y1;
if (b <= 0.f)
{
n1 = 0.f;
}
else
{
n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i, j + PRIME_Y, x1, y1);
}
}
else
{
float x1 = x0 + (G2 - 1.f);
float y1 = y0 + G2;
float b = 0.5f - x1 * x1 - y1 * y1;
if (b <= 0.f)
{
n1 = 0.f;
}
else
{
n1 = (b * b) * (b * b) * _fnlGradCoord2D(seed, i + PRIME_X, j, x1, y1);
}
}
return (n0 + n1 + n2) * 99.83685446303647;
}
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.f / 3.f);
// 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 = x - float(i);
float y0 = y - float(j);
float z0 = z - float(k);
int xNSign = int(-1.f - x0) | 1;
int yNSign = int(-1.f - y0) | 1;
int zNSign = int(-1.f - z0) | 1;
float ax0 = float(xNSign) * -x0;
float ay0 = float(yNSign) * -y0;
float az0 = float(zNSign) * -z0;
i *= PRIME_X;
j *= PRIME_Y;
k *= PRIME_Z;
float value = 0.f;
float a = (0.6f - x0 * x0) - (y0 * y0 + z0 * z0);
for (int l = 0; ; l++)
{
if (a > 0.f)
{
value += (a * a) * (a * a) * _fnlGradCoord3D(seed, i, j, k, x0, y0, z0);
}
float b = a + 1.f;
int i1 = i;
int j1 = j;
int k1 = k;
float x1 = x0;
float y1 = y0;
float z1 = z0;
if (ax0 >= ay0 && ax0 >= az0)
{
x1 += float(xNSign);
b -= float(xNSign) * 2.f * x1;
i1 -= xNSign * PRIME_X;
}
else if (ay0 > ax0 && ay0 >= az0)
{
y1 += float(yNSign);
b -= float(yNSign) * 2.f * y1;
j1 -= yNSign * PRIME_Y;
}
else
{
z1 += float(zNSign);
b -= float(zNSign) * 2.f * z1;
k1 -= zNSign * PRIME_Z;
}
if (b > 0.f)
{
value += (b * b) * (b * b) * _fnlGradCoord3D(seed, i1, j1, k1, x1, y1, z1);
}
if (l == 1) break;
ax0 = 0.5f - ax0;
ay0 = 0.5f - ay0;
az0 = 0.5f - az0;
x0 = float(xNSign) * ax0;
y0 = float(yNSign) * ay0;
z0 = float(zNSign) * az0;
a += (0.75f - ax0) - (ay0 + az0);
i += (xNSign >> 1) & PRIME_X;
j += (yNSign >> 1) & PRIME_Y;
k += (zNSign >> 1) & PRIME_Z;
xNSign = -xNSign;
yNSign = -yNSign;
zNSign = -zNSign;
seed = ~seed;
}
return value * 32.69428253173828125;
}
// OpenSimplex2S Noise
float _fnlSingleOpenSimplex2S2D(int seed, FNLfloat x, FNLfloat y)
{
// 2D OpenSimplex2S case is a modified 2D simplex noise.
const FNLfloat SQRT3 = FNLfloat(1.7320508075688772935274463415059);
const FNLfloat G2 = (3.f - SQRT3) / 6.f;
// --- 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 = x - float(i);
float yi = y - float(j);
i *= PRIME_X;
j *= PRIME_Y;
int i1 = i + PRIME_X;
int j1 = j + PRIME_Y;
float t = (xi + yi) * G2;
float x0 = xi - t;
float y0 = yi - t;
int aMask = int((xi + yi + 1.f) * -0.5f);
int bMask = int((xi - (float(aMask) + 2.f)) * 0.5f - yi);
int cMask = int((yi - (float(aMask) + 2.f)) * 0.5f - xi);
float a0 = (2.f / 3.f) - x0 * x0 - y0 * y0;
float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord2D(seed, i, j, x0, y0);
float a1 = (2.f * (1.f - 2.f * G2) * (1.f / G2 - 2.f)) * t + ((-2.f * (1.f - 2.f * G2) * (1.f - 2.f * G2)) + a0);
float x1 = x0 - (1.f - 2.f * G2);
float y1 = y0 - (1.f - 2.f * G2);
value += (a1 * a1) * (a1 * a1) * _fnlGradCoord2D(seed, i1, j1, x1, y1);
int di2 = ~(aMask | cMask) | 1;
int ndj2 = (aMask & bMask) << 1;
float t2 = float(di2 - ndj2) * G2;
float x2 = x0 - float(di2) + t2;
float y2 = y0 + float(ndj2) + t2;
float a2 = (2.f / 3.f) - x2 * x2 - y2 * y2;
if (a2 > 0.f)
{
value += (a2 * a2) * (a2 * a2) * _fnlGradCoord2D(seed, i1 + (di2 & (-PRIME_X << 1)), j + (ndj2 & (PRIME_Y << 1)), x2, y2);
}
int ndi3 = (aMask & cMask) << 1;
int dj3 = ~(aMask | bMask) | 1;
float t3 = float(dj3 - ndi3) * G2;
float x3 = x0 + float(ndi3) + t3;
float y3 = y0 - float(dj3) + t3;
float a3 = (2.f / 3.f) - x3 * x3 - y3 * y3;
if (a3 > 0.f)
{
value += (a3 * a3) * (a3 * a3) * _fnlGradCoord2D(seed, i + (ndi3 & (PRIME_X << 1)), j1 + (dj3 & (-PRIME_Y << 1)), x3, y3);
}
return value * 18.24196194486065;
}
float _fnlSingleOpenSimplex2S3D(int seed, FNLfloat x, FNLfloat y, FNLfloat z)
{
// 3D OpenSimplex2S case uses two offset rotated cube grids.
// --- Rotation moved to TransformNoiseCoordinate method ---
// const FNLfloat R3 = (FNLfloat)(2.f / 3.f);
// FNLfloat r = (x + y + z) * R3; // Rotation, not skew
// x = r - x; y = r - y; z = r - z;
int i = _fnlFastFloor(x);
int j = _fnlFastFloor(y);
int k = _fnlFastFloor(z);
float xi = x - float(i);
float yi = y - float(j);
float zi = z - float(k);
i *= PRIME_X;
j *= PRIME_Y;
k *= PRIME_Z;
int seed2 = seed + 1293373;
int xNMask = int(-0.5f - xi);
int yNMask = int(-0.5f - yi);
int zNMask = int(-0.5f - zi);
float x0 = xi + float(xNMask);
float y0 = yi + float(yNMask);
float z0 = zi + float(zNMask);
float a0 = 0.75f - x0 * x0 - y0 * y0 - z0 * z0;
float value = (a0 * a0) * (a0 * a0) * _fnlGradCoord3D(seed,
i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x0, y0, z0);
float x1 = xi - 0.5f;
float y1 = yi - 0.5f;
float z1 = zi - 0.5f;
float a1 = 0.75f - x1 * x1 - y1 * y1 - z1 * z1;
value += (a1 * a1) * (a1 * a1) * _fnlGradCoord3D(seed2,
i + PRIME_X, j + PRIME_Y, k + PRIME_Z, x1, y1, z1);
float xAFlipMask0 = float((xNMask | 1) << 1) * x1;
float yAFlipMask0 = float((yNMask | 1) << 1) * y1;
float zAFlipMask0 = float((zNMask | 1) << 1) * z1;
float xAFlipMask1 = float(-2 - (xNMask << 2)) * x1 - 1.f;
float yAFlipMask1 = float(-2 - (yNMask << 2)) * y1 - 1.f;
float zAFlipMask1 = float(-2 - (zNMask << 2)) * z1 - 1.f;
bool skip5 = false;
float a2 = xAFlipMask0 + a0;
if (a2 > 0.f)
{
float x2 = x0 - float(xNMask | 1);
float y2 = y0;
float z2 = z0;
value += (a2 * a2) * (a2 * a2) * _fnlGradCoord3D(seed,
i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x2, y2, z2);
}
else
{
float a3 = yAFlipMask0 + zAFlipMask0 + a0;
if (a3 > 0.f)
{
float x3 = x0;
float y3 = y0 - float(yNMask | 1);
float z3 = z0 - float(zNMask | 1);
value += (a3 * a3) * (a3 * a3) * _fnlGradCoord3D(seed,
i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x3, y3, z3);
}
float a4 = xAFlipMask1 + a1;
if (a4 > 0.f)
{
float x4 = float(xNMask | 1) + x1;
float y4 = y1;
float z4 = z1;
value += (a4 * a4) * (a4 * a4) * _fnlGradCoord3D(seed2,
i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + PRIME_Z, x4, y4, z4);
skip5 = true;
}
}
bool skip9 = false;
float a6 = yAFlipMask0 + a0;
if (a6 > 0.f)
{
float x6 = x0;
float y6 = y0 - float(yNMask | 1);
float z6 = z0;
value += (a6 * a6) * (a6 * a6) * _fnlGradCoord3D(seed,
i + (xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), x6, y6, z6);
}
else
{
float a7 = xAFlipMask0 + zAFlipMask0 + a0;
if (a7 > 0.f)
{
float x7 = x0 - float(xNMask | 1);
float y7 = y0;
float z7 = z0 - float(zNMask | 1);
value += (a7 * a7) * (a7 * a7) * _fnlGradCoord3D(seed,
i + (~xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), x7, y7, z7);
}
float a8 = yAFlipMask1 + a1;
if (a8 > 0.f)
{
float x8 = x1;
float y8 = float(yNMask | 1) + y1;
float z8 = z1;
value += (a8 * a8) * (a8 * a8) * _fnlGradCoord3D(seed2,
i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + PRIME_Z, x8, y8, z8);
skip9 = true;
}
}
bool skipD = false;
float aA = zAFlipMask0 + a0;
if (aA > 0.f)
{
float xA = x0;
float yA = y0;
float zA = z0 - float(zNMask | 1);
value += (aA * aA) * (aA * aA) * _fnlGradCoord3D(seed,
i + (xNMask & PRIME_X), j + (yNMask & PRIME_Y), k + (~zNMask & PRIME_Z), xA, yA, zA);
}
else
{
float aB = xAFlipMask0 + yAFlipMask0 + a0;
if (aB > 0.f)
{
float xB = x0 - float(xNMask | 1);
float yB = y0 - float(yNMask | 1);
float zB = z0;
value += (aB * aB) * (aB * aB) * _fnlGradCoord3D(seed,
i + (~xNMask & PRIME_X), j + (~yNMask & PRIME_Y), k + (zNMask & PRIME_Z), xB, yB, zB);
}
float aC = zAFlipMask1 + a1;
if (aC > 0.f)
{
float xC = x1;
float yC = y1;
float zC = float(zNMask | 1) + z1;
value += (aC * aC) * (aC * aC) * _fnlGradCoord3D(seed2,
i + PRIME_X, j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), xC, yC, zC);
skipD = true;
}
}
if (!skip5)
{
float a5 = yAFlipMask1 + zAFlipMask1 + a1;
if (a5 > 0.f)
{
float x5 = x1;
float y5 = float(yNMask | 1) + y1;
float z5 = float(zNMask | 1) + z1;
value += (a5 * a5) * (a5 * a5) * _fnlGradCoord3D(seed2,
i + PRIME_X, j + (yNMask & (PRIME_Y << 1)), k + (zNMask & (PRIME_Z << 1)), x5, y5, z5);
}
}
if (!skip9)
{
float a9 = xAFlipMask1 + zAFlipMask1 + a1;
if (a9 > 0.f)
{
float x9 = float(xNMask | 1) + x1;
float y9 = y1;
float z9 = float(zNMask | 1) + z1;
value += (a9 * a9) * (a9 * a9) * _fnlGradCoord3D(seed2,
i + (xNMask & (PRIME_X * 2)), j + PRIME_Y, k + (zNMask & (PRIME_Z << 1)), x9, y9, z9);
}
}