├── .gitattributes ├── .gitignore ├── Assets ├── DFNoise2D.cs ├── DFNoise2D.cs.meta ├── DFNoise2D.unity ├── DFNoise2D.unity.meta ├── DFNoise3D.cs ├── DFNoise3D.cs.meta ├── DFNoise3D.unity ├── DFNoise3D.unity.meta ├── Particle.mat ├── Particle.mat.meta ├── Particle2D.cs ├── Particle2D.cs.meta ├── Particle2D.unity ├── Particle2D.unity.meta ├── Particle3D.cs ├── Particle3D.cs.meta ├── Particle3D.unity ├── Particle3D.unity.meta ├── Perlin.cs ├── Perlin.cs.meta ├── Sphere.fbx ├── Sphere.fbx.meta ├── Sphere.mat └── Sphere.mat.meta ├── ProjectSettings ├── AudioManager.asset ├── ClusterInputManager.asset ├── DynamicsManager.asset ├── EditorBuildSettings.asset ├── EditorSettings.asset ├── GraphicsSettings.asset ├── InputManager.asset ├── NavMeshAreas.asset ├── NetworkManager.asset ├── Physics2DSettings.asset ├── ProjectSettings.asset ├── ProjectVersion.txt ├── QualitySettings.asset ├── TagManager.asset ├── TimeManager.asset ├── UnityAdsSettings.asset └── UnityConnectSettings.asset └── README.md /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | 4 | # Custom for Visual Studio 5 | *.cs diff=csharp 6 | 7 | # Standard to msysgit 8 | *.doc diff=astextplain 9 | *.DOC diff=astextplain 10 | *.docx diff=astextplain 11 | *.DOCX diff=astextplain 12 | *.dot diff=astextplain 13 | *.DOT diff=astextplain 14 | *.pdf diff=astextplain 15 | *.PDF diff=astextplain 16 | *.rtf diff=astextplain 17 | *.RTF diff=astextplain 18 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /[Ll]ibrary/ 2 | /[Tt]emp/ 3 | /[Oo]bj/ 4 | /[Bb]uild/ 5 | 6 | # Autogenerated VS/MD solution and project files 7 | *.csproj 8 | *.unityproj 9 | *.sln 10 | *.suo 11 | *.tmp 12 | *.user 13 | *.userprefs 14 | *.pidb 15 | *.booproj 16 | 17 | # Unity3D generated meta files 18 | *.pidb.meta 19 | 20 | # Unity3D Generated File On Crash Reports 21 | sysinfo.txt 22 | 23 | # ========================= 24 | # Operating System Files 25 | # ========================= 26 | 27 | # OSX 28 | # ========================= 29 | 30 | .DS_Store 31 | .AppleDouble 32 | .LSOverride 33 | 34 | # Thumbnails 35 | ._* 36 | 37 | # Files that might appear in the root of a volume 38 | .DocumentRevisions-V100 39 | .fseventsd 40 | .Spotlight-V100 41 | .TemporaryItems 42 | .Trashes 43 | .VolumeIcon.icns 44 | 45 | # Directories potentially created on remote AFP share 46 | .AppleDB 47 | .AppleDesktop 48 | Network Trash Folder 49 | Temporary Items 50 | .apdisk 51 | 52 | # Windows 53 | # ========================= 54 | 55 | # Windows image file caches 56 | Thumbs.db 57 | ehthumbs.db 58 | 59 | # Folder config file 60 | Desktop.ini 61 | 62 | # Recycle Bin used on file shares 63 | $RECYCLE.BIN/ 64 | 65 | # Windows Installer files 66 | *.cab 67 | *.msi 68 | *.msm 69 | *.msp 70 | 71 | # Windows shortcuts 72 | *.lnk 73 | -------------------------------------------------------------------------------- /Assets/DFNoise2D.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | 3 | [ExecuteInEditMode] 4 | public class DFNoise2D : MonoBehaviour 5 | { 6 | public enum LineMode { Gradient, DFNoise } 7 | 8 | [Header("Noise Parameters")] 9 | [SerializeField] float _frequency = 3; 10 | [SerializeField] float _animationSpeed = 0.2f; 11 | 12 | [Header("Vector Analysis")] 13 | [SerializeField] float _delta = 0.0001f; 14 | 15 | [Header("Visualization")] 16 | [SerializeField] LineMode _lineMode; 17 | [SerializeField] int _columns = 16; 18 | [SerializeField] int _rows = 16; 19 | [SerializeField] float _lineScale = 0.1f; 20 | [SerializeField] Color _lineColor = Color.red; 21 | 22 | float GetNoise(Vector2 p) 23 | { 24 | p *= _frequency; 25 | var t = Time.time * _animationSpeed; 26 | return Perlin.Noise(new Vector3(p.x, p.y, t)); 27 | } 28 | 29 | Vector2 GetGradient(Vector2 p) 30 | { 31 | var n0 = GetNoise(p); 32 | var n1 = GetNoise(p + new Vector2(_delta, 0)); 33 | var n2 = GetNoise(p + new Vector2(0, _delta)); 34 | return new Vector3(n1 - n0, n2 - n0) / _delta; 35 | } 36 | 37 | Vector2 GetDFNoise(Vector2 p) 38 | { 39 | var g = GetGradient(p); 40 | return new Vector2(g.y, -g.x); 41 | } 42 | 43 | void OnDrawGizmos() 44 | { 45 | var cubeScale = new Vector3(1.0f / _columns, 1.0f / _rows, 1); 46 | var lineScale = _lineScale / Mathf.Max(_columns, _rows); 47 | 48 | for (var ix = 0; ix < _columns; ix++) 49 | { 50 | for (var iy = 0; iy < _rows; iy++) 51 | { 52 | var px = (ix + 0.5f) / _columns - 0.5f; 53 | var py = (iy + 0.5f) / _rows - 0.5f; 54 | var p = new Vector2(px, py); 55 | 56 | var n = GetNoise(p); 57 | var cn = (n + 1) / 2; 58 | 59 | var dp = _lineMode == LineMode.Gradient ? 60 | GetGradient(p) : GetDFNoise(p); 61 | 62 | Gizmos.color = new Color(cn, cn, cn, 1); 63 | Gizmos.DrawCube(new Vector3(px, py, 1), cubeScale); 64 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[Header("Visualization")] 10 | [SerializeField] int _gridCount = 16; 11 | [SerializeField] float _lineScale = 0.1f; 12 | 13 | const float _epsilon = 0.0001f; 14 | static Vector3 _noiseOffset = new Vector3(77.7f, 33.3f, 11.1f); 15 | 16 | float GetNoise(Vector3 p) 17 | { 18 | return Perlin.Noise(p * _frequency); 19 | } 20 | 21 | Vector3 GetGradient(Vector3 p) 22 | { 23 | var n0 = GetNoise(p); 24 | var nx = GetNoise(p + Vector3.right * _epsilon); 25 | var ny = GetNoise(p + Vector3.up * _epsilon); 26 | var nz = GetNoise(p + Vector3.forward * _epsilon); 27 | return new Vector3(nx - n0, ny - n0, nz - n0) / _epsilon; 28 | } 29 | 30 | Vector3 GetDFNoise(Vector3 p) 31 | { 32 | var g1 = GetGradient(p); 33 | var g2 = GetGradient(p + _noiseOffset); 34 | return Vector3.Cross(g1, g2); 35 | } 36 | 37 | void OnDrawGizmos() 38 | { 39 | var lineScale = _lineScale / _gridCount; 40 | 41 | for (var ix = 0; ix < _gridCount; ix++) 42 | { 43 | for (var iy = 0; iy < _gridCount; iy++) 44 | { 45 | for (var iz = 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| 22 | float GetNoise(Vector2 p) 23 | { 24 | p *= _frequency; 25 | var t = Time.time * _animationSpeed; 26 | return Perlin.Noise(new Vector3(p.x, p.y, t)); 27 | } 28 | 29 | Vector2 GetGradient(Vector2 p) 30 | { 31 | var n0 = GetNoise(p); 32 | var n1 = GetNoise(p + new Vector2(_epsilon, 0)); 33 | var n2 = GetNoise(p + new Vector2(0, _epsilon)); 34 | return new Vector3(n1 - n0, n2 - n0) / _epsilon; 35 | } 36 | 37 | Vector2 GetDFNoise(Vector2 p) 38 | { 39 | var g = GetGradient(p); 40 | return new Vector2(g.y, -g.x); 41 | } 42 | 43 | void MoveParticle(ref ParticleSystem.Particle p) 44 | { 45 | var n2 = GetDFNoise(p.position); 46 | var n3 = new Vector3(n2.x, n2.y, 0); 47 | p.velocity = 48 | p.velocity * (1.0f - _damping) + 49 | n3 * Time.fixedDeltaTime * _advection; 50 | } 51 | 52 | void FixedUpdate() 53 | { 54 | var maxParticles = _particleSystem.maxParticles; 55 | 56 | if (_particles == null || _particles.Length < maxParticles) 57 | _particles = new ParticleSystem.Particle[maxParticles]; 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b5dc12cd0c956894abf7de26fac513b4, type: 3} 1713 | m_Name: 1714 | m_EditorClassIdentifier: 1715 | _frequency: 6 1716 | _animationSpeed: 0.8 1717 | _advection: 0.02 1718 | _damping: 0.004 1719 | _particleSystem: {fileID: 1885470064} 1720 | -------------------------------------------------------------------------------- /Assets/Particle2D.unity.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: a1d12229664687f4fb7b34d2f0756d5d 3 | timeCreated: 1448631761 4 | licenseType: Pro 5 | DefaultImporter: 6 | userData: 7 | assetBundleName: 8 | assetBundleVariant: 9 | -------------------------------------------------------------------------------- /Assets/Particle3D.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | 3 | namespace DFNoise 4 | { 5 | public class Particle3D : MonoBehaviour 6 | { 7 | [Header("Noise")] 8 | [SerializeField] float _frequency = 3; 9 | [SerializeField] float _animationSpeed = 0.2f; 10 | 11 | [Header("Dynamics")] 12 | [SerializeField] float _advection = 0.1f; 13 | [SerializeField] float _damping = 0.01f; 14 | 15 | [Header("Visualization")] 16 | [SerializeField] ParticleSystem _particleSystem; 17 | 18 | const float _epsilon = 0.0001f; 19 | static Vector3 _noiseOffset = new Vector3(77.7f, 33.3f, 11.1f); 20 | 21 | ParticleSystem.Particle[] _particles; 22 | 23 | float GetNoise(Vector3 p) 24 | { 25 | return Perlin.Noise(p * _frequency); 26 | } 27 | 28 | Vector3 GetGradient(Vector3 p) 29 | { 30 | var n0 = GetNoise(p); 31 | var nx = GetNoise(p + Vector3.right * _epsilon); 32 | var ny = GetNoise(p + Vector3.up * _epsilon); 33 | var nz = GetNoise(p + Vector3.forward * _epsilon); 34 | return new Vector3(nx - n0, ny - n0, nz - n0) / _epsilon; 35 | } 36 | 37 | Vector3 GetDFNoise(Vector3 p) 38 | { 39 | var g1 = GetGradient(p); 40 | var g2 = GetGradient(p + _noiseOffset); 41 | return Vector3.Cross(g1, g2); 42 | } 43 | 44 | void 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assetBundleVariant: 9 | -------------------------------------------------------------------------------- /Assets/Perlin.cs: -------------------------------------------------------------------------------- 1 | // 2 | // Perlin noise generator for Unity 3 | // Keijiro Takahashi, 2013, 2015 4 | // https://github.com/keijiro/PerlinNoise 5 | // 6 | // Based on the original implementation by Ken Perlin 7 | // http://mrl.nyu.edu/~perlin/noise/ 8 | // 9 | using UnityEngine; 10 | 11 | public static class Perlin 12 | { 13 | #region Noise functions 14 | 15 | public static float Noise(float x, float y) 16 | { 17 | var X = Mathf.FloorToInt(x) & 0xff; 18 | var Y = Mathf.FloorToInt(y) & 0xff; 19 | x -= Mathf.Floor(x); 20 | y -= Mathf.Floor(y); 21 | var u = Fade(x); 22 | var v = Fade(y); 23 | var A = (perm[X ] + Y) & 0xff; 24 | var B = (perm[X+1] + Y) & 0xff; 25 | return Lerp(v, Lerp(u, Grad(perm[A ], x, y ), Grad(perm[B ], x-1, y )), 26 | Lerp(u, Grad(perm[A+1], x, y-1), Grad(perm[B+1], x-1, y-1))); 27 | } 28 | 29 | public static float Noise(Vector2 coord) 30 | { 31 | return Noise(coord.x, coord.y); 32 | } 33 | 34 | public static float Noise(float x, float y, float z) 35 | { 36 | var X = Mathf.FloorToInt(x) & 0xff; 37 | var Y = Mathf.FloorToInt(y) & 0xff; 38 | var Z = Mathf.FloorToInt(z) & 0xff; 39 | x -= Mathf.Floor(x); 40 | y -= Mathf.Floor(y); 41 | z -= Mathf.Floor(z); 42 | var u = Fade(x); 43 | var v = Fade(y); 44 | var w = Fade(z); 45 | var A = (perm[X ] + Y) & 0xff; 46 | var B = (perm[X+1] + Y) & 0xff; 47 | var AA = (perm[A ] + Z) & 0xff; 48 | var BA = (perm[B ] + Z) & 0xff; 49 | var AB = (perm[A+1] + Z) & 0xff; 50 | var BB = (perm[B+1] + Z) & 0xff; 51 | return Lerp(w, Lerp(v, Lerp(u, Grad(perm[AA ], x, y , z ), Grad(perm[BA ], x-1, y , z )), 52 | Lerp(u, Grad(perm[AB ], x, y-1, z ), Grad(perm[BB ], x-1, y-1, z ))), 53 | Lerp(v, Lerp(u, Grad(perm[AA+1], x, y , z-1), Grad(perm[BA+1], x-1, y , z-1)), 54 | Lerp(u, Grad(perm[AB+1], x, y-1, z-1), Grad(perm[BB+1], x-1, y-1, z-1)))); 55 | } 56 | 57 | public static float Noise(Vector3 coord) 58 | { 59 | return Noise(coord.x, coord.y, coord.z); 60 | } 61 | 62 | #endregion 63 | 64 | #region fBm functions 65 | 66 | public static float Fbm(Vector2 coord, int octave) 67 | { 68 | var f = 0.0f; 69 | var w = 0.5f; 70 | for (var i = 0; i < octave; i++) { 71 | f += w * Noise(coord); 72 | coord *= 2.0f; 73 | w *= 0.5f; 74 | } 75 | return f; 76 | } 77 | 78 | public static float Fbm(float x, float y, int octave) 79 | { 80 | return Fbm(new Vector2(x, y), octave); 81 | } 82 | 83 | public static float Fbm(Vector3 coord, int octave) 84 | { 85 | var f = 0.0f; 86 | var w = 0.5f; 87 | for (var i = 0; i < octave; i++) { 88 | f += w * Noise(coord); 89 | coord *= 2.0f; 90 | w *= 0.5f; 91 | } 92 | return f; 93 | } 94 | 95 | public static float Fbm(float x, float y, float z, int octave) 96 | { 97 | return Fbm(new Vector3(x, y, z), octave); 98 | } 99 | 100 | #endregion 101 | 102 | #region Private functions 103 | 104 | static float Fade(float t) 105 | { 106 | return t * t * t * (t * (t * 6 - 15) + 10); 107 | } 108 | 109 | static float Lerp(float t, float a, float b) 110 | { 111 | return a + t * (b - a); 112 | } 113 | 114 | static float Grad(int hash, float x, float y) 115 | { 116 | return ((hash & 1) == 0 ? x : -x) + ((hash & 2) == 0 ? y : -y); 117 | } 118 | 119 | static float Grad(int hash, float x, float y, float z) 120 | { 121 | var h = hash & 15; 122 | var u = h < 8 ? x : y; 123 | var v = h < 4 ? y : (h == 12 || h == 14 ? x : z); 124 | return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v); 125 | } 126 | 127 | static int[] perm = { 128 | 151,160,137,91,90,15, 129 | 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, 130 | 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, 131 | 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, 132 | 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, 133 | 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, 134 | 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, 135 | 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, 136 | 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, 137 | 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, 138 | 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, 139 | 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, 140 | 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180, 141 | 151 142 | }; 143 | 144 | #endregion 145 | } 146 | -------------------------------------------------------------------------------- /Assets/Perlin.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 390477dc3d65d5e488d6a68e7e454113 3 | timeCreated: 1448600214 4 | licenseType: Pro 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%YAML 1.1 2 | %TAG !u! tag:unity3d.com,2011: 3 | --- !u!292 &1 4 | UnityAdsSettings: 5 | m_ObjectHideFlags: 0 6 | m_Enabled: 0 7 | m_InitializeOnStartup: 1 8 | m_TestMode: 0 9 | m_EnabledPlatforms: 4294967295 10 | m_IosGameId: 11 | m_AndroidGameId: 12 | -------------------------------------------------------------------------------- /ProjectSettings/UnityConnectSettings.asset: -------------------------------------------------------------------------------- 1 | %YAML 1.1 2 | %TAG !u! tag:unity3d.com,2011: 3 | --- !u!310 &1 4 | UnityConnectSettings: 5 | m_ObjectHideFlags: 0 6 | UnityPurchasingSettings: 7 | m_Enabled: 0 8 | m_TestMode: 0 9 | UnityAnalyticsSettings: 10 | m_Enabled: 0 11 | m_InitializeOnStartup: 1 12 | m_TestMode: 0 13 | m_TestEventUrl: 14 | m_TestConfigUrl: 15 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | This repository contains experimental implementation of a divergence-free noise 2 | function, which was originally proposed by Ivan DeWol. For futher details of 3 | the algorithm, see the original paper. 4 | 5 | http://martian-labs.com/martiantoolz/files/DFnoiseR.pdf 6 | 7 | ![screenshot](http://41.media.tumblr.com/f8c9ded1b40f8dec561ae0cbe6d25ec2/tumblr_nyh99iPeop1qio469o1_400.png) 8 | ![gif](http://49.media.tumblr.com/b179798de44cab44a65b794fa58eb250/tumblr_nyj4zxbbRR1qio469o1_400.gif) 9 | --------------------------------------------------------------------------------