1// SimplexNoise1234
2// Copyright © 2003-2011, Stefan Gustavson
3//
4// Contact: stegu@itn.liu.se
5//
6// This library is public domain software, released by the author
7// into the public domain in February 2011. You may do anything
8// you like with it. You may even remove all attributions,
9// but of course I'd appreciate it if you kept my name somewhere.
10//
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14// General Public License for more details.
15
16// Modified by the LOVE Development Team to remove 3D and 4D implementations due
17// to patent issues.
18
19/** \file
20 \brief Implements the SimplexNoise1234 class for producing Perlin simplex noise.
21 \author Stefan Gustavson (stegu@itn.liu.se)
22*/
23
24/*
25 * This implementation is "Simplex Noise" as presented by
26 * Ken Perlin at a relatively obscure and not often cited course
27 * session "Real-Time Shading" at Siggraph 2001 (before real
28 * time shading actually took on), under the title "hardware noise".
29 * The 3D function is numerically equivalent to his Java reference
30 * code available in the PDF course notes, although I re-implemented
31 * it from scratch to get more readable code. The 1D, 2D and 4D cases
32 * were implemented from scratch by me from Ken Perlin's text.
33 *
34 * This is a highly reusable class. It has no dependencies
35 * on any other file, apart from its own header file.
36 */
37
38
39#include "simplexnoise1234.h"
40
41#define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) )
42
43//---------------------------------------------------------------------
44// Static data
45
46/*
47 * Permutation table. This is just a random jumble of all numbers 0-255,
48 * repeated twice to avoid wrapping the index at 255 for each lookup.
49 * This needs to be exactly the same for all instances on all platforms,
50 * so it's easiest to just keep it as static explicit data.
51 * This also removes the need for any initialisation of this class.
52 *
53 * Note that making this an int[] instead of a char[] might make the
54 * code run faster on platforms with a high penalty for unaligned single
55 * byte addressing. Intel x86 is generally single-byte-friendly, but
56 * some other CPUs are faster with 4-aligned reads.
57 * However, a char[] is smaller, which avoids cache trashing, and that
58 * is probably the most important aspect on most architectures.
59 * This array is accessed a *lot* by the noise functions.
60 * A vector-valued noise over 3D accesses it 96 times, and a
61 * float-valued 4D noise 64 times. We want this to fit in the cache!
62 */
63unsigned char SimplexNoise1234::perm[512] = {151,160,137,91,90,15,
64 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
65 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
66 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
67 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
68 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
69 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
70 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
71 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
72 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
73 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
74 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
75 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
76 151,160,137,91,90,15,
77 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
78 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
79 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
80 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
81 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
82 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
83 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
84 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
85 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
86 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
87 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
88 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
89};
90
91//---------------------------------------------------------------------
92
93/*
94 * Helper functions to compute gradients-dot-residualvectors (1D to 4D)
95 * Note that these generate gradients of more than unit length. To make
96 * a close match with the value range of classic Perlin noise, the final
97 * noise values need to be rescaled to fit nicely within [-1,1].
98 * (The simplex noise functions as such also have different scaling.)
99 * Note also that these noise functions are the most practical and useful
100 * signed version of Perlin noise. To return values according to the
101 * RenderMan specification from the SL noise() and pnoise() functions,
102 * the noise values need to be scaled and offset to [0,1], like this:
103 * float SLnoise = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5;
104 */
105
106float SimplexNoise1234::grad( int hash, float x ) {
107 int h = hash & 15;
108 float grad = 1.0f + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0
109 if (h&8) grad = -grad; // Set a random sign for the gradient
110 return ( grad * x ); // Multiply the gradient with the distance
111}
112
113float SimplexNoise1234::grad( int hash, float x, float y ) {
114 int h = hash & 7; // Convert low 3 bits of hash code
115 float u = h<4 ? x : y; // into 8 simple gradient directions,
116 float v = h<4 ? y : x; // and compute the dot product with (x,y).
117 return ((h&1)? -u : u) + ((h&2)? -2.0f*v : 2.0f*v);
118}
119
120// 1D simplex noise
121float SimplexNoise1234::noise(float x) {
122
123 int i0 = FASTFLOOR(x);
124 int i1 = i0 + 1;
125 float x0 = x - i0;
126 float x1 = x0 - 1.0f;
127
128 float n0, n1;
129
130 float t0 = 1.0f - x0*x0;
131// if(t0 < 0.0f) t0 = 0.0f;
132 t0 *= t0;
133 n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);
134
135 float t1 = 1.0f - x1*x1;
136// if(t1 < 0.0f) t1 = 0.0f;
137 t1 *= t1;
138 n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
139 // The maximum value of this noise is 8*(3/4)^4 = 2.53125
140 // A factor of 0.395 will scale to fit exactly within [-1,1]
141 return 0.395f * (n0 + n1);
142
143}
144
145// 2D simplex noise
146float SimplexNoise1234::noise(float x, float y) {
147
148#define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0)
149#define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0
150
151 float n0, n1, n2; // Noise contributions from the three corners
152
153 // Skew the input space to determine which simplex cell we're in
154 float s = (x+y)*F2; // Hairy factor for 2D
155 float xs = x + s;
156 float ys = y + s;
157 int i = FASTFLOOR(xs);
158 int j = FASTFLOOR(ys);
159
160 float t = (float)(i+j)*G2;
161 float X0 = i-t; // Unskew the cell origin back to (x,y) space
162 float Y0 = j-t;
163 float x0 = x-X0; // The x,y distances from the cell origin
164 float y0 = y-Y0;
165
166 // For the 2D case, the simplex shape is an equilateral triangle.
167 // Determine which simplex we are in.
168 int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
169 if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
170 else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
171
172 // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
173 // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
174 // c = (3-sqrt(3))/6
175
176 float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
177 float y1 = y0 - j1 + G2;
178 float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
179 float y2 = y0 - 1.0f + 2.0f * G2;
180
181 // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
182 int ii = i & 0xff;
183 int jj = j & 0xff;
184
185 // Calculate the contribution from the three corners
186 float t0 = 0.5f - x0*x0-y0*y0;
187 if(t0 < 0.0f) n0 = 0.0f;
188 else {
189 t0 *= t0;
190 n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0);
191 }
192
193 float t1 = 0.5f - x1*x1-y1*y1;
194 if(t1 < 0.0f) n1 = 0.0f;
195 else {
196 t1 *= t1;
197 n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1);
198 }
199
200 float t2 = 0.5f - x2*x2-y2*y2;
201 if(t2 < 0.0f) n2 = 0.0f;
202 else {
203 t2 *= t2;
204 n2 = t2 * t2 * grad(perm[ii+1+perm[jj+1]], x2, y2);
205 }
206
207 // Add contributions from each corner to get the final noise value.
208 // The result is scaled to return values in the interval [-1,1].
209 return 45.23f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
210 }
211