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You may do anything +// you like with it. You may even remove all attributions, +// but of course I'd appreciate it if you kept my name somewhere. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. + +/** \file + \brief Implements the SimplexNoise1234 class for producing Perlin simplex noise. + \author Stefan Gustavson (stegu@itn.liu.se) +*/ + +/* + * This implementation is "Simplex Noise" as presented by + * Ken Perlin at a relatively obscure and not often cited course + * session "Real-Time Shading" at Siggraph 2001 (before real + * time shading actually took on), under the title "hardware noise". + * The 3D function is numerically equivalent to his Java reference + * code available in the PDF course notes, although I re-implemented + * it from scratch to get more readable code. The 1D, 2D and 4D cases + * were implemented from scratch by me from Ken Perlin's text. + * + * This is a highly reusable class. It has no dependencies + * on any other file, apart from its own header file. + */ + + +#include "simplexnoise1234.h" + +#define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) ) + +//--------------------------------------------------------------------- +// Static data + +/* + * Permutation table. This is just a random jumble of all numbers 0-255, + * repeated twice to avoid wrapping the index at 255 for each lookup. + * This needs to be exactly the same for all instances on all platforms, + * so it's easiest to just keep it as static explicit data. + * This also removes the need for any initialisation of this class. + * + * Note that making this an int[] instead of a char[] might make the + * code run faster on platforms with a high penalty for unaligned single + * byte addressing. Intel x86 is generally single-byte-friendly, but + * some other CPUs are faster with 4-aligned reads. + * However, a char[] is smaller, which avoids cache trashing, and that + * is probably the most important aspect on most architectures. + * This array is accessed a *lot* by the noise functions. + * A vector-valued noise over 3D accesses it 96 times, and a + * float-valued 4D noise 64 times. We want this to fit in the cache! + */ +unsigned char SimplexNoise1234::perm[512] = {151,160,137,91,90,15, + 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, + 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, + 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, + 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, + 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, + 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, + 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, + 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, + 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, + 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, + 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, + 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180, + 151,160,137,91,90,15, + 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, + 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, + 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, + 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, + 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, + 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, + 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, + 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, + 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, + 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, + 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, + 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 +}; + +//--------------------------------------------------------------------- + +/* + * Helper functions to compute gradients-dot-residualvectors (1D to 4D) + * Note that these generate gradients of more than unit length. To make + * a close match with the value range of classic Perlin noise, the final + * noise values need to be rescaled to fit nicely within [-1,1]. + * (The simplex noise functions as such also have different scaling.) + * Note also that these noise functions are the most practical and useful + * signed version of Perlin noise. To return values according to the + * RenderMan specification from the SL noise() and pnoise() functions, + * the noise values need to be scaled and offset to [0,1], like this: + * float SLnoise = (SimplexNoise1234::noise(x,y,z) + 1.0) * 0.5; + */ + +float SimplexNoise1234::grad( int hash, float x ) { + int h = hash & 15; + float grad = 1.0f + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0 + if (h&8) grad = -grad; // Set a random sign for the gradient + return ( grad * x ); // Multiply the gradient with the distance +} + +float SimplexNoise1234::grad( int hash, float x, float y ) { + int h = hash & 7; // Convert low 3 bits of hash code + float u = h<4 ? x : y; // into 8 simple gradient directions, + float v = h<4 ? y : x; // and compute the dot product with (x,y). + return ((h&1)? -u : u) + ((h&2)? -2.0f*v : 2.0f*v); +} + +float SimplexNoise1234::grad( int hash, float x, float y , float z ) { + int h = hash & 15; // Convert low 4 bits of hash code into 12 simple + float u = h<8 ? x : y; // gradient directions, and compute dot product. + float v = h<4 ? y : h==12||h==14 ? x : z; // Fix repeats at h = 12 to 15 + return ((h&1)? -u : u) + ((h&2)? -v : v); +} + +float SimplexNoise1234::grad( int hash, float x, float y, float z, float t ) { + int h = hash & 31; // Convert low 5 bits of hash code into 32 simple + float u = h<24 ? x : y; // gradient directions, and compute dot product. + float v = h<16 ? y : z; + float w = h<8 ? z : t; + return ((h&1)? -u : u) + ((h&2)? -v : v) + ((h&4)? -w : w); +} + + // A lookup table to traverse the simplex around a given point in 4D. + // Details can be found where this table is used, in the 4D noise method. + /* TODO: This should not be required, backport it from Bill's GLSL code! */ + static unsigned char simplex[64][4] = { + {0,1,2,3},{0,1,3,2},{0,0,0,0},{0,2,3,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,2,3,0}, + {0,2,1,3},{0,0,0,0},{0,3,1,2},{0,3,2,1},{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,3,2,0}, + {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, + {1,2,0,3},{0,0,0,0},{1,3,0,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,3,0,1},{2,3,1,0}, + {1,0,2,3},{1,0,3,2},{0,0,0,0},{0,0,0,0},{0,0,0,0},{2,0,3,1},{0,0,0,0},{2,1,3,0}, + {0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}, + {2,0,1,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,0,1,2},{3,0,2,1},{0,0,0,0},{3,1,2,0}, + {2,1,0,3},{0,0,0,0},{0,0,0,0},{0,0,0,0},{3,1,0,2},{0,0,0,0},{3,2,0,1},{3,2,1,0}}; + +// 1D simplex noise +float SimplexNoise1234::noise(float x) { + + int i0 = FASTFLOOR(x); + int i1 = i0 + 1; + float x0 = x - i0; + float x1 = x0 - 1.0f; + + float n0, n1; + + float t0 = 1.0f - x0*x0; +// if(t0 < 0.0f) t0 = 0.0f; + t0 *= t0; + n0 = t0 * t0 * grad(perm[i0 & 0xff], x0); + + float t1 = 1.0f - x1*x1; +// if(t1 < 0.0f) t1 = 0.0f; + t1 *= t1; + n1 = t1 * t1 * grad(perm[i1 & 0xff], x1); + // The maximum value of this noise is 8*(3/4)^4 = 2.53125 + // A factor of 0.395 will scale to fit exactly within [-1,1] + return 0.395f * (n0 + n1); + +} + +// 2D simplex noise +float SimplexNoise1234::noise(float x, float y) { + +#define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0) +#define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0 + + float n0, n1, n2; // Noise contributions from the three corners + + // Skew the input space to determine which simplex cell we're in + float s = (x+y)*F2; // Hairy factor for 2D + float xs = x + s; + float ys = y + s; + int i = FASTFLOOR(xs); + int j = FASTFLOOR(ys); + + float t = (float)(i+j)*G2; + float X0 = i-t; // Unskew the cell origin back to (x,y) space + float Y0 = j-t; + float x0 = x-X0; // The x,y distances from the cell origin + float y0 = y-Y0; + + // For the 2D case, the simplex shape is an equilateral triangle. + // Determine which simplex we are in. + int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords + if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1) + else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1) + + // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and + // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where + // c = (3-sqrt(3))/6 + + float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords + float y1 = y0 - j1 + G2; + float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords + float y2 = y0 - 1.0f + 2.0f * G2; + + // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds + int ii = i & 0xff; + int jj = j & 0xff; + + // Calculate the contribution from the three corners + float t0 = 0.5f - x0*x0-y0*y0; + if(t0 < 0.0f) n0 = 0.0f; + else { + t0 *= t0; + n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0); + } + + float t1 = 0.5f - x1*x1-y1*y1; + if(t1 < 0.0f) n1 = 0.0f; + else { + t1 *= t1; + n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1); + } + + float t2 = 0.5f - x2*x2-y2*y2; + if(t2 < 0.0f) n2 = 0.0f; + else { + t2 *= t2; + n2 = t2 * t2 * grad(perm[ii+1+perm[jj+1]], x2, y2); + } + + // Add contributions from each corner to get the final noise value. + // The result is scaled to return values in the interval [-1,1]. + return 45.23f * (n0 + n1 + n2); // TODO: The scale factor is preliminary! + } + +// 3D simplex noise +float SimplexNoise1234::noise(float x, float y, float z) { + +// Simple skewing factors for the 3D case +#define F3 0.333333333 +#define G3 0.166666667 + + float n0, n1, n2, n3; // Noise contributions from the four corners + + // Skew the input space to determine which simplex cell we're in + float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D + float xs = x+s; + float ys = y+s; + float zs = z+s; + int i = FASTFLOOR(xs); + int j = FASTFLOOR(ys); + int k = FASTFLOOR(zs); + + float t = (float)(i+j+k)*G3; + float X0 = i-t; // Unskew the cell origin back to (x,y,z) space + float Y0 = j-t; + float Z0 = k-t; + float x0 = x-X0; // The x,y,z distances from the cell origin + float y0 = y-Y0; + float z0 = z-Z0; + + // For the 3D case, the simplex shape is a slightly irregular tetrahedron. + // Determine which simplex we are in. + int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords + int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords + +/* This code would benefit from a backport from the GLSL version! */ + if(x0>=y0) { + if(y0>=z0) + { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order + else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order + else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order + } + else { // x0 y0) ? 32 : 0; + int c2 = (x0 > z0) ? 16 : 0; + int c3 = (y0 > z0) ? 8 : 0; + int c4 = (x0 > w0) ? 4 : 0; + int c5 = (y0 > w0) ? 2 : 0; + int c6 = (z0 > w0) ? 1 : 0; + int c = c1 + c2 + c3 + c4 + c5 + c6; + + int i1, j1, k1, l1; // The integer offsets for the second simplex corner + int i2, j2, k2, l2; // The integer offsets for the third simplex corner + int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner + + // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. + // Many values of c will never occur, since e.g. x>y>z>w makes x=3 ? 1 : 0; + j1 = simplex[c][1]>=3 ? 1 : 0; + k1 = simplex[c][2]>=3 ? 1 : 0; + l1 = simplex[c][3]>=3 ? 1 : 0; + // The number 2 in the "simplex" array is at the second largest coordinate. + i2 = simplex[c][0]>=2 ? 1 : 0; + j2 = simplex[c][1]>=2 ? 1 : 0; + k2 = simplex[c][2]>=2 ? 1 : 0; + l2 = simplex[c][3]>=2 ? 1 : 0; + // The number 1 in the "simplex" array is at the second smallest coordinate. + i3 = simplex[c][0]>=1 ? 1 : 0; + j3 = simplex[c][1]>=1 ? 1 : 0; + k3 = simplex[c][2]>=1 ? 1 : 0; + l3 = simplex[c][3]>=1 ? 1 : 0; + // The fifth corner has all coordinate offsets = 1, so no need to look that up. + + float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords + float y1 = y0 - j1 + G4; + float z1 = z0 - k1 + G4; + float w1 = w0 - l1 + G4; + float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords + float y2 = y0 - j2 + 2.0f*G4; + float z2 = z0 - k2 + 2.0f*G4; + float w2 = w0 - l2 + 2.0f*G4; + float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords + float y3 = y0 - j3 + 3.0f*G4; + float z3 = z0 - k3 + 3.0f*G4; + float w3 = w0 - l3 + 3.0f*G4; + float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords + float y4 = y0 - 1.0f + 4.0f*G4; + float z4 = z0 - 1.0f + 4.0f*G4; + float w4 = w0 - 1.0f + 4.0f*G4; + + // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds + int ii = i & 0xff; + int jj = j & 0xff; + int kk = k & 0xff; + int ll = l & 0xff; + + // Calculate the contribution from the five corners + float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0; + if(t0 < 0.0f) n0 = 0.0f; + else { + t0 *= t0; + n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0); + } + + float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1; + if(t1 < 0.0f) n1 = 0.0f; + else { + t1 *= t1; + n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1); + } + + float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2; + if(t2 < 0.0f) n2 = 0.0f; + else { + t2 *= t2; + n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2); + } + + float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3; + if(t3 < 0.0f) n3 = 0.0f; + else { + t3 *= t3; + n3 = t3 * t3 * grad(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3); + } + + float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4; + if(t4 < 0.0f) n4 = 0.0f; + else { + t4 *= t4; + n4 = t4 * t4 * grad(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4); + } + + // Sum up and scale the result to cover the range [-1,1] + return 27.3f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary! + } +//--------------------------------------------------------------------- diff --git a/src/libraries/noise1234/simplexnoise1234.h b/src/libraries/noise1234/simplexnoise1234.h new file mode 100644 index 000000000..1f74226c0 --- /dev/null +++ b/src/libraries/noise1234/simplexnoise1234.h @@ -0,0 +1,60 @@ +// SimplexNoise1234 +// Copyright � 2003-2011, Stefan Gustavson +// +// Contact: stegu@itn.liu.se +// +// This library is public domain software, released by the author +// into the public domain in February 2011. You may do anything +// you like with it. You may even remove all attributions, +// but of course I'd appreciate it if you kept my name somewhere. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. + +/** \file + \brief Declares the SimplexNoise1234 class for producing Perlin simplex noise. + \author Stefan Gustavson (stegu@itn.liu.se) +*/ + +/* + * This is a clean, fast, modern and free Perlin Simplex noise class in C++. + * Being a stand-alone class with no external dependencies, it is + * highly reusable without source code modifications. + * + * + * Note: + * Replacing the "float" type with "double" can actually make this run faster + * on some platforms. A templatized version of SimplexNoise1234 could be useful. + */ + +class SimplexNoise1234 { + + public: + SimplexNoise1234() {} + ~SimplexNoise1234() {} + +/** 1D, 2D, 3D and 4D float Perlin noise + */ + static float noise( float x ); + static float noise( float x, float y ); + static float noise( float x, float y, float z ); + static float noise( float x, float y, float z, float w ); + +/** 1D, 2D, 3D and 4D float Perlin noise, with a specified integer period + */ + static float pnoise( float x, int px ); + static float pnoise( float x, float y, int px, int py ); + static float pnoise( float x, float y, float z, int px, int py, int pz ); + static float pnoise( float x, float y, float z, float w, + int px, int py, int pz, int pw ); + + private: + static unsigned char perm[]; + static float grad( int hash, float x ); + static float grad( int hash, float x, float y ); + static float grad( int hash, float x, float y , float z ); + static float grad( int hash, float x, float y, float z, float t ); + +}; diff --git a/src/modules/math/MathModule.h b/src/modules/math/MathModule.h index 483018aa2..9c18e1d07 100644 --- a/src/modules/math/MathModule.h +++ b/src/modules/math/MathModule.h @@ -27,6 +27,10 @@ #include "common/Module.h" #include "common/math.h" #include "common/int.h" +#include "common/StringMap.h" + +// Noise +#include "libraries/noise1234/simplexnoise1234.h" // STL #include @@ -106,6 +110,16 @@ public: **/ std::vector triangulate(const std::vector &polygon); + /** + * Calculate Simplex noise for the specified coordinate(s). + * + * @return Noise value in the range of [0,1]. + **/ + float simplexNoise1(float x) const; + float simplexNoise2(float x, float y) const; + float simplexNoise3(float x, float y, float z) const; + float simplexNoise4(float x, float y, float z, float w) const; + static Math instance; private: @@ -114,6 +128,26 @@ private: }; // Math +inline float Math::simplexNoise1(float x) const +{ + return SimplexNoise1234::noise(x); +} + +inline float Math::simplexNoise2(float x, float y) const +{ + return SimplexNoise1234::noise(x, y); +} + +inline float Math::simplexNoise3(float x, float y, float z) const +{ + return SimplexNoise1234::noise(x, y, z); +} + +inline float Math::simplexNoise4(float x, float y, float z, float w) const +{ + return SimplexNoise1234::noise(x, y, z, w); +} + } // math } // love diff --git a/src/modules/math/wrap_Math.cpp b/src/modules/math/wrap_Math.cpp index c6f009e2b..a3a0a5710 100644 --- a/src/modules/math/wrap_Math.cpp +++ b/src/modules/math/wrap_Math.cpp @@ -148,6 +148,42 @@ int w_triangulate(lua_State *L) return 1; } +int w_noise(lua_State *L) +{ + float w, x, y, z; + float val; + + switch (lua_gettop(L)) + { + case 1: + x = luaL_checknumber(L, 1); + val = Math::instance.simplexNoise1(x); + break; + case 2: + x = luaL_checknumber(L, 1); + y = luaL_checknumber(L, 2); + val = Math::instance.simplexNoise2(x, y); + break; + case 3: + x = luaL_checknumber(L, 1); + y = luaL_checknumber(L, 2); + z = luaL_checknumber(L, 3); + val = Math::instance.simplexNoise3(x, y, z); + break; + case 4: + default: + x = luaL_checknumber(L, 1); + y = luaL_checknumber(L, 2); + z = luaL_checknumber(L, 3); + w = luaL_checknumber(L, 4); + val = Math::instance.simplexNoise4(x, y, z, w); + break; + } + + lua_pushnumber(L, (lua_Number) val); + return 1; +} + // List of functions to wrap. static const luaL_Reg functions[] = { @@ -156,6 +192,7 @@ static const luaL_Reg functions[] = { "randomnormal", w_randomnormal }, { "newRandomGenerator", w_newRandomGenerator }, { "triangulate", w_triangulate }, + { "noise", w_noise }, { 0, 0 } }; diff --git a/src/modules/math/wrap_Math.h b/src/modules/math/wrap_Math.h index e523994cf..3d312f110 100644 --- a/src/modules/math/wrap_Math.h +++ b/src/modules/math/wrap_Math.h @@ -35,6 +35,7 @@ int w_random(lua_State *L); int w_randomnormal(lua_State *L); int w_newRandomGenerator(lua_State *L); int w_triangulate(lua_State *L); +int w_noise(lua_State *L); extern "C" LOVE_EXPORT int luaopen_love_math(lua_State *L); } // random