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Perlin.c
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Perlin.c
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/************************
Author : Gwenaël Larmet
Perlin.c
*************************/
#include "Perlin.h"
//-----------------------------------------------------------
static Vector _vectorInterpolate(Vector v1, Vector v2, double blend)
{
return V_add( V_multiply(1-blend,v1), V_multiply(blend,v2));
}
//-----------------------------------------------------------
// This is a polynomial function which :
// - for x=0 yields y=0
// - for x=1 yields y=1
// - for x=0 and x=1 has a zero first derivative.
static double _contrast(double x)
{
return x*x*(3-2*x);
}
//-----------------------------------------------------------
// For alpha=0, the return value is x
// For alpha=1, the return value is y
// For intermediate values -> interpolation
//-----------------------------------------------------------
static double _scalarCubicInterpolate(Vector p, double *grid_values)
{
double res, fx,fy,fz; // fractional part
int nx = (int)(floor(p.x));
int ny = (int)(floor(p.y));
int nz = (int)(floor(p.z));
fx = p.x - nx;
fy = p.y - ny;
fz = p.z - nz;
fx = _contrast(fx);
fy = _contrast(fy);
fz = _contrast(fz);
res=0.0;
res += (1-fx)*(1-fy)*(1-fz)*grid_values[PRLN_000];
res += fx *(1-fy)*(1-fz)*grid_values[PRLN_100];
res += (1-fx)* fy *(1-fz)*grid_values[PRLN_010];
res += fx * fy *(1-fz)*grid_values[PRLN_110];
res += (1-fx)*(1-fy)* fz *grid_values[PRLN_001];
res += fx *(1-fy)* fz *grid_values[PRLN_101];
res += (1-fx)* fy * fz *grid_values[PRLN_011];
res += fx * fy * fz *grid_values[PRLN_111];
return res;
}
//-----------------------------------------------------------
static Vector _vectorLinearInterpolate(Vector p, Vector *grid_vectors)
{
double fx,fy,fz; // fractional part
int nx = (int)(floor(p.x));
int ny = (int)(floor(p.y));
int nz = (int)(floor(p.z));
fx = p.x - nx;
fy = p.y - ny;
fz = p.z - nz;
fx = _contrast(fx);
fy = _contrast(fy);
fz = _contrast(fz);
Vector interp_y0z0 = _vectorInterpolate(grid_vectors[PRLN_000],grid_vectors[PRLN_100],fx);
Vector interp_y1z0 = _vectorInterpolate(grid_vectors[PRLN_010],grid_vectors[PRLN_110],fx);
Vector interp_y0z1 = _vectorInterpolate(grid_vectors[PRLN_001],grid_vectors[PRLN_101],fx);
Vector interp_y1z1 = _vectorInterpolate(grid_vectors[PRLN_011],grid_vectors[PRLN_111],fx);
Vector interp_z0 = _vectorInterpolate(interp_y0z0,interp_y1z0,fy);
Vector interp_z1 = _vectorInterpolate(interp_y0z1,interp_y1z1,fy);
Vector interp_vector = _vectorInterpolate(interp_z0,interp_z1,fz);
return interp_vector;
}
//-----------------------------------------------------------
static void _computeDotProducts(Vector p, Vector *random_vectors, double *dot_products)
{
int nx = (int)(floor(p.x));
int ny = (int)(floor(p.y));
int nz = (int)(floor(p.z));
int i;
for(i=0;i<8;i++)
{
int nnx=nx,nny=ny,nnz=nz;
if(i>=4) nnz++;
if(i%4 > 1) nny++;
if(i%2 > 0) nnx++;
Vector A = V_new(nnx,nny,nnz);
Vector Ap = V_substract(p,A);
dot_products[i] = V_dot(random_vectors[i],Ap);
}
}
//-----------------------------------------------------------
static void _computeCrossProducts(Vector p, Vector *random_vectors, Vector *cross_products)
{
int nx = (int)(floor(p.x));
int ny = (int)(floor(p.y));
int nz = (int)(floor(p.z));
int i;
for(i=0;i<8;i++)
{
int nnx=nx,nny=ny,nnz=nz;
if(i>=4) nnz++;
if(i%4 > 1) nny++;
if(i%2 > 0) nnx++;
Vector A = V_new(nnx,nny,nnz);
Vector Ap = V_substract(p,A);
cross_products[i] = V_cross(random_vectors[i],Ap);
}
}
//-----------------------------------------------------------
static double myRand(long int x)
{
x = (x<<13) ^ x;
return 1.0 - ( (x * (x * x * 15731 + 789221) + 1376312589) & 0x7fffffff) / 1073741824.0;
}
//-----------------------------------------------------------
// 2^32 = (approximately) 2^11 * 2^11 * 2^10
// If we don't want to have the same seed for two different
// points in space we have to write :
// seed = 2^11*2^11*nx + 2^11*ny + nz
// Even better, instead of 2^11*2^11 and 2^10, we could find
// prime numbers in those vicinities.
static Vector _computeRandomVector(int nx, int ny, int nz)
{
long seed = 2097013*nx+2039*ny+nz;
double x = myRand(seed);
double y = myRand(seed+1);
double z = myRand(seed+2);
Vector v_rand = V_new(x,y,z);
return V_unit(v_rand);
}
//-----------------------------------------------------------
static void _computeRandomVertexVectors(Vector p, Vector *v_rand)
{
int nx = (int)(floor(p.x));
int ny = (int)(floor(p.y));
int nz = (int)(floor(p.z));
v_rand[PRLN_000] = _computeRandomVector(nx, ny, nz);
v_rand[PRLN_100] = _computeRandomVector(nx+1,ny, nz);
v_rand[PRLN_010] = _computeRandomVector(nx, ny+1,nz);
v_rand[PRLN_110] = _computeRandomVector(nx+1,ny+1,nz);
v_rand[PRLN_001] = _computeRandomVector(nx, ny, nz+1);
v_rand[PRLN_101] = _computeRandomVector(nx+1,ny, nz+1);
v_rand[PRLN_011] = _computeRandomVector(nx, ny+1,nz+1);
v_rand[PRLN_111] = _computeRandomVector(nx+1,ny+1,nz+1);
}
//-----------------------------------------------------------
static double _scalarNoise(Vector p, double frequency, double amplitude)
{
Vector random_vectors[8];
double dot_products[8];
Vector lp = V_multiply(frequency,p);
_computeRandomVertexVectors(lp,random_vectors);
_computeDotProducts(lp,random_vectors,dot_products);
// double noise_value = amplitude*_scalarLinearInterpolate(lp,dot_products);
double noise_value = amplitude*_scalarCubicInterpolate(lp,dot_products);
return noise_value;
}
//-----------------------------------------------------------
static Vector _vectorNoise(Vector p, double frequency, double amplitude)
{
Vector random_vectors[8];
Vector cross_products[8];
Vector lp = V_multiply(frequency,p);
_computeRandomVertexVectors(lp,random_vectors);
_computeCrossProducts(lp,random_vectors,cross_products);
Vector noise_vector = _vectorLinearInterpolate(lp,cross_products);
return V_multiply(amplitude,noise_vector);
}
//-----------------------------------------------------------
// double PRLN_scalarNoise(Vector p, double period, double amplitude, int nb_octaves, double lacunarity, double gain)
double PRLN_scalarNoise(Vector p)
{
double period = 0.25;
double amplitude = 1.0;
int nb_octaves = 1.0;
double lacunarity = 2.0;
double gain = 0.5;
double noise_value = 0.0;
double frequency = 1.0/period;
int noct;
for(noct=0;noct<nb_octaves;noct++)
{
noise_value += _scalarNoise(p,frequency,amplitude);
frequency *= lacunarity;
amplitude *= gain;
}
return noise_value;
}
//-----------------------------------------------------------
// Vector PRLN_vectorNoise(Vector p, double period, double amplitude, int nb_octaves, double lacunarity, double gain)
Vector PRLN_vectorNoise(Vector p)
{
double period = 2.0;
double amplitude = 0.35;
int nb_octaves = 1.0;
double lacunarity = 2.0;
double gain = 0.5;
Vector noise_vector = V_new(0,0,0);
double frequency = 1.0/period;
int noct;
for(noct=0;noct<nb_octaves;noct++)
{
Vector tmp = V_add(noise_vector,_vectorNoise(p,frequency,amplitude));
noise_vector = tmp;
frequency *= lacunarity;
amplitude *= gain;
}
return noise_vector;
}