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/*
Copyright (c) 2010, The Barbarian Group
All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that
the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this list of conditions and
the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this list of conditions and
the following disclaimer in the documentation and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "cinder/Perlin.h"
#include "cinder/CinderMath.h"
#include "cinder/Rand.h"
namespace cinder {
static inline float fade( float t ) { return t * t * t * (t * (t * 6 - 15) + 10); }
static inline float dfade( float t ) { return 30.0f * t * t * ( t * ( t - 2.0f ) + 1.0f ); }
inline float nlerp(float t, float a, float b) { return a + t * (b - a); }
Perlin::Perlin( uint8_t aOctaves, int32_t aSeed )
: mOctaves( aOctaves ), mSeed( aSeed ){
initPermutationTable();
}
Perlin::Perlin( uint8_t aOctaves )
: mOctaves( aOctaves ), mSeed( 0x214 )
{
initPermutationTable();
}
void Perlin::initPermutationTable()
{
Rand rand( mSeed );
for( size_t t = 0; t < 256; ++t ) {
mPerms[t] = mPerms[t + 256] = rand.nextInt() & 255;
}
}
void Perlin::setSeed( int32_t aSeed )
{
mSeed = aSeed;
initPermutationTable();
}
/////////////////////////////////////////////////////////////////////////////////////////////////
// fBm
float Perlin::fBm( float v ) const
{
float result = 0.0f;
float amp = 0.5f;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += noise( v ) * amp;
v *= 2.0f;
amp *= 0.5f;
}
return result;
}
float Perlin::fBm( const Vec2f &v ) const
{
float result = 0.0f;
float amp = 0.5f;
float x = v.x, y = v.y;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += noise( x, y ) * amp;
x *= 2.0f; y *= 2.0f;
amp *= 0.5f;
}
return result;
}
float Perlin::fBm( const Vec3f &v ) const
{
float result = 0.0f;
float amp = 0.5f;
float x = v.x, y = v.y, z = v.z;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += noise( x, y, z ) * amp;
x *= 2.0f; y *= 2.0f; z *= 2.0f;
amp *= 0.5f;
}
return result;
}
/////////////////////////////////////////////////////////////////////////////////////////////////
// dfBm
/*float Perlin::dfBm( float v ) const
{
float result = 0.0f;
float amp = 0.5f;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += dnoise( v ) * amp;
v *= 2.0f;
amp *= 0.5f;
}
return result;
}*/
Vec2f Perlin::dfBm( const Vec2f &v ) const
{
Vec2f result = Vec2f::zero();
float amp = 0.5f;
float x = v.x, y = v.y;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += dnoise( x, y ) * amp;
x *= 2.0f; y *= 2.0f;
amp *= 0.5f;
}
return result;
}
Vec3f Perlin::dfBm( const Vec3f &v ) const
{
Vec3f result = Vec3f::zero();
float amp = 0.5f;
float x = v.x, y = v.y, z = v.z;
for( uint8_t i = 0; i < mOctaves; i++ ) {
result += dnoise( x, y, z ) * amp;
x *= 2.0f; y *= 2.0f; z *= 2.0f;
amp *= 0.5f;
}
return result;
}
/////////////////////////////////////////////////////////////////////////////////////////////////
// noise
float Perlin::noise( float x ) const
{
int32_t X = ((int32_t)floorf(x)) & 255;
x -= floorf(x);
float u = fade( x );
int32_t A = mPerms[X], AA = mPerms[A], B = mPerms[X+1], BA = mPerms[B];
return nlerp( u, grad( mPerms[AA ], x ), grad( mPerms[BA], x-1 ) );
}
float Perlin::noise( float x, float y ) const
{
int32_t X = ((int32_t)floorf(x)) & 255, Y = ((int32_t)floorf(y)) & 255;
x -= floorf(x); y -= floorf(y);
float u = fade( x ), v = fade( y );
int32_t A = mPerms[X ]+Y, AA = mPerms[A], AB = mPerms[A+1],
B = mPerms[X+1]+Y, BA = mPerms[B], BB = mPerms[B+1];
return nlerp(v, nlerp(u, grad(mPerms[AA ], x , y ),
grad(mPerms[BA ], x-1, y )),
nlerp(u, grad(mPerms[AB ], x , y-1 ),
grad(mPerms[BB ], x-1, y-1 )));
}
float Perlin::noise( float x, float y, float z ) const
{
// These floors need to remain that due to behavior with negatives.
int32_t X = ((int32_t)floorf(x)) & 255, Y = ((int32_t)floorf(y)) & 255, Z = ((int32_t)floorf(z)) & 255;
x -= floorf(x); y -= floorf(y); z -= floorf(z);
float u = fade(x), v = fade(y), w = fade(z);
int32_t A = mPerms[X ]+Y, AA = mPerms[A]+Z, AB = mPerms[A+1]+Z,
B = mPerms[X+1]+Y, BA = mPerms[B]+Z, BB = mPerms[B+1]+Z;
float a = grad(mPerms[AA ], x , y , z );
float b = grad(mPerms[BA ], x-1, y , z );
float c = grad(mPerms[AB ], x , y-1, z );
float d = grad(mPerms[BB ], x-1, y-1, z );
float e = grad(mPerms[AA+1], x , y , z-1 );
float f = grad(mPerms[BA+1], x-1, y , z-1 );
float g = grad(mPerms[AB+1], x , y-1, z-1 );
float h = grad(mPerms[BB+1], x-1, y-1, z-1 );
return nlerp(w, nlerp( v, nlerp( u, a, b ),
nlerp( u, c, d ) ),
nlerp(v, nlerp( u, e, f ),
nlerp( u, g, h ) ) );
}
/////////////////////////////////////////////////////////////////////////////////////////////////
// dnoise
/*
float Perlin::dnoise( float x ) const
{
int X = ((int)x) & 255;
x -= ((int)x);
float u = fade( x );
int A = mPerms[X], AA = mPerms[A], B = mPerms[X+1], BA = mPerms[B];
return nlerp( u, grad( mPerms[AA ], x ), grad( mPerms[BA], x-1 ) );
throw; //TODO
return 0;
}
*/
// Credit for the ideas for analytical Perlin derivatives below are due to Iñigo Quílez
Vec2f Perlin::dnoise( float x, float y ) const
{
int32_t X = ((int32_t)x) & 255, Y = ((int32_t)y) & 255;
x -= floorf(x); y -= floorf(y);
float u = fade( x ), v = fade( y );
float du = dfade( x ), dv = dfade( y );
int32_t A = mPerms[X ]+Y, AA = mPerms[A]+0, AB = mPerms[A+1]+0,
B = mPerms[X+1]+Y, BA = mPerms[B]+0, BB = mPerms[B+1]+0;
if( du < 0.000001f ) du = 1.0f;
if( dv < 0.000001f ) dv = 1.0f;
float a = grad( mPerms[AA], x , y );
float b = grad( mPerms[BA], x-1, y );
float c = grad( mPerms[AB], x , y-1 );
float d = grad( mPerms[BB], x-1, y-1 );
const float k1 = b - a;
const float k2 = c - a;
const float k4 = a - b - c + d;
return Vec2f( du * ( k1 + k4 * v ), dv * ( k2 + k4 * u ) );
}
Vec3f Perlin::dnoise( float x, float y, float z ) const
{
int32_t X = ((int32_t)floorf(x)) & 255, Y = ((int32_t)floorf(y)) & 255, Z = ((int32_t)floorf(z)) & 255;
x -= floorf(x); y -= floorf(y); z -= floorf(z);
float u = fade( x ), v = fade( y ), w = fade( z );
float du = dfade( x ), dv = dfade( y ), dw = dfade( z );
int32_t A = mPerms[X ]+Y, AA = mPerms[A]+Z, AB = mPerms[A+1]+Z,
B = mPerms[X+1]+Y, BA = mPerms[B]+Z, BB = mPerms[B+1]+Z;
if( du < 0.000001f ) du = 1.0f;
if( dv < 0.000001f ) dv = 1.0f;
if( dw < 0.000001f ) dw = 1.0f;
float a = grad( mPerms[AA ], x , y , z );
float b = grad( mPerms[BA ], x-1, y , z );
float c = grad( mPerms[AB ], x , y-1, z );
float d = grad( mPerms[BB ], x-1, y-1, z );
float e = grad( mPerms[AA+1], x , y , z-1 );
float f = grad( mPerms[BA+1], x-1, y , z-1 );
float g = grad( mPerms[AB+1], x , y-1, z-1 );
float h = grad( mPerms[BB+1], x-1, y-1, z-1 );
const float k1 = b - a;
const float k2 = c - a;
const float k3 = e - a;
const float k4 = a - b - c + d;
const float k5 = a - c - e + g;
const float k6 = a - b - e + f;
const float k7 = -a + b + c - d + e - f - g + h;
return Vec3f( du * ( k1 + k4*v + k6*w + k7*v*w ),
dv * ( k2 + k5*w + k4*u + k7*w*u ),
dw * ( k3 + k6*u + k5*v + k7*u*v ) );
}
/////////////////////////////////////////////////////////////////////////////////////////////////
// grad
float Perlin::grad( int32_t hash, float x ) const
{
int32_t h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
float u = h<8 ? x : 0, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? 0 : h==12||h==14 ? x : 0;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
float Perlin::grad( int32_t hash, float x, float y ) const
{
int32_t h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
float u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? y : h==12||h==14 ? x : 0;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
float Perlin::grad( int32_t hash, float x, float y, float z ) const
{
int32_t h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE
float u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS.
v = h<4 ? y : h==12||h==14 ? x : z;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
} // namespace cinder
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