Permalink
Switch branches/tags
Nothing to show
Find file
Fetching contributors…
Cannot retrieve contributors at this time
530 lines (432 sloc) 19.2 KB
// noise1234
//
// Author: Stefan Gustavson, 2003-2005
// Contact: stegu@itn.liu.se
//
// This code was GPL licensed until February 2011.
// As the original author of this code, I hereby
// release it into the public domain.
// Please feel free to use it for whatever you want.
// Credit is appreciated where appropriate, and I also
// appreciate being told where this code finds any use,
// but you may do as you like.
/** \file
\brief Implements the noise1 to noise4 functions for Perlin noise.
\author Stefan Gustavson (stegu@itn.liu.se)
*/
/*
* This implementation is "Improved Noise" as presented by
* Ken Perlin at Siggraph 2002. The 3D function is a direct port
* of his Java reference code available on www.noisemachine.com
* (although I cleaned it up, made it faster and made the code
* more readable), but the 1D, 2D and 4D cases were implemented
* from scratch by me.
*
* This is a backport to C of my improved noise class in C++.
* It is highly reusable without source code modifications.
*
*/
#include "noise1234.h"
// This is the new and improved, C(2) continuous interpolant
#define FADE(t) ( t * t * t * ( t * ( t * 6 - 15 ) + 10 ) )
#define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : ((int)x-1 ) )
#define LERP(t, a, b) ((a) + (t)*((b)-(a)))
//---------------------------------------------------------------------
// 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 perm[] = {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 match the RenderMan noise in a
* statistical sense, the approximate scaling values (empirically
* determined from test renderings) are:
* 1D noise needs rescaling with 0.188
* 2D noise needs rescaling with 0.507
* 3D noise needs rescaling with 0.936
* 4D noise needs rescaling with 0.87
* Note 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 = (noise3(x,y,z) + 1.0) * 0.5;
*/
float grad1( int hash, float x ) {
int h = hash & 15;
float grad = 1.0 + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0
if (h&8) grad = -grad; // and a random sign for the gradient
return ( grad * x ); // Multiply the gradient with the distance
}
float grad2( 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)? -2.0*v : 2.0*v);
}
float grad3( 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 grad4( 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);
}
//---------------------------------------------------------------------
/** 1D float Perlin noise, SL "noise()"
*/
float noise1( float x )
{
int ix0, ix1;
float fx0, fx1;
float s, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
fx0 = x - ix0; // Fractional part of x
fx1 = fx0 - 1.0f;
ix1 = ( ix0+1 ) & 0xff;
ix0 = ix0 & 0xff; // Wrap to 0..255
s = FADE( fx0 );
n0 = grad1( perm[ ix0 ], fx0 );
n1 = grad1( perm[ ix1 ], fx1 );
return 0.188f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 1D float Perlin periodic noise, SL "pnoise()"
*/
float pnoise1( float x, int px )
{
int ix0, ix1;
float fx0, fx1;
float s, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
fx0 = x - ix0; // Fractional part of x
fx1 = fx0 - 1.0f;
ix1 = (( ix0 + 1 ) % px) & 0xff; // Wrap to 0..px-1 *and* wrap to 0..255
ix0 = ( ix0 % px ) & 0xff; // (because px might be greater than 256)
s = FADE( fx0 );
n0 = grad1( perm[ ix0 ], fx0 );
n1 = grad1( perm[ ix1 ], fx1 );
return 0.188f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 2D float Perlin noise.
*/
float noise2( float x, float y )
{
int ix0, iy0, ix1, iy1;
float fx0, fy0, fx1, fy1;
float s, t, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
ix1 = (ix0 + 1) & 0xff; // Wrap to 0..255
iy1 = (iy0 + 1) & 0xff;
ix0 = ix0 & 0xff;
iy0 = iy0 & 0xff;
t = FADE( fy0 );
s = FADE( fx0 );
nx0 = grad2(perm[ix0 + perm[iy0]], fx0, fy0);
nx1 = grad2(perm[ix0 + perm[iy1]], fx0, fy1);
n0 = LERP( t, nx0, nx1 );
nx0 = grad2(perm[ix1 + perm[iy0]], fx1, fy0);
nx1 = grad2(perm[ix1 + perm[iy1]], fx1, fy1);
n1 = LERP(t, nx0, nx1);
return 0.507f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 2D float Perlin periodic noise.
*/
float pnoise2( float x, float y, int px, int py )
{
int ix0, iy0, ix1, iy1;
float fx0, fy0, fx1, fy1;
float s, t, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
ix1 = (( ix0 + 1 ) % px) & 0xff; // Wrap to 0..px-1 and wrap to 0..255
iy1 = (( iy0 + 1 ) % py) & 0xff; // Wrap to 0..py-1 and wrap to 0..255
ix0 = ( ix0 % px ) & 0xff;
iy0 = ( iy0 % py ) & 0xff;
t = FADE( fy0 );
s = FADE( fx0 );
nx0 = grad2(perm[ix0 + perm[iy0]], fx0, fy0);
nx1 = grad2(perm[ix0 + perm[iy1]], fx0, fy1);
n0 = LERP( t, nx0, nx1 );
nx0 = grad2(perm[ix1 + perm[iy0]], fx1, fy0);
nx1 = grad2(perm[ix1 + perm[iy1]], fx1, fy1);
n1 = LERP(t, nx0, nx1);
return 0.507f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 3D float Perlin noise.
*/
float noise3( float x, float y, float z )
{
int ix0, iy0, ix1, iy1, iz0, iz1;
float fx0, fy0, fz0, fx1, fy1, fz1;
float s, t, r;
float nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of z
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
ix1 = ( ix0 + 1 ) & 0xff; // Wrap to 0..255
iy1 = ( iy0 + 1 ) & 0xff;
iz1 = ( iz0 + 1 ) & 0xff;
ix0 = ix0 & 0xff;
iy0 = iy0 & 0xff;
iz0 = iz0 & 0xff;
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxy0 = grad3(perm[ix0 + perm[iy0 + perm[iz0]]], fx0, fy0, fz0);
nxy1 = grad3(perm[ix0 + perm[iy0 + perm[iz1]]], fx0, fy0, fz1);
nx0 = LERP( r, nxy0, nxy1 );
nxy0 = grad3(perm[ix0 + perm[iy1 + perm[iz0]]], fx0, fy1, fz0);
nxy1 = grad3(perm[ix0 + perm[iy1 + perm[iz1]]], fx0, fy1, fz1);
nx1 = LERP( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxy0 = grad3(perm[ix1 + perm[iy0 + perm[iz0]]], fx1, fy0, fz0);
nxy1 = grad3(perm[ix1 + perm[iy0 + perm[iz1]]], fx1, fy0, fz1);
nx0 = LERP( r, nxy0, nxy1 );
nxy0 = grad3(perm[ix1 + perm[iy1 + perm[iz0]]], fx1, fy1, fz0);
nxy1 = grad3(perm[ix1 + perm[iy1 + perm[iz1]]], fx1, fy1, fz1);
nx1 = LERP( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.936f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 3D float Perlin periodic noise.
*/
float pnoise3( float x, float y, float z, int px, int py, int pz )
{
int ix0, iy0, ix1, iy1, iz0, iz1;
float fx0, fy0, fz0, fx1, fy1, fz1;
float s, t, r;
float nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of z
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
ix1 = (( ix0 + 1 ) % px ) & 0xff; // Wrap to 0..px-1 and wrap to 0..255
iy1 = (( iy0 + 1 ) % py ) & 0xff; // Wrap to 0..py-1 and wrap to 0..255
iz1 = (( iz0 + 1 ) % pz ) & 0xff; // Wrap to 0..pz-1 and wrap to 0..255
ix0 = ( ix0 % px ) & 0xff;
iy0 = ( iy0 % py ) & 0xff;
iz0 = ( iz0 % pz ) & 0xff;
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxy0 = grad3(perm[ix0 + perm[iy0 + perm[iz0]]], fx0, fy0, fz0);
nxy1 = grad3(perm[ix0 + perm[iy0 + perm[iz1]]], fx0, fy0, fz1);
nx0 = LERP( r, nxy0, nxy1 );
nxy0 = grad3(perm[ix0 + perm[iy1 + perm[iz0]]], fx0, fy1, fz0);
nxy1 = grad3(perm[ix0 + perm[iy1 + perm[iz1]]], fx0, fy1, fz1);
nx1 = LERP( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxy0 = grad3(perm[ix1 + perm[iy0 + perm[iz0]]], fx1, fy0, fz0);
nxy1 = grad3(perm[ix1 + perm[iy0 + perm[iz1]]], fx1, fy0, fz1);
nx0 = LERP( r, nxy0, nxy1 );
nxy0 = grad3(perm[ix1 + perm[iy1 + perm[iz0]]], fx1, fy1, fz0);
nxy1 = grad3(perm[ix1 + perm[iy1 + perm[iz1]]], fx1, fy1, fz1);
nx1 = LERP( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.936f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 4D float Perlin noise.
*/
float noise4( float x, float y, float z, float w )
{
int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
float s, t, r, q;
float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of y
iw0 = FASTFLOOR( w ); // Integer part of w
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fw0 = w - iw0; // Fractional part of w
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
fw1 = fw0 - 1.0f;
ix1 = ( ix0 + 1 ) & 0xff; // Wrap to 0..255
iy1 = ( iy0 + 1 ) & 0xff;
iz1 = ( iz0 + 1 ) & 0xff;
iw1 = ( iw0 + 1 ) & 0xff;
ix0 = ix0 & 0xff;
iy0 = iy0 & 0xff;
iz0 = iz0 & 0xff;
iw0 = iw0 & 0xff;
q = FADE( fw0 );
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.87f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------
/** 4D float Perlin periodic noise.
*/
float pnoise4( float x, float y, float z, float w,
int px, int py, int pz, int pw )
{
int ix0, iy0, iz0, iw0, ix1, iy1, iz1, iw1;
float fx0, fy0, fz0, fw0, fx1, fy1, fz1, fw1;
float s, t, r, q;
float nxyz0, nxyz1, nxy0, nxy1, nx0, nx1, n0, n1;
ix0 = FASTFLOOR( x ); // Integer part of x
iy0 = FASTFLOOR( y ); // Integer part of y
iz0 = FASTFLOOR( z ); // Integer part of y
iw0 = FASTFLOOR( w ); // Integer part of w
fx0 = x - ix0; // Fractional part of x
fy0 = y - iy0; // Fractional part of y
fz0 = z - iz0; // Fractional part of z
fw0 = w - iw0; // Fractional part of w
fx1 = fx0 - 1.0f;
fy1 = fy0 - 1.0f;
fz1 = fz0 - 1.0f;
fw1 = fw0 - 1.0f;
ix1 = (( ix0 + 1 ) % px ) & 0xff; // Wrap to 0..px-1 and wrap to 0..255
iy1 = (( iy0 + 1 ) % py ) & 0xff; // Wrap to 0..py-1 and wrap to 0..255
iz1 = (( iz0 + 1 ) % pz ) & 0xff; // Wrap to 0..pz-1 and wrap to 0..255
iw1 = (( iw0 + 1 ) % pw ) & 0xff; // Wrap to 0..pw-1 and wrap to 0..255
ix0 = ( ix0 % px ) & 0xff;
iy0 = ( iy0 % py ) & 0xff;
iz0 = ( iz0 % pz ) & 0xff;
iw0 = ( iw0 % pw ) & 0xff;
q = FADE( fw0 );
r = FADE( fz0 );
t = FADE( fy0 );
s = FADE( fx0 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx0, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx0, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx0, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx0, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx0, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx0, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx0, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix0 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx0, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n0 = LERP( t, nx0, nx1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw0]]]], fx1, fy0, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz0 + perm[iw1]]]], fx1, fy0, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw0]]]], fx1, fy0, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy0 + perm[iz1 + perm[iw1]]]], fx1, fy0, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx0 = LERP ( r, nxy0, nxy1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw0]]]], fx1, fy1, fz0, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz0 + perm[iw1]]]], fx1, fy1, fz0, fw1);
nxy0 = LERP( q, nxyz0, nxyz1 );
nxyz0 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw0]]]], fx1, fy1, fz1, fw0);
nxyz1 = grad4(perm[ix1 + perm[iy1 + perm[iz1 + perm[iw1]]]], fx1, fy1, fz1, fw1);
nxy1 = LERP( q, nxyz0, nxyz1 );
nx1 = LERP ( r, nxy0, nxy1 );
n1 = LERP( t, nx0, nx1 );
return 0.87f * ( LERP( s, n0, n1 ) );
}
//---------------------------------------------------------------------