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/** \file smoke/intern/INTERPOLATE.h
* \ingroup smoke
*/
//////////////////////////////////////////////////////////////////////
// This file is part of Wavelet Turbulence.
//
// Wavelet Turbulence is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Wavelet Turbulence 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.
//
// You should have received a copy of the GNU General Public License
// along with Wavelet Turbulence. If not, see <http://www.gnu.org/licenses/>.
//
// Copyright 2008 Theodore Kim and Nils Thuerey
//
//////////////////////////////////////////////////////////////////////
#ifndef INTERPOLATE_H
#define INTERPOLATE_H
#include <iostream>
#include <VEC3.h>
namespace INTERPOLATE {
//////////////////////////////////////////////////////////////////////
// linear interpolators
//////////////////////////////////////////////////////////////////////
static inline float lerp(float t, float a, float b) {
return ( a + t * (b - a) );
}
static inline float lerp(float* field, float x, float y, int res) {
// clamp backtrace to grid boundaries
if (x < 0.5f) x = 0.5f;
if (x > res - 1.5f) x = res - 1.5f;
if (y < 0.5f) y = 0.5f;
if (y > res - 1.5f) y = res - 1.5f;
const int x0 = (int)x;
const int y0 = (int)y;
x -= x0;
y -= y0;
float d00, d10, d01, d11;
// lerp the velocities
d00 = field[x0 + y0 * res];
d10 = field[(x0 + 1) + y0 * res];
d01 = field[x0 + (y0 + 1) * res];
d11 = field[(x0 + 1) + (y0 + 1) * res];
return lerp(y, lerp(x, d00, d10),
lerp(x, d01, d11));
}
//////////////////////////////////////////////////////////////////////////////////////////
// 3d linear interpolation
//////////////////////////////////////////////////////////////////////////////////////////
static inline float lerp3d(float* field, float x, float y, float z, int xres, int yres, int zres) {
// clamp pos to grid boundaries
if (x < 0.5f) x = 0.5f;
if (x > xres - 1.5f) x = xres - 1.5f;
if (y < 0.5f) y = 0.5f;
if (y > yres - 1.5f) y = yres - 1.5f;
if (z < 0.5f) z = 0.5f;
if (z > zres - 1.5f) z = zres - 1.5f;
// locate neighbors to interpolate
const int x0 = (int)x;
const int x1 = x0 + 1;
const int y0 = (int)y;
const int y1 = y0 + 1;
const int z0 = (int)z;
const int z1 = z0 + 1;
// get interpolation weights
const float s1 = x - (float)x0;
const float s0 = 1.0f - s1;
const float t1 = y - (float)y0;
const float t0 = 1.0f - t1;
const float u1 = z - (float)z0;
const float u0 = 1.0f - u1;
const int slabSize = xres*yres;
const int i000 = x0 + y0 * xres + z0 * slabSize;
const int i010 = x0 + y1 * xres + z0 * slabSize;
const int i100 = x1 + y0 * xres + z0 * slabSize;
const int i110 = x1 + y1 * xres + z0 * slabSize;
const int i001 = x0 + y0 * xres + z1 * slabSize;
const int i011 = x0 + y1 * xres + z1 * slabSize;
const int i101 = x1 + y0 * xres + z1 * slabSize;
const int i111 = x1 + y1 * xres + z1 * slabSize;
// interpolate (indices could be computed once)
return ( u0 * (s0 * (t0 * field[i000] +
t1 * field[i010]) +
s1 * (t0 * field[i100] +
t1 * field[i110])) +
u1 * (s0 * (t0 * field[i001] +
t1 * field[i011]) +
s1 * (t0 * field[i101] +
t1 * field[i111])) );
}
//////////////////////////////////////////////////////////////////////////////////////////
// convert field entries of type T to floats, then interpolate
//////////////////////////////////////////////////////////////////////////////////////////
template <class T>
static inline float lerp3dToFloat(T* field1,
float x, float y, float z, int xres, int yres, int zres) {
// clamp pos to grid boundaries
if (x < 0.5f) x = 0.5f;
if (x > xres - 1.5f) x = xres - 1.5f;
if (y < 0.5f) y = 0.5f;
if (y > yres - 1.5f) y = yres - 1.5f;
if (z < 0.5f) z = 0.5f;
if (z > zres - 1.5f) z = zres - 1.5f;
// locate neighbors to interpolate
const int x0 = (int)x;
const int x1 = x0 + 1;
const int y0 = (int)y;
const int y1 = y0 + 1;
const int z0 = (int)z;
const int z1 = z0 + 1;
// get interpolation weights
const float s1 = x - (float)x0;
const float s0 = 1.0f - s1;
const float t1 = y - (float)y0;
const float t0 = 1.0f - t1;
const float u1 = z - (float)z0;
const float u0 = 1.0f - u1;
const int slabSize = xres*yres;
const int i000 = x0 + y0 * xres + z0 * slabSize;
const int i010 = x0 + y1 * xres + z0 * slabSize;
const int i100 = x1 + y0 * xres + z0 * slabSize;
const int i110 = x1 + y1 * xres + z0 * slabSize;
const int i001 = x0 + y0 * xres + z1 * slabSize;
const int i011 = x0 + y1 * xres + z1 * slabSize;
const int i101 = x1 + y0 * xres + z1 * slabSize;
const int i111 = x1 + y1 * xres + z1 * slabSize;
// interpolate (indices could be computed once)
return (float)(
( u0 * (s0 * (t0 * (float)field1[i000] +
t1 * (float)field1[i010]) +
s1 * (t0 * (float)field1[i100] +
t1 * (float)field1[i110])) +
u1 * (s0 * (t0 * (float)field1[i001] +
t1 * (float)field1[i011]) +
s1 * (t0 * (float)field1[i101] +
t1 * (float)field1[i111])) ) );
}
//////////////////////////////////////////////////////////////////////////////////////////
// interpolate a vector from 3 fields
//////////////////////////////////////////////////////////////////////////////////////////
static inline Vec3 lerp3dVec(float* field1, float* field2, float* field3,
float x, float y, float z, int xres, int yres, int zres) {
// clamp pos to grid boundaries
if (x < 0.5f) x = 0.5f;
if (x > xres - 1.5f) x = xres - 1.5f;
if (y < 0.5f) y = 0.5f;
if (y > yres - 1.5f) y = yres - 1.5f;
if (z < 0.5f) z = 0.5f;
if (z > zres - 1.5f) z = zres - 1.5f;
// locate neighbors to interpolate
const int x0 = (int)x;
const int x1 = x0 + 1;
const int y0 = (int)y;
const int y1 = y0 + 1;
const int z0 = (int)z;
const int z1 = z0 + 1;
// get interpolation weights
const float s1 = x - (float)x0;
const float s0 = 1.0f - s1;
const float t1 = y - (float)y0;
const float t0 = 1.0f - t1;
const float u1 = z - (float)z0;
const float u0 = 1.0f - u1;
const int slabSize = xres*yres;
const int i000 = x0 + y0 * xres + z0 * slabSize;
const int i010 = x0 + y1 * xres + z0 * slabSize;
const int i100 = x1 + y0 * xres + z0 * slabSize;
const int i110 = x1 + y1 * xres + z0 * slabSize;
const int i001 = x0 + y0 * xres + z1 * slabSize;
const int i011 = x0 + y1 * xres + z1 * slabSize;
const int i101 = x1 + y0 * xres + z1 * slabSize;
const int i111 = x1 + y1 * xres + z1 * slabSize;
// interpolate (indices could be computed once)
return Vec3(
( u0 * (s0 * (t0 * field1[i000] +
t1 * field1[i010]) +
s1 * (t0 * field1[i100] +
t1 * field1[i110])) +
u1 * (s0 * (t0 * field1[i001] +
t1 * field1[i011]) +
s1 * (t0 * field1[i101] +
t1 * field1[i111])) ) ,
( u0 * (s0 * (t0 * field2[i000] +
t1 * field2[i010]) +
s1 * (t0 * field2[i100] +
t1 * field2[i110])) +
u1 * (s0 * (t0 * field2[i001] +
t1 * field2[i011]) +
s1 * (t0 * field2[i101] +
t1 * field2[i111])) ) ,
( u0 * (s0 * (t0 * field3[i000] +
t1 * field3[i010]) +
s1 * (t0 * field3[i100] +
t1 * field3[i110])) +
u1 * (s0 * (t0 * field3[i001] +
t1 * field3[i011]) +
s1 * (t0 * field3[i101] +
t1 * field3[i111])) )
);
}
};
#endif
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