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/******************************************************************************
*
* MantaFlow fluid solver framework
* Copyright 2014 Tobias Pfaff, Nils Thuerey
*
* This program is free software, distributed under the terms of the
* Apache License, Version 2.0
* http://www.apache.org/licenses/LICENSE-2.0
*
* Helper functions for higher order interpolation
*
******************************************************************************/
#ifndef _INTERPOLHIGH_H
#define _INTERPOLHIGH_H
#include "vectorbase.h"
namespace Manta {
template<class T> inline T cubicInterp(const Real interp, const T *points)
{
T d0 = (points[2] - points[0]) * 0.5;
T d1 = (points[3] - points[1]) * 0.5;
T deltak = (points[2] - points[1]);
// disabled: if (deltak * d0 < 0.0) d0 = 0;
// disabled: if (deltak * d1 < 0.0) d1 = 0;
T a0 = points[1];
T a1 = d0;
T a2 = 3.0 * deltak - 2.0 * d0 - d1;
T a3 = -2.0 * deltak + d0 + d1;
Real squared = interp * interp;
Real cubed = squared * interp;
return a3 * cubed + a2 * squared + a1 * interp + a0;
}
template<class T> inline T interpolCubic2D(const T *data, const Vec3i &size, const Vec3 &pos)
{
const Real px = pos.x - 0.5f, py = pos.y - 0.5f;
const int x1 = (int)px;
const int x2 = x1 + 1;
const int x3 = x1 + 2;
const int x0 = x1 - 1;
const int y1 = (int)py;
const int y2 = y1 + 1;
const int y3 = y1 + 2;
const int y0 = y1 - 1;
if (x0 < 0 || y0 < 0 || x3 >= size[0] || y3 >= size[1]) {
return interpol(data, size, 0, pos);
}
const Real xInterp = px - x1;
const Real yInterp = py - y1;
const int y0x = y0 * size[0];
const int y1x = y1 * size[0];
const int y2x = y2 * size[0];
const int y3x = y3 * size[0];
const T p0[] = {data[x0 + y0x], data[x1 + y0x], data[x2 + y0x], data[x3 + y0x]};
const T p1[] = {data[x0 + y1x], data[x1 + y1x], data[x2 + y1x], data[x3 + y1x]};
const T p2[] = {data[x0 + y2x], data[x1 + y2x], data[x2 + y2x], data[x3 + y2x]};
const T p3[] = {data[x0 + y3x], data[x1 + y3x], data[x2 + y3x], data[x3 + y3x]};
const T finalPoints[] = {cubicInterp(xInterp, p0),
cubicInterp(xInterp, p1),
cubicInterp(xInterp, p2),
cubicInterp(xInterp, p3)};
return cubicInterp(yInterp, finalPoints);
}
template<class T>
inline T interpolCubic(const T *data, const Vec3i &size, const int Z, const Vec3 &pos)
{
if (Z == 0)
return interpolCubic2D(data, size, pos);
const Real px = pos.x - 0.5f, py = pos.y - 0.5f, pz = pos.z - 0.5f;
const int x1 = (int)px;
const int x2 = x1 + 1;
const int x3 = x1 + 2;
const int x0 = x1 - 1;
const int y1 = (int)py;
const int y2 = y1 + 1;
const int y3 = y1 + 2;
const int y0 = y1 - 1;
const int z1 = (int)pz;
const int z2 = z1 + 1;
const int z3 = z1 + 2;
const int z0 = z1 - 1;
if (x0 < 0 || y0 < 0 || z0 < 0 || x3 >= size[0] || y3 >= size[1] || z3 >= size[2]) {
return interpol(data, size, Z, pos);
}
const Real xInterp = px - x1;
const Real yInterp = py - y1;
const Real zInterp = pz - z1;
const int slabsize = size[0] * size[1];
const int z0Slab = z0 * slabsize;
const int z1Slab = z1 * slabsize;
const int z2Slab = z2 * slabsize;
const int z3Slab = z3 * slabsize;
const int y0x = y0 * size[0];
const int y1x = y1 * size[0];
const int y2x = y2 * size[0];
const int y3x = y3 * size[0];
const int y0z0 = y0x + z0Slab;
const int y1z0 = y1x + z0Slab;
const int y2z0 = y2x + z0Slab;
const int y3z0 = y3x + z0Slab;
const int y0z1 = y0x + z1Slab;
const int y1z1 = y1x + z1Slab;
const int y2z1 = y2x + z1Slab;
const int y3z1 = y3x + z1Slab;
const int y0z2 = y0x + z2Slab;
const int y1z2 = y1x + z2Slab;
const int y2z2 = y2x + z2Slab;
const int y3z2 = y3x + z2Slab;
const int y0z3 = y0x + z3Slab;
const int y1z3 = y1x + z3Slab;
const int y2z3 = y2x + z3Slab;
const int y3z3 = y3x + z3Slab;
// get the z0 slice
const T p0[] = {data[x0 + y0z0], data[x1 + y0z0], data[x2 + y0z0], data[x3 + y0z0]};
const T p1[] = {data[x0 + y1z0], data[x1 + y1z0], data[x2 + y1z0], data[x3 + y1z0]};
const T p2[] = {data[x0 + y2z0], data[x1 + y2z0], data[x2 + y2z0], data[x3 + y2z0]};
const T p3[] = {data[x0 + y3z0], data[x1 + y3z0], data[x2 + y3z0], data[x3 + y3z0]};
// get the z1 slice
const T p4[] = {data[x0 + y0z1], data[x1 + y0z1], data[x2 + y0z1], data[x3 + y0z1]};
const T p5[] = {data[x0 + y1z1], data[x1 + y1z1], data[x2 + y1z1], data[x3 + y1z1]};
const T p6[] = {data[x0 + y2z1], data[x1 + y2z1], data[x2 + y2z1], data[x3 + y2z1]};
const T p7[] = {data[x0 + y3z1], data[x1 + y3z1], data[x2 + y3z1], data[x3 + y3z1]};
// get the z2 slice
const T p8[] = {data[x0 + y0z2], data[x1 + y0z2], data[x2 + y0z2], data[x3 + y0z2]};
const T p9[] = {data[x0 + y1z2], data[x1 + y1z2], data[x2 + y1z2], data[x3 + y1z2]};
const T p10[] = {data[x0 + y2z2], data[x1 + y2z2], data[x2 + y2z2], data[x3 + y2z2]};
const T p11[] = {data[x0 + y3z2], data[x1 + y3z2], data[x2 + y3z2], data[x3 + y3z2]};
// get the z3 slice
const T p12[] = {data[x0 + y0z3], data[x1 + y0z3], data[x2 + y0z3], data[x3 + y0z3]};
const T p13[] = {data[x0 + y1z3], data[x1 + y1z3], data[x2 + y1z3], data[x3 + y1z3]};
const T p14[] = {data[x0 + y2z3], data[x1 + y2z3], data[x2 + y2z3], data[x3 + y2z3]};
const T p15[] = {data[x0 + y3z3], data[x1 + y3z3], data[x2 + y3z3], data[x3 + y3z3]};
// interpolate
const T z0Points[] = {cubicInterp(xInterp, p0),
cubicInterp(xInterp, p1),
cubicInterp(xInterp, p2),
cubicInterp(xInterp, p3)};
const T z1Points[] = {cubicInterp(xInterp, p4),
cubicInterp(xInterp, p5),
cubicInterp(xInterp, p6),
cubicInterp(xInterp, p7)};
const T z2Points[] = {cubicInterp(xInterp, p8),
cubicInterp(xInterp, p9),
cubicInterp(xInterp, p10),
cubicInterp(xInterp, p11)};
const T z3Points[] = {cubicInterp(xInterp, p12),
cubicInterp(xInterp, p13),
cubicInterp(xInterp, p14),
cubicInterp(xInterp, p15)};
const T finalPoints[] = {cubicInterp(yInterp, z0Points),
cubicInterp(yInterp, z1Points),
cubicInterp(yInterp, z2Points),
cubicInterp(yInterp, z3Points)};
return cubicInterp(zInterp, finalPoints);
}
inline Vec3 interpolCubicMAC(const Vec3 *data, const Vec3i &size, const int Z, const Vec3 &pos)
{
// warning - not yet optimized...
Real vx = interpolCubic<Vec3>(data, size, Z, pos + Vec3(0.5, 0, 0))[0];
Real vy = interpolCubic<Vec3>(data, size, Z, pos + Vec3(0, 0.5, 0))[1];
Real vz = 0.f;
if (Z != 0)
vz = interpolCubic<Vec3>(data, size, Z, pos + Vec3(0, 0, 0.5))[2];
return Vec3(vx, vy, vz);
}
} // namespace Manta
#endif
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