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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5ApprPolyFit4.h"
#include "Wm5LinearSystem.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Real* PolyFit4 (int numSamples, const Real* xSamples, const Real* ySamples,
const Real* zSamples, const Real* wSamples, int xDegree, int yDegree,
int zDegree)
{
int xBound = xDegree + 1;
int yBound = yDegree + 1;
int zBound = zDegree + 1;
int quantity = xBound*yBound*zBound;
Real* coeff = new1<Real>(quantity);
int i0, j0, k0, i1, j1, k1, s;
// Powers of x, y, z.
Real** xPower = new2<Real>(2*xDegree+1, numSamples);
Real** yPower = new2<Real>(2*yDegree+1, numSamples);
Real** zPower = new2<Real>(2*zDegree+1, numSamples);
for (s = 0; s < numSamples; ++s)
{
xPower[s][0] = (Real)1;
for (i0 = 1; i0 <= 2*xDegree; ++i0)
{
xPower[s][i0] = xSamples[s]*xPower[s][i0-1];
}
yPower[s][0] = (Real)1;
for (j0 = 1; j0 <= 2*yDegree; ++j0)
{
yPower[s][j0] = ySamples[s]*yPower[s][j0-1];
}
zPower[s][0] = (Real)1;
for (k0 = 1; k0 <= 2*zDegree; ++k0)
{
zPower[s][k0] = zSamples[s]*zPower[s][k0-1];
}
}
// Vandermonde matrix and right-hand side of linear system.
GMatrix<Real> A(quantity, quantity);
Real* B = new1<Real>(quantity);
for (k0 = 0; k0 <= zDegree; ++k0)
{
for (j0 = 0; j0 <= yDegree; ++j0)
{
for (i0 = 0; i0 <= xDegree; ++i0)
{
int index0 = i0 + xBound*(j0 + yBound*k0);
Real sum = (Real)0;
for (s = 0; s < numSamples; ++s)
{
sum += wSamples[s] * xPower[s][i0] * yPower[s][j0] *
zPower[s][k0];
}
B[index0] = sum;
for (k1 = 0; k1 <= zDegree; ++k1)
{
for (j1 = 0; j1 <= yDegree; ++j1)
{
for (i1 = 0; i1 <= xDegree; ++i1)
{
int index1 = i1 + xBound*(j1 + yBound*k1);
sum = (Real)0;
for (s = 0; s < numSamples; ++s)
{
sum += xPower[s][i0+i1] * yPower[s][j0+j1] *
zPower[s][k0+k1];
}
A(index0,index1) = sum;
}
}
}
}
}
}
// Solve for the polynomial coefficients.
bool hasSolution = LinearSystem<Real>().Solve(A, B, coeff);
assertion(hasSolution, "Failed to solve linear system\n");
WM5_UNUSED(hasSolution);
delete1(B);
delete2(xPower);
delete2(yPower);
delete2(zPower);
return coeff;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
float* PolyFit4<float> (int, const float*, const float*, const float*,
const float*, int, int, int);
template WM5_MATHEMATICS_ITEM
double* PolyFit4<double> (int, const double*, const double*, const double*,
const double*, int, int, int);
//----------------------------------------------------------------------------
}
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