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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: 5.6.1 (2012/07/07)
#include "ThinPlateSplines.h"
WM5_CONSOLE_APPLICATION(ThinPlateSplines);
//----------------------------------------------------------------------------
ThinPlateSplines::ThinPlateSplines ()
:
ConsoleApplication("SampleMathematics/ThinPlateSplines")
{
}
//----------------------------------------------------------------------------
ThinPlateSplines::~ThinPlateSplines ()
{
}
//----------------------------------------------------------------------------
void TestThinPlateSplines2D ()
{
FILE* outFile = fopen("output2.txt", "wt");
// Tabulated data on a 3x3 regular grid, points of form (x,y,f(x,y)).
const int numPoints = 9;
double x[numPoints] =
{
0.0, 0.5, 1.0,
0.0, 0.5, 1.0,
0.0, 0.5, 1.0
};
double y[numPoints] =
{
0.0, 0.0, 0.0,
0.5, 0.5, 0.5,
1.0, 1.0, 1.0
};
double f[numPoints] =
{
1.0, 2.0, 3.0,
3.0, 2.0, 1.0,
1.0, 2.0, 3.0
};
// Resample on a 7x7 regular grid.
const int numResample = 6;
const double invResample = 1.0/(double)numResample;
double smooth, interp, functional;
int i, j;
// No smoothing, exact interpolation at grid points.
smooth = 0.0;
IntpThinPlateSpline2d noSmooth(numPoints, x, y, f, smooth, false, false);
fprintf(outFile, "no smoothing (smooth parameter is 0.0)\n");
for (j = 0; j <= numResample; ++j)
{
for (i = 0; i <= numResample; ++i)
{
interp = noSmooth(invResample*i, invResample*j);
fprintf(outFile, "%lf ", interp);
}
fprintf(outFile, "\n");
}
functional = noSmooth.ComputeFunctional();
fprintf(outFile, "functional = %lg\n", functional);
fprintf(outFile, "\n");
// Increasing amounts of smoothing.
smooth = 0.1;
for (int k = 1; k <= 6; ++k, smooth *= 10.0)
{
IntpThinPlateSpline2d spline(numPoints, x, y, f, smooth, false, false);
fprintf(outFile, "smoothing (parameter is %lf)\n", smooth);
for (j = 0; j <= numResample; ++j)
{
for (i = 0; i <= numResample; ++i)
{
interp = spline(invResample*i, invResample*j);
fprintf(outFile, "%lf ", interp);
}
fprintf(outFile, "\n");
}
functional = spline.ComputeFunctional();
fprintf(outFile, "functional = %lg\n", functional);
fprintf(outFile, "\n");
}
fclose(outFile);
}
//----------------------------------------------------------------------------
void TestThinPlateSplines3D ()
{
FILE* outFile = fopen("output3.txt", "wt");
// Tabulated data on a 3x3x3 regular grid, points (x,y,z,f(x,y,z)).
const int numPoints = 27;
double x[numPoints], y[numPoints], z[numPoints], f[numPoints];
double xdomain, ydomain, zdomain;
int i, j, k, index = 0;
for (k = 0; k < 3; ++k)
{
zdomain = 0.5*k;
for (j = 0; j < 3; ++j)
{
ydomain = 0.5*j;
for (i = 0; i < 3; ++i, ++index)
{
xdomain = 0.5*i;
x[index] = xdomain;
y[index] = ydomain;
z[index] = zdomain;
f[index] = Mathd::UnitRandom();
}
}
}
// Resample on a 7x7x7 regular grid.
const int numResample = 6;
const double invResample = 1.0/(double)numResample;
double smooth, interp, functional;
// No smoothing, exact interpolation at grid points.
smooth = 0.0;
IntpThinPlateSpline3d noSmooth(numPoints, x, y, z, f, smooth, false, false);
fprintf(outFile, "no smoothing (smooth parameter is 0.0)\n");
for (k = 0; k <= numResample; ++k)
{
zdomain = invResample*k;
for (j = 0; j <= numResample; ++j)
{
ydomain = invResample*j;
for (i = 0; i <= numResample; ++i)
{
xdomain = invResample*i;
interp = noSmooth(xdomain, ydomain, zdomain);
fprintf(outFile, "%lf ", interp);
}
fprintf(outFile, "\n");
}
fprintf(outFile, "\n");
}
functional = noSmooth.ComputeFunctional();
fprintf(outFile, "functional = %lg\n", functional);
fprintf(outFile, "\n");
// Increasing amounts of smoothing.
smooth = 0.1;
for (int ell = 1; ell <= 6; ++ell, smooth *= 10.0)
{
IntpThinPlateSpline3d spline(numPoints, x, y, z, f, smooth, false,
false);
fprintf(outFile, "smoothing (parameter is %lf)\n", smooth);
for (k = 0; k <= numResample; ++k)
{
zdomain = invResample*k;
for (j = 0; j <= numResample; ++j)
{
ydomain = invResample*j;
for (i = 0; i <= numResample; ++i)
{
xdomain = invResample*i;
interp = spline(xdomain, ydomain, zdomain);
fprintf(outFile, "%lf ", interp);
}
fprintf(outFile, "\n");
}
fprintf(outFile, "\n");
}
functional = spline.ComputeFunctional();
fprintf(outFile, "functional = %lg\n", functional);
fprintf(outFile, "\n");
}
fclose(outFile);
}
//----------------------------------------------------------------------------
int ThinPlateSplines::Main (int, char**)
{
TestThinPlateSplines2D();
TestThinPlateSplines3D();
return 0;
}
//----------------------------------------------------------------------------
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