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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: 5.0.2 (2011/07/23)
#include "Wm5MathematicsPCH.h"
#include "Wm5IntpBicubic2.h"
#include "Wm5Math.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntpBicubic2<Real>::IntpBicubic2 (int xBound, int yBound, Real xMin,
Real xSpacing, Real yMin, Real ySpacing, Real** F, bool catmullRom)
{
// At least a 3x3 block of data points are needed to construct the
// estimates of the boundary derivatives.
assertion(xBound >= 3 && yBound >= 3 && F, "Invalid input\n");
assertion(xSpacing > (Real)0 && ySpacing > (Real)0, "Invalid input\n");
mXBound = xBound;
mYBound = yBound;
mQuantity = xBound*yBound;
mXMin = xMin;
mXSpacing = xSpacing;
mInvXSpacing = ((Real)1)/xSpacing;
mYMin = yMin;
mYSpacing = ySpacing;
mInvYSpacing = ((Real)1)/ySpacing;
mXMax = xMin + xSpacing*(xBound - 1);
mYMax = yMin + ySpacing*(yBound - 1);
mF = F;
mBlend = (catmullRom ? msCRBlend : msBSBlend);
}
//----------------------------------------------------------------------------
template <typename Real>
int IntpBicubic2<Real>::GetXBound () const
{
return mXBound;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntpBicubic2<Real>::GetYBound () const
{
return mYBound;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntpBicubic2<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
Real** IntpBicubic2<Real>::GetF () const
{
return mF;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetXMin () const
{
return mXMin;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetXMax () const
{
return mXMax;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetXSpacing () const
{
return mXSpacing;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetYMin () const
{
return mYMin;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetYMax () const
{
return mYMax;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::GetYSpacing () const
{
return mYSpacing;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::operator() (Real x, Real y) const
{
// Compute x-index and clamp to image.
Real xIndex = (x - mXMin)*mInvXSpacing;
int ix = (int)xIndex;
if (ix < 0 || ix > mXBound - 1)
{
return Math<Real>::MAX_REAL;
}
// Compute y-index and clamp to image.
Real yIndex = (y - mYMin)*mInvYSpacing;
int iy = (int)yIndex;
if (iy < 0 || iy > mYBound - 1)
{
return Math<Real>::MAX_REAL;
}
Real U[4];
U[0] = (Real)1;
U[1] = xIndex - ix;
U[2] = U[1]*U[1];
U[3] = U[1]*U[2];
Real V[4];
V[0] = (Real)1;
V[1] = yIndex - iy;
V[2] = V[1]*V[1];
V[3] = V[1]*V[2];
// Compute P = M*U and Q = M*V.
Real P[4], Q[4];
int row, col;
for (row = 0; row < 4; ++row)
{
P[row] = (Real)0;
Q[row] = (Real)0;
for (col = 0; col < 4; ++col)
{
P[row] += mBlend[row][col]*U[col];
Q[row] += mBlend[row][col]*V[col];
}
}
// Compute (M*U)^t D (M*V) where D is the 4x4 subimage containing (x,y).
--ix;
--iy;
Real result = (Real)0;
for (row = 0; row < 4; ++row)
{
int yClamp = iy + row;
if (yClamp < 0)
{
yClamp = 0;
}
else if (yClamp > mYBound - 1)
{
yClamp = mYBound - 1;
}
for (col = 0; col < 4; ++col)
{
int xClamp = ix + col;
if (xClamp < 0)
{
xClamp = 0;
}
else if (xClamp > mXBound - 1)
{
xClamp = mXBound - 1;
}
result += Q[row]*mF[yClamp][xClamp]*P[col];
}
}
return result;
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntpBicubic2<Real>::operator() (int xOrder, int yOrder, Real x, Real y)
const
{
// Compute x-index and clamp to image.
Real xIndex = (x - mXMin)*mInvXSpacing;
int ix = (int)xIndex;
if (ix < 0 || ix > mXBound - 1)
{
return Math<Real>::MAX_REAL;
}
// Compute y-index and clamp to image.
Real yIndex = (y - mYMin)*mInvYSpacing;
int iy = (int)yIndex;
if (iy < 0 || iy > mYBound - 1)
{
return Math<Real>::MAX_REAL;
}
Real U[4], dx, xMult;
switch (xOrder)
{
case 0:
dx = xIndex - ix;
U[0] = (Real)1;
U[1] = dx;
U[2] = dx*U[1];
U[3] = dx*U[2];
xMult = (Real)1;
break;
case 1:
dx = xIndex - ix;
U[0] = (Real)0;
U[1] = (Real)1;
U[2] = ((Real)2)*dx;
U[3] = ((Real)3)*dx*dx;
xMult = mInvXSpacing;
break;
case 2:
dx = xIndex - ix;
U[0] = (Real)0;
U[1] = (Real)0;
U[2] = (Real)2;
U[3] = (Real)6*dx;
xMult = mInvXSpacing*mInvXSpacing;
break;
case 3:
U[0] = (Real)0;
U[1] = (Real)0;
U[2] = (Real)0;
U[3] = (Real)6;
xMult = mInvXSpacing*mInvXSpacing*mInvXSpacing;
break;
default:
return (Real)0;
}
Real V[4], dy, yMult;
switch (yOrder)
{
case 0:
dy = yIndex - iy;
V[0] = (Real)1;
V[1] = dy;
V[2] = dy*V[1];
V[3] = dy*V[2];
yMult = (Real)1;
break;
case 1:
dy = yIndex - iy;
V[0] = (Real)0;
V[1] = (Real)1;
V[2] = ((Real)2)*dy;
V[3] = ((Real)3)*dy*dy;
yMult = mInvYSpacing;
break;
case 2:
dy = yIndex - iy;
V[0] = (Real)0;
V[1] = (Real)0;
V[2] = (Real)2;
V[3] = ((Real)6)*dy;
yMult = mInvYSpacing*mInvYSpacing;
break;
case 3:
V[0] = (Real)0;
V[1] = (Real)0;
V[2] = (Real)0;
V[3] = (Real)6;
yMult = mInvYSpacing*mInvYSpacing*mInvYSpacing;
break;
default:
return (Real)0;
}
// Compute P = M*U and Q = M*V.
Real P[4], Q[4];
int row, col;
for (row = 0; row < 4; ++row)
{
P[row] = (Real)0;
Q[row] = (Real)0;
for (col = 0; col < 4; ++col)
{
P[row] += mBlend[row][col]*U[col];
Q[row] += mBlend[row][col]*V[col];
}
}
// Compute (M*U)^t D (M*V) where D is the 4x4 subimage containing (x,y).
--ix;
--iy;
Real result = (Real)0;
for (row = 0; row < 4; ++row)
{
int yClamp = iy + row;
if (yClamp < 0)
{
yClamp = 0;
}
else if (yClamp > mYBound - 1)
{
yClamp = mYBound - 1;
}
for (col = 0; col < 4; ++col)
{
int xClamp = ix + col;
if (xClamp < 0)
{
xClamp = 0;
}
else if (xClamp > mXBound - 1)
{
xClamp = mXBound - 1;
}
result += Q[row]*mF[yClamp][xClamp]*P[col];
}
}
result *= xMult*yMult;
return result;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation
//----------------------------------------------------------------------------
template<>
const float IntpBicubic2<float>::msCRBlend[4][4] =
{
{ 0.0f, -0.5f, 1.0f, -0.5f },
{ 1.0f, 0.0f, -2.5f, 1.5f },
{ 0.0f, 0.5f, 2.0f, -1.5f },
{ 0.0f, 0.0f, -0.5f, 0.5f }
};
template<>
const float IntpBicubic2<float>::msBSBlend[4][4] =
{
{ 1.0f/6.0f, -3.0f/6.0f, 3.0f/6.0f, -1.0f/6.0f },
{ 4.0f/6.0f, 0.0f/6.0f, -6.0f/6.0f, 3.0f/6.0f },
{ 1.0f/6.0f, 3.0f/6.0f, 3.0f/6.0f, -3.0f/6.0f },
{ 0.0f/6.0f, 0.0f/6.0f, 0.0f/6.0f, 1.0f/6.0f }
};
template WM5_MATHEMATICS_ITEM
class IntpBicubic2<float>;
template<>
const double IntpBicubic2<double>::msCRBlend[4][4] =
{
{ 0.0, -0.5, 1.0, -0.5 },
{ 1.0, 0.0, -2.5, 1.5 },
{ 0.0, 0.5, 2.0, -1.5 },
{ 0.0, 0.0, -0.5, 0.5 }
};
template<>
const double IntpBicubic2<double>::msBSBlend[4][4] =
{
{ 1.0/6.0, -3.0/6.0, 3.0/6.0, -1.0/6.0 },
{ 4.0/6.0, 0.0/6.0, -6.0/6.0, 3.0/6.0 },
{ 1.0/6.0, 3.0/6.0, 3.0/6.0, -3.0/6.0 },
{ 0.0/6.0, 0.0/6.0, 0.0/6.0, 1.0/6.0 }
};
template WM5_MATHEMATICS_ITEM
class IntpBicubic2<double>;
//----------------------------------------------------------------------------
}
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