Interpolation.h

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// Interpolation.h:
// ----------------
//

#ifndef __IPSDKMATH_INTERPOLATION_H__
#define __IPSDKMATH_INTERPOLATION_H__

#include <IPSDKMath/IPSDKMathExports.h>
#include <IPSDKUtil/BaseTypes.h>
#include <IPSDKUtil/Tools/ForceInline.h>

namespace ipsdk {
namespace math {


IPSDK_FORCEINLINE ipReal64
linearInterpolation(const ipReal64 x, const ipReal64 f0, const ipReal64 f1)
{
    return (1-x)*f0 + x*f1;
}

IPSDK_FORCEINLINE ipReal64
biLinearInterpolation(const ipReal64 x, const ipReal64 y,
                      const ipReal64 fX0Y0, const ipReal64 fX1Y0,
                      const ipReal64 fX0Y1, const ipReal64 fX1Y1)
{
    const ipReal64 fY0 = linearInterpolation(x, fX0Y0, fX1Y0);
    const ipReal64 fY1 = linearInterpolation(x, fX0Y1, fX1Y1);
    return linearInterpolation(y, fY0, fY1);
}

IPSDK_FORCEINLINE ipReal64
triLinearInterpolation(const ipReal64 x, const ipReal64 y, const ipReal64 z,
                       const ipReal64 fX0Y0Z0, const ipReal64 fX1Y0Z0,
                       const ipReal64 fX0Y1Z0, const ipReal64 fX1Y1Z0,
                       const ipReal64 fX0Y0Z1, const ipReal64 fX1Y0Z1,
                       const ipReal64 fX0Y1Z1, const ipReal64 fX1Y1Z1)
{
    const ipReal64 fZ0 = biLinearInterpolation(x, y, fX0Y0Z0, fX1Y0Z0, fX0Y1Z0, fX1Y1Z0);
    const ipReal64 fZ1 = biLinearInterpolation(x, y, fX0Y0Z1, fX1Y0Z1, fX0Y1Z1, fX1Y1Z1);
    return linearInterpolation(z, fZ0, fZ1);
}

IPSDK_FORCEINLINE ipReal64
cubicInterpolation(const ipReal64 x,
                   const ipReal64 fM1, const ipReal64 f0,
                   const ipReal64 f1, const ipReal64 f2)
{
    return f0 + 0.5 * x*(f1 - fM1 + x*(2.0*fM1 - 5.0*f0 + 4.0*f1 - f2 + x*(3.0*(f0 - f1) + f2 - fM1)));
}

IPSDK_FORCEINLINE ipReal64
biCubicInterpolation(const ipReal64 x, const ipReal64 y,
                     const ipReal64 f[4][4])
{
    const ipReal64 fYM1 = cubicInterpolation(x, f[0][0], f[0][1], f[0][2], f[0][3]);
    const ipReal64 fY0 = cubicInterpolation(x, f[1][0], f[1][1], f[1][2], f[1][3]);
    const ipReal64 fY1 = cubicInterpolation(x, f[2][0], f[2][1], f[2][2], f[2][3]);
    const ipReal64 fY2 = cubicInterpolation(x, f[3][0], f[3][1], f[3][2], f[3][3]);
    return cubicInterpolation(y, fYM1, fY0, fY1, fY2);
}

IPSDK_FORCEINLINE ipReal64
triCubicInterpolation(const ipReal64 x, const ipReal64 y, const ipReal64 z,
                      const ipReal64 f[4][4][4])
{
    const ipReal64 fZM1 = biCubicInterpolation(x, y, f[0]);
    const ipReal64 fZ0 = biCubicInterpolation(x, y, f[1]);
    const ipReal64 fZ1 = biCubicInterpolation(x, y, f[2]);
    const ipReal64 fZ2 = biCubicInterpolation(x, y, f[3]);
    return cubicInterpolation(z, fZM1, fZ0, fZ1, fZ2);
}


} // end of namespace math
} // end of namespace ipsdk

#endif // __IPSDKMATH_INTERPOLATION_H__