GteIntpAkimaNonuniform1.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// 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: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteIntpAkima1.h>

namespace gte
{

template <typename Real>
class IntpAkimaNonuniform1 : public IntpAkima1<Real>
{
public:
    // Construction.  The interpolator is for arbitrarily spaced x-values.
    // The input arrays must have 'quantity' elements and the X[] array
    // must store increasing values:  X[i + 1] > X[i] for all i.
    IntpAkimaNonuniform1(int quantity, Real const* X, Real const* F);

    // Member access.
    Real const* GetX() const;
    virtual Real GetXMin() const override;
    virtual Real GetXMax() const override;

protected:
    virtual void Lookup(Real x, int& index, Real& dx) const override;

    Real const* mX;
};

template <typename Real>
IntpAkimaNonuniform1<Real>::IntpAkimaNonuniform1(int quantity, Real const* X,
    Real const* F)
    :
    IntpAkima1<Real>(quantity, F),
    mX(X)
{
#if !defined(GTE_NO_LOGGER)
    LogAssert(X != nullptr, "Invalid input.");
    for (int j0 = 0, j1 = 1; j1 < quantity; ++j0, ++j1)
    {
        LogAssert(X[j1] > X[j0], "Invalid input.");
    }
#endif

    // Compute slopes.
    std::vector<Real> slope(quantity + 3);
    int i, ip1, ip2;
    for (i = 0, ip1 = 1, ip2 = 2; i < quantity - 1; ++i, ++ip1, ++ip2)
    {
        Real dx = X[ip1] - X[i];
        Real df = F[ip1] - F[i];
        slope[ip2] = df / dx;
    }

    slope[1] = ((Real)2) * slope[2] - slope[3];
    slope[0] = ((Real)2) * slope[1] - slope[2];
    slope[quantity + 1] = ((Real)2) * slope[quantity] - slope[quantity - 1];
    slope[quantity + 2] = ((Real)2) * slope[quantity + 1] - slope[quantity];

    // Construct derivatives.
    std::vector<Real> FDer(quantity);
    for (i = 0; i < quantity; ++i)
    {
        FDer[i] = this->ComputeDerivative(&slope[i]);
    }

    // Construct polynomials.
    for (i = 0, ip1 = 1; i < quantity - 1; ++i, ++ip1)
    {
        auto& poly = this->mPoly[i];

        Real F0 = F[i];
        Real F1 = F[ip1];
        Real FDer0 = FDer[i];
        Real FDer1 = FDer[ip1];
        Real df = F1 - F0;
        Real dx = X[ip1] - X[i];
        Real dx2 = dx * dx;
        Real dx3 = dx2 * dx;

        poly[0] = F0;
        poly[1] = FDer0;
        poly[2] = (((Real)3) * df - dx * (FDer1 + ((Real)2) * FDer0)) / dx2;
        poly[3] = (dx * (FDer0 + FDer1) - ((Real)2) * df) / dx3;
    }
}

template <typename Real>
Real const* IntpAkimaNonuniform1<Real>::GetX() const
{
    return mX;
}

template <typename Real>
Real IntpAkimaNonuniform1<Real>::GetXMin() const
{
    return mX[0];
}

template <typename Real>
Real IntpAkimaNonuniform1<Real>::GetXMax() const
{
    return mX[this->mQuantity - 1];
}

template <typename Real>
void IntpAkimaNonuniform1<Real>::Lookup(Real x, int& index, Real& dx) const
{
    // The caller has ensured that mXMin <= x <= mXMax.
    for (index = 0; index + 1 < this->mQuantity; ++index)
    {
        if (x < mX[index + 1])
        {
            dx = x - mX[index];
            return;
        }
    }

    --index;
    dx = x - mX[index];
}

}