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109 lines
3.3 KiB
109 lines
3.3 KiB
3 months ago
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// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/IntpAkima1.h>
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namespace gte
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{
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template <typename Real>
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class IntpAkimaUniform1 : public IntpAkima1<Real>
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{
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public:
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// Construction and destruction. The interpolator is for uniformly
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// spaced x-values.
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IntpAkimaUniform1(int quantity, Real xMin, Real xSpacing, Real const* F)
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:
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IntpAkima1<Real>(quantity, F),
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mXMin(xMin),
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mXSpacing(xSpacing)
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{
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LogAssert(mXSpacing > (Real)0, "Spacing must be positive.");
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mXMax = mXMin + mXSpacing * static_cast<Real>(quantity - 1);
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// Compute slopes.
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Real invDX = (Real)1 / mXSpacing;
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std::vector<Real> slope(quantity + 3);
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int i, ip1, ip2;
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for (i = 0, ip1 = 1, ip2 = 2; i < quantity - 1; ++i, ++ip1, ++ip2)
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{
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slope[ip2] = (this->mF[ip1] - this->mF[i]) * invDX;
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}
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slope[1] = (Real)2 * slope[2] - slope[3];
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slope[0] = (Real)2 * slope[1] - slope[2];
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slope[quantity + 1] = (Real)2 * slope[quantity] - slope[quantity - 1];
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slope[quantity + 2] = (Real)2 * slope[quantity + 1] - slope[quantity];
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// Construct derivatives.
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std::vector<Real> FDer(quantity);
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for (i = 0; i < quantity; ++i)
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{
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FDer[i] = this->ComputeDerivative(&slope[i]);
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}
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// Construct polynomials.
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Real invDX2 = (Real)1 / (mXSpacing * mXSpacing);
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Real invDX3 = invDX2 / mXSpacing;
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for (i = 0, ip1 = 1; i < quantity - 1; ++i, ++ip1)
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{
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auto& poly = this->mPoly[i];
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Real F0 = F[i];
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Real F1 = F[ip1];
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Real df = F1 - F0;
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Real FDer0 = FDer[i];
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Real FDer1 = FDer[ip1];
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poly[0] = F0;
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poly[1] = FDer0;
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poly[2] = ((Real)3 * df - mXSpacing * (FDer1 + (Real)2 * FDer0)) * invDX2;
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poly[3] = (mXSpacing * (FDer0 + FDer1) - (Real)2 * df) * invDX3;
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}
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}
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virtual ~IntpAkimaUniform1() = default;
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// Member access.
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inline virtual Real GetXMin() const override
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{
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return mXMin;
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}
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inline virtual Real GetXMax() const override
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{
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return mXMax;
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}
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inline Real GetXSpacing() const
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{
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return mXSpacing;
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}
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protected:
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virtual void Lookup(Real x, int& index, Real& dx) const override
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{
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// The caller has ensured that mXMin <= x <= mXMax.
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for (index = 0; index + 1 < this->mQuantity; ++index)
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{
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if (x < mXMin + mXSpacing * (index + 1))
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{
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dx = x - (mXMin + mXSpacing * index);
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return;
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}
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}
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--index;
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dx = x - (mXMin + mXSpacing * index);
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}
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Real mXMin, mXMax, mXSpacing;
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};
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}
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