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71 lines
2.4 KiB
71 lines
2.4 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/RiemannianGeodesic.h>
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#include <Mathematics/BSplineSurface.h>
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namespace gte
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{
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template <typename Real>
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class BSplineGeodesic : public RiemannianGeodesic<Real>
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{
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public:
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BSplineGeodesic(BSplineSurface<3, Real> const& spline)
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:
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RiemannianGeodesic<Real>(2),
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mSpline(&spline)
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{
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}
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virtual ~BSplineGeodesic()
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{
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}
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private:
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virtual void ComputeMetric(const GVector<Real>& point) override
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{
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mSpline->Evaluate(point[0], point[1], 2, mJet);
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Vector<3, Real> const& der0 = mJet[1];
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Vector<3, Real> const& der1 = mJet[2];
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this->mMetric(0, 0) = Dot(der0, der0);
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this->mMetric(0, 1) = Dot(der0, der1);
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this->mMetric(1, 0) = this->mMetric(0, 1);
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this->mMetric(1, 1) = Dot(der1, der1);
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}
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virtual void ComputeChristoffel1(const GVector<Real>&) override
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{
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Vector<3, Real> const& der0 = mJet[1];
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Vector<3, Real> const& der1 = mJet[2];
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Vector<3, Real> const& der00 = mJet[3];
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Vector<3, Real> const& der01 = mJet[4];
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Vector<3, Real> const& der11 = mJet[5];
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this->mChristoffel1[0](0, 0) = Dot(der00, der0);
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this->mChristoffel1[0](0, 1) = Dot(der01, der0);
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this->mChristoffel1[0](1, 0) = this->mChristoffel1[0](0, 1);
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this->mChristoffel1[0](1, 1) = Dot(der11, der0);
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this->mChristoffel1[1](0, 0) = Dot(der00, der1);
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this->mChristoffel1[1](0, 1) = Dot(der01, der1);
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this->mChristoffel1[1](1, 0) = this->mChristoffel1[1](0, 1);
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this->mChristoffel1[1](1, 1) = Dot(der11, der1);
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}
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BSplineSurface<3, Real> const* mSpline;
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// We are guaranteed that RiemannianGeodesic calls ComputeMetric
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// before ComputeChristoffel1. Thus, we can compute the B-spline
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// first- and second-order derivatives in ComputeMetric and cache
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// the results for use in ComputeChristoffel1.
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Vector<3, Real> mJet[6];
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};
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}
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