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132 lines
3.9 KiB
132 lines
3.9 KiB
// 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/ParametricCurve.h>
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#include <Mathematics/Vector2.h>
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#include <Mathematics/Vector3.h>
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#include <memory>
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namespace gte
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{
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template <typename Real>
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class FrenetFrame2
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{
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public:
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// Construction. The curve must persist as long as the FrenetFrame2
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// object does.
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FrenetFrame2(std::shared_ptr<ParametricCurve<2, Real>> const& curve)
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:
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mCurve(curve)
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{
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}
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// The normal is perpendicular to the tangent, rotated clockwise by
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// pi/2 radians.
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void operator()(Real t, Vector2<Real>& position, Vector2<Real>& tangent,
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Vector2<Real>& normal) const
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{
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std::array<Vector2<Real>, 2> jet;
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mCurve->Evaluate(t, 1, jet.data());
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position = jet[0];
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tangent = jet[1];
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Normalize(tangent);
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normal = Perp(tangent);
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}
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Real GetCurvature(Real t) const
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{
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std::array<Vector2<Real>, 3> jet;
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mCurve->Evaluate(t, 2, jet.data());
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Real speedSqr = Dot(jet[1], jet[1]);
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if (speedSqr > (Real)0)
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{
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Real numer = DotPerp(jet[1], jet[2]);
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Real denom = std::pow(speedSqr, (Real)1.5);
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return numer / denom;
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}
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else
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{
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// Curvature is indeterminate, just return 0.
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return (Real)0;
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}
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}
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private:
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std::shared_ptr<ParametricCurve<2, Real>> mCurve;
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};
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template <typename Real>
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class FrenetFrame3
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{
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public:
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// Construction. The curve must persist as long as the FrenetFrame3
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// object does.
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FrenetFrame3(std::shared_ptr<ParametricCurve<3, Real>> const& curve)
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:
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mCurve(curve)
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{
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}
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// The binormal is Cross(tangent, normal).
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void operator()(Real t, Vector3<Real>& position, Vector3<Real>& tangent,
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Vector3<Real>& normal, Vector3<Real>& binormal) const
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{
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std::array<Vector3<Real>, 3> jet;
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mCurve->Evaluate(t, 2, jet.data());
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position = jet[0];
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Real VDotV = Dot(jet[1], jet[1]);
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Real VDotA = Dot(jet[1], jet[2]);
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normal = VDotV * jet[2] - VDotA * jet[1];
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Normalize(normal);
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tangent = jet[1];
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Normalize(tangent);
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binormal = Cross(tangent, normal);
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}
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Real GetCurvature(Real t) const
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{
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std::array<Vector3<Real>, 3> jet;
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mCurve->Evaluate(t, 2, jet.data());
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Real speedSqr = Dot(jet[1], jet[1]);
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if (speedSqr > (Real)0)
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{
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Real numer = Length(Cross(jet[1], jet[2]));
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Real denom = std::pow(speedSqr, (Real)1.5);
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return numer / denom;
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}
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else
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{
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// Curvature is indeterminate, just return 0.
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return (Real)0;
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}
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}
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Real GetTorsion(Real t) const
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{
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std::array<Vector3<Real>, 4> jet;
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mCurve->Evaluate(t, 3, jet.data());
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Vector3<Real> cross = Cross(jet[1], jet[2]);
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Real denom = Dot(cross, cross);
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if (denom > (Real)0)
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{
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Real numer = Dot(cross, jet[3]);
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return numer / denom;
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}
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else
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{
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// Torsion is indeterminate, just return 0.
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return (Real)0;
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}
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}
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private:
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std::shared_ptr<ParametricCurve<3, Real>> mCurve;
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};
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}
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