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67 lines
2.4 KiB
67 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/DCPQuery.h>
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#include <Mathematics/Circle3.h>
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// The 3D point-circle distance algorithm is described in
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// https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf
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// The notation used in the code matches that of the document.
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namespace gte
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{
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template <typename Real>
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class DCPQuery<Real, Vector3<Real>, Circle3<Real>>
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{
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public:
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// Either a single point on the circle is closest to 'point', in
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// which case 'equidistant' is false, or the entire circle is
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// closest to 'point', in which case 'equidistant' is true. In the
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// latter case, the query returns the circle point C+r*U, where C is
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// the circle center, r is the circle radius, and U is a vector
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// perpendicular to the normal N for the plane of the circle.
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struct Result
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{
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Real distance, sqrDistance;
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Vector3<Real> circleClosest;
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bool equidistant;
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};
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Result operator()(Vector3<Real> const& point, Circle3<Real> const& circle)
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{
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Result result;
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// Projection of P-C onto plane is Q-C = P-C - Dot(N,P-C)*N.
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Vector3<Real> PmC = point - circle.center;
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Vector3<Real> QmC = PmC - Dot(circle.normal, PmC) * circle.normal;
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Real lengthQmC = Length(QmC);
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if (lengthQmC > (Real)0)
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{
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result.circleClosest = circle.center + (circle.radius / lengthQmC) * QmC;
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result.equidistant = false;
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}
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else
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{
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// All circle points are equidistant from P. Return one of
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// them.
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Vector3<Real> basis[3];
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basis[0] = circle.normal;
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ComputeOrthogonalComplement(1, basis);
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result.circleClosest = circle.center + circle.radius * basis[1];
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result.equidistant = true;
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}
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Vector3<Real> diff = point - result.circleClosest;
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result.sqrDistance = Dot(diff, diff);
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result.distance = std::sqrt(result.sqrDistance);
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return result;
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}
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};
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}
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