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103 lines
3.5 KiB
103 lines
3.5 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/DCPQuery.h>
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#include <Mathematics/Line.h>
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#include <Mathematics/Segment.h>
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namespace gte
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{
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template <int N, typename Real>
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class DCPQuery<Real, Line<N, Real>, Segment<N, Real>>
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{
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public:
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struct Result
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{
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Real distance, sqrDistance;
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Real parameter[2];
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Vector<N, Real> closestPoint[2];
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};
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// The centered form of the 'segment' is used. Thus, parameter[1] of
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// the result is in [-e,e], where e = |segment.p[1] - segment.p[0]|/2.
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Result operator()(Line<N, Real> const& line, Segment<N, Real> const& segment)
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{
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Result result;
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Vector<N, Real> segCenter, segDirection;
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Real segExtent;
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segment.GetCenteredForm(segCenter, segDirection, segExtent);
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Vector<N, Real> diff = line.origin - segCenter;
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Real a01 = -Dot(line.direction, segDirection);
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Real b0 = Dot(diff, line.direction);
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Real s0, s1;
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if (std::fabs(a01) < (Real)1)
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{
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// The line and segment are not parallel.
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Real det = (Real)1 - a01 * a01;
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Real extDet = segExtent * det;
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Real b1 = -Dot(diff, segDirection);
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s1 = a01 * b0 - b1;
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if (s1 >= -extDet)
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{
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if (s1 <= extDet)
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{
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// Two interior points are closest, one on the line
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// and one on the segment.
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s0 = (a01 * b1 - b0) / det;
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s1 /= det;
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}
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else
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{
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// The endpoint e1 of the segment and an interior
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// point of the line are closest.
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s1 = segExtent;
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s0 = -(a01 * s1 + b0);
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}
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}
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else
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{
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// The endpoint e0 of the segment and an interior point
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// of the line are closest.
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s1 = -segExtent;
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s0 = -(a01 * s1 + b0);
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}
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}
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else
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{
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// The line and segment are parallel. Choose the closest pair
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// so that one point is at segment origin.
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s1 = (Real)0;
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s0 = -b0;
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}
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result.parameter[0] = s0;
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result.parameter[1] = s1;
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result.closestPoint[0] = line.origin + s0 * line.direction;
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result.closestPoint[1] = segCenter + s1 * segDirection;
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diff = result.closestPoint[0] - result.closestPoint[1];
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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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// Template aliases for convenience.
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template <int N, typename Real>
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using DCPLineSegment = DCPQuery<Real, Line<N, Real>, Segment<N, Real>>;
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template <typename Real>
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using DCPLine2Segment2 = DCPLineSegment<2, Real>;
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template <typename Real>
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using DCPLine3Segment3 = DCPLineSegment<3, Real>;
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}
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