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62 lines
2.0 KiB
62 lines
2.0 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/Hypersphere.h>
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#include <Mathematics/LinearSystem.h>
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namespace gte
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{
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// All functions return 'true' if the circle has been constructed, 'false'
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// otherwise (input points are linearly dependent).
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// Circle circumscribing triangle.
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template <typename Real>
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bool Circumscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
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Vector2<Real> const& v2, Circle2<Real>& circle)
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{
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Vector2<Real> e10 = v1 - v0;
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Vector2<Real> e20 = v2 - v0;
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Matrix2x2<Real> A{ e10[0], e10[1], e20[0], e20[1] };
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Vector2<Real> B{ (Real)0.5 * Dot(e10, e10), (Real)0.5 * Dot(e20, e20) };
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Vector2<Real> solution;
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if (LinearSystem<Real>::Solve(A, B, solution))
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{
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circle.center = v0 + solution;
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circle.radius = Length(solution);
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return true;
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}
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return false;
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}
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// Circle inscribing triangle.
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template <typename Real>
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bool Inscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
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Vector2<Real> const& v2, Circle2<Real>& circle)
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{
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Vector2<Real> d10 = v1 - v0;
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Vector2<Real> d20 = v2 - v0;
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Vector2<Real> d21 = v2 - v1;
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Real len10 = Length(d10);
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Real len20 = Length(d20);
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Real len21 = Length(d21);
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Real perimeter = len10 + len20 + len21;
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if (perimeter > (Real)0)
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{
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Real inv = (Real)1 / perimeter;
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len10 *= inv;
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len20 *= inv;
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len21 *= inv;
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circle.center = len21 * v0 + len20 * v1 + len10 * v2;
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circle.radius = inv * std::fabs(DotPerp(d10, d20));
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return circle.radius > (Real)0;
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}
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return false;
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}
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}
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