GteContScribeCircle2.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Mathematics/GteHypersphere.h>
#include <Mathematics/GteLinearSystem.h>

namespace gte
{

// All functions return 'true' if the circle has been constructed, 'false'
// otherwise (input points are linearly dependent).

// Circle circumscribing triangle.
template <typename Real>
bool Circumscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
    Vector2<Real> const& v2, Circle2<Real>& circle);

// Circle inscribing triangle.
template <typename Real>
bool Inscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
    Vector2<Real> const& v2, Circle2<Real>& circle);


template <typename Real>
bool Circumscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
    Vector2<Real> const& v2, Circle2<Real>& circle)
{
    Vector2<Real> e10 = v1 - v0;
    Vector2<Real> e20 = v2 - v0;
    Matrix2x2<Real> A{ e10[0], e10[1], e20[0], e20[1] };
    Vector2<Real> B{ ((Real)0.5)*Dot(e10, e10), ((Real)0.5)*Dot(e20, e20) };
    Vector2<Real> solution;
    if (LinearSystem<Real>::Solve(A, B, solution))
    {
        circle.center = v0 + solution;
        circle.radius = Length(solution);
        return true;
    }
    return false;
}

template <typename Real>
bool Inscribe(Vector2<Real> const& v0, Vector2<Real> const& v1,
    Vector2<Real> const& v2, Circle2<Real>& circle)
{
    Vector2<Real> d10 = v1 - v0;
    Vector2<Real> d20 = v2 - v0;
    Vector2<Real> d21 = v2 - v1;
    Real len10 = Length(d10);
    Real len20 = Length(d20);
    Real len21 = Length(d21);
    Real perimeter = len10 + len20 + len21;
    if (perimeter > (Real)0)
    {
        Real inv = ((Real)1) / perimeter;
        len10 *= inv;
        len20 *= inv;
        len21 *= inv;
        circle.center = len21*v0 + len20*v1 + len10*v2;
        circle.radius = inv*std::abs(DotPerp(d10, d20));
        return circle.radius > (Real)0;
    }
    return false;
}


}