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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// 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: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5ContScribeCircle3Sphere3.h"
#include "Wm5LinearSystem.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
bool Circumscribe (const Vector3<Real>& v0, const Vector3<Real>& v1,
const Vector3<Real>& v2, Circle3<Real>& circle)
{
Vector3<Real> E02 = v0 - v2;
Vector3<Real> E12 = v1 - v2;
Real e02e02 = E02.Dot(E02);
Real e02e12 = E02.Dot(E12);
Real e12e12 = E12.Dot(E12);
Real det = e02e02*e12e12 - e02e12*e02e12;
if (Math<Real>::FAbs(det) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
Real halfInvDet = ((Real)0.5)/det;
Real u0 = halfInvDet*e12e12*(e02e02 - e02e12);
Real u1 = halfInvDet*e02e02*(e12e12 - e02e12);
Vector3<Real> tmp = u0*E02 + u1*E12;
circle.Center = v2 + tmp;
circle.Radius = tmp.Length();
circle.Normal = E02.UnitCross(E12);
if (Math<Real>::FAbs(circle.Normal.X())
>= Math<Real>::FAbs(circle.Normal.Y())
&& Math<Real>::FAbs(circle.Normal.X())
>= Math<Real>::FAbs(circle.Normal.Z()))
{
circle.Direction0.X() = -circle.Normal.Y();
circle.Direction0.Y() = circle.Normal.X();
circle.Direction0.Z() = (Real)0;
}
else
{
circle.Direction0.X() = (Real)0;
circle.Direction0.Y() = circle.Normal.Z();
circle.Direction0.Z() = -circle.Normal.Y();
}
circle.Direction0.Normalize();
circle.Direction1 = circle.Normal.Cross(circle.Direction0);
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
bool Circumscribe (const Vector3<Real>& v0, const Vector3<Real>& v1,
const Vector3<Real>& v2, const Vector3<Real>& v3,
Sphere3<Real>& sphere)
{
Vector3<Real> E10 = v1 - v0;
Vector3<Real> E20 = v2 - v0;
Vector3<Real> E30 = v3 - v0;
Real A[3][3] =
{
{E10.X(), E10.Y(), E10.Z()},
{E20.X(), E20.Y(), E20.Z()},
{E30.X(), E30.Y(), E30.Z()}
};
Real B[3] =
{
((Real)0.5)*E10.SquaredLength(),
((Real)0.5)*E20.SquaredLength(),
((Real)0.5)*E30.SquaredLength()
};
Vector3<Real> solution;
if (LinearSystem<Real>().Solve3(A, B,(Real*)&solution))
{
sphere.Center = v0 + solution;
sphere.Radius = solution.Length();
return true;
}
return false;
}
//----------------------------------------------------------------------------
template <typename Real>
bool Inscribe (const Vector3<Real>& v0, const Vector3<Real>& v1,
const Vector3<Real>& v2, Circle3<Real>& circle)
{
// Edges.
Vector3<Real> E0 = v1 - v0;
Vector3<Real> E1 = v2 - v1;
Vector3<Real> E2 = v0 - v2;
// Plane normal.
circle.Normal = E1.Cross(E0);
// Edge normals within the plane.
Vector3<Real> N0 = circle.Normal.UnitCross(E0);
Vector3<Real> N1 = circle.Normal.UnitCross(E1);
Vector3<Real> N2 = circle.Normal.UnitCross(E2);
Real a0 = N1.Dot(E0);
if (Math<Real>::FAbs(a0) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
Real a1 = N2.Dot(E1);
if (Math<Real>::FAbs(a1) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
Real a2 = N0.Dot(E2);
if (Math<Real>::FAbs(a2) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
Real invA0 = ((Real)1)/a0;
Real invA1 = ((Real)1)/a1;
Real invA2 = ((Real)1)/a2;
circle.Radius = ((Real)1)/(invA0 + invA1 + invA2);
circle.Center = circle.Radius*(invA0*v0 + invA1*v1 + invA2*v2);
circle.Normal.Normalize();
circle.Direction0 = N0;
circle.Direction1 = circle.Normal.Cross(circle.Direction0);
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
bool Inscribe (const Vector3<Real>& v0, const Vector3<Real>& v1,
const Vector3<Real>& v2, const Vector3<Real>& v3,
Sphere3<Real>& sphere)
{
// Edges.
Vector3<Real> E10 = v1 - v0;
Vector3<Real> E20 = v2 - v0;
Vector3<Real> E30 = v3 - v0;
Vector3<Real> E21 = v2 - v1;
Vector3<Real> E31 = v3 - v1;
// Normals.
Vector3<Real> N0 = E31.Cross(E21);
Vector3<Real> N1 = E20.Cross(E30);
Vector3<Real> N2 = E30.Cross(E10);
Vector3<Real> N3 = E10.Cross(E20);
// Normalize the normals.
if (Math<Real>::FAbs(N0.Normalize()) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
if (Math<Real>::FAbs(N1.Normalize()) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
if (Math<Real>::FAbs(N2.Normalize()) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
if (Math<Real>::FAbs(N3.Normalize()) < Math<Real>::ZERO_TOLERANCE)
{
return false;
}
Real A[3][3] =
{
{N1.X() - N0.X(), N1.Y() - N0.Y(), N1.Z() - N0.Z()},
{N2.X() - N0.X(), N2.Y() - N0.Y(), N2.Z() - N0.Z()},
{N3.X() - N0.X(), N3.Y() - N0.Y(), N3.Z() - N0.Z()}
};
Real B[3] =
{
(Real)0,
(Real)0,
-N3.Dot(E30)
};
Vector3<Real> solution;
if (LinearSystem<Real>().Solve3(A, B, (Real*)&solution))
{
sphere.Center = v3 + solution;
sphere.Radius = Math<Real>::FAbs(N0.Dot(solution));
return true;
}
return false;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
bool Circumscribe<float> (const Vector3<float>&, const Vector3<float>&,
const Vector3<float>&, Circle3<float>&);
template WM5_MATHEMATICS_ITEM
bool Circumscribe<float> (const Vector3<float>&, const Vector3<float>&,
const Vector3<float>&, const Vector3<float>&, Sphere3<float>&);
template WM5_MATHEMATICS_ITEM
bool Inscribe<float> (const Vector3<float>&, const Vector3<float>&,
const Vector3<float>&, Circle3<float>&);
template WM5_MATHEMATICS_ITEM
bool Inscribe<float> (const Vector3<float>&, const Vector3<float>&,
const Vector3<float>&, const Vector3<float>&, Sphere3<float>&);
template WM5_MATHEMATICS_ITEM
bool Circumscribe<double> (const Vector3<double>&, const Vector3<double>&,
const Vector3<double>&, Circle3<double>&);
template WM5_MATHEMATICS_ITEM
bool Circumscribe<double> (const Vector3<double>&, const Vector3<double>&,
const Vector3<double>&, const Vector3<double>&, Sphere3<double>&);
template WM5_MATHEMATICS_ITEM
bool Inscribe<double> (const Vector3<double>&, const Vector3<double>&,
const Vector3<double>&, Circle3<double>&);
template WM5_MATHEMATICS_ITEM
bool Inscribe<double> (const Vector3<double>&, const Vector3<double>&,
const Vector3<double>&, const Vector3<double>&, Sphere3<double>&);
//----------------------------------------------------------------------------
}
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