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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 "Wm5IntrCircle3Plane3.h"
#include "Wm5IntrPlane3Plane3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrCircle3Plane3<Real>::IntrCircle3Plane3 (const Circle3<Real>& circle,
const Plane3<Real>& plane)
:
mCircle(&circle),
mPlane(&plane)
{
}
//----------------------------------------------------------------------------
template <typename Real>
const Circle3<Real>& IntrCircle3Plane3<Real>::GetCircle () const
{
return *mCircle;
}
//----------------------------------------------------------------------------
template <typename Real>
const Plane3<Real>& IntrCircle3Plane3<Real>::GetPlane () const
{
return *mPlane;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrCircle3Plane3<Real>::Test ()
{
mQuantity = 0;
// Construct the plane of the circle.
Plane3<Real> CPlane(mCircle->Normal,mCircle->Center);
// Compute the intersection of this plane with the input plane.
IntrPlane3Plane3<Real> intr(*mPlane,CPlane);
if (!intr.Find())
{
// Planes are parallel and nonintersecting.
mIntersectionType = IT_EMPTY;
return false;
}
if (intr.GetIntersectionType() == IT_PLANE)
{
// Planes are the same, the circle is the common intersection set.
mIntersectionType = IT_OTHER;
return true;
}
// The planes intersect in a line.
const Line3<Real>& line = intr.GetIntersectionLine();
// Locate one or two points that are on the circle and line. If the
// line is t*D+P, the circle center is C, and the circle radius is r,
// then r^2 = |t*D+P-C|^2 = |D|^2*t^2 + 2*Dot(D,P-C)*t + |P-C|^2. This
// is a quadratic equation of the form: a2*t^2 + 2*a1*t + a0 = 0.
Vector3<Real> diff = line.Origin - mCircle->Center;
Real a2 = line.Direction.SquaredLength();
Real a1 = diff.Dot(line.Direction);
Real a0 = diff.SquaredLength() - mCircle->Radius*mCircle->Radius;
// Real-valued roots imply an intersection.
Real discr = a1*a1 - a0*a2;
mIntersectionType = (discr >= (Real)0 ? IT_POINT : IT_EMPTY);
return mIntersectionType != IT_EMPTY;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrCircle3Plane3<Real>::Find ()
{
mQuantity = 0;
// Construct the plane of the circle.
Plane3<Real> CPlane(mCircle->Normal,mCircle->Center);
// Compute the intersection of this plane with the input plane.
IntrPlane3Plane3<Real> intr(*mPlane,CPlane);
if (!intr.Find())
{
// Planes are parallel and nonintersecting.
mIntersectionType = IT_EMPTY;
return false;
}
if (intr.GetIntersectionType() == IT_PLANE)
{
// Planes are the same, the circle is the common intersection set.
mIntersectionType = IT_OTHER;
return true;
}
// The planes intersect in a line.
const Line3<Real>& line = intr.GetIntersectionLine();
// Locate one or two points that are on the circle and line. If the
// line is t*D+P, the circle center is C, and the circle radius is r,
// then r^2 = |t*D+P-C|^2 = |D|^2*t^2 + 2*Dot(D,P-C)*t + |P-C|^2. This
// is a quadratic equation of the form: a2*t^2 + 2*a1*t + a0 = 0.
Vector3<Real> diff = line.Origin - mCircle->Center;
Real a2 = line.Direction.SquaredLength();
Real a1 = diff.Dot(line.Direction);
Real a0 = diff.SquaredLength() - mCircle->Radius*mCircle->Radius;
Real discr = a1*a1 - a0*a2;
if (discr < (Real)0)
{
// No real roots, the circle does not intersect the plane.
mIntersectionType = IT_EMPTY;
return false;
}
mIntersectionType = IT_POINT;
Real inv = ((Real)1)/a2;
if (discr < Math<Real>::ZERO_TOLERANCE)
{
// One repeated root, the circle just touches the plane.
mQuantity = 1;
mPoint[0] = line.Origin - (a1*inv)*line.Direction;
return true;
}
// Two distinct, real-valued roots, the circle intersects the plane in
// two points.
Real root = Math<Real>::Sqrt(discr);
mQuantity = 2;
mPoint[0] = line.Origin - ((a1 + root)*inv)*line.Direction;
mPoint[1] = line.Origin - ((a1 - root)*inv)*line.Direction;
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrCircle3Plane3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrCircle3Plane3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
template <typename Real>
const Circle3<Real>& IntrCircle3Plane3<Real>::GetIntersectionCircle () const
{
return *mCircle;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrCircle3Plane3<float>;
template WM5_MATHEMATICS_ITEM
class IntrCircle3Plane3<double>;
//----------------------------------------------------------------------------
}
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