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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 "Wm5IntrSegment3Sphere3.h"
#include "Wm5IntrSegment3Capsule3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
IntrSegment3Sphere3<Real>::IntrSegment3Sphere3 (
const Segment3<Real>& segment, const Sphere3<Real>& sphere)
:
mSegment(&segment),
mSphere(&sphere)
{
mQuantity = 0;
ZeroThreshold = Math<Real>::ZERO_TOLERANCE;
}
//----------------------------------------------------------------------------
template <typename Real>
const Segment3<Real>& IntrSegment3Sphere3<Real>::GetSegment () const
{
return *mSegment;
}
//----------------------------------------------------------------------------
template <typename Real>
const Sphere3<Real>& IntrSegment3Sphere3<Real>::GetSphere () const
{
return *mSphere;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSegment3Sphere3<Real>::Test ()
{
Vector3<Real> diff = mSegment->Center - mSphere->Center;
Real a0 = diff.Dot(diff) - mSphere->Radius*mSphere->Radius;
Real a1 = mSegment->Direction.Dot(diff);
Real discr = a1*a1 - a0;
if (discr < (Real)0)
{
return false;
}
Real tmp0 = mSegment->Extent*mSegment->Extent + a0;
Real tmp1 = ((Real)2)*a1*mSegment->Extent;
Real qm = tmp0 - tmp1;
Real qp = tmp0 + tmp1;
if (qm*qp <= (Real)0)
{
return true;
}
return qm > (Real)0 && Math<Real>::FAbs(a1) < mSegment->Extent;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSegment3Sphere3<Real>::Find ()
{
Vector3<Real> diff = mSegment->Center - mSphere->Center;
Real a0 = diff.Dot(diff) - mSphere->Radius*mSphere->Radius;
Real a1 = mSegment->Direction.Dot(diff);
Real discr = a1*a1 - a0;
if (discr < (Real)0)
{
mQuantity = 0;
return false;
}
Real tmp0 = mSegment->Extent*mSegment->Extent + a0;
Real tmp1 = ((Real)2)*a1*mSegment->Extent;
Real qm = tmp0 - tmp1;
Real qp = tmp0 + tmp1;
Real root;
if (qm*qp <= (Real)0)
{
root = Math<Real>::Sqrt(discr);
mSegmentParameter[0] = (qm > (Real)0 ? -a1 - root : -a1 + root);
mPoint[0] = mSegment->Center + mSegmentParameter[0] *
mSegment->Direction;
mQuantity = 1;
mIntersectionType = IT_POINT;
return true;
}
if (qm > (Real)0 && Math<Real>::FAbs(a1) < mSegment->Extent)
{
if (discr >= ZeroThreshold)
{
root = Math<Real>::Sqrt(discr);
mSegmentParameter[0] = -a1 - root;
mSegmentParameter[1] = -a1 + root;
mPoint[0] = mSegment->Center + mSegmentParameter[0] *
mSegment->Direction;
mPoint[1] = mSegment->Center + mSegmentParameter[1] *
mSegment->Direction;
mQuantity = 2;
mIntersectionType = IT_SEGMENT;
}
else
{
mSegmentParameter[0] = -a1;
mPoint[0] = mSegment->Center + mSegmentParameter[0] *
mSegment->Direction;
mQuantity = 1;
mIntersectionType = IT_POINT;
}
}
else
{
mQuantity = 0;
mIntersectionType = IT_EMPTY;
}
return mQuantity > 0;
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSegment3Sphere3<Real>::Test (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
// Check if initially intersecting.
if (Test())
{
return true;
}
// Substract the segment velocity from the sphere velocity so that
// the calculations are based in the coordinate system of the segment.
// In this system, the line is of course stationary. The sphere spans
// a capsule, but instead we will "grow" the segment by the sphere radius
// and shrink the sphere to its center. The problem is now to detect
// the first time the moving center intersects the capsule formed by
// the line segment and sphere radius.
Capsule3<Real> capsule;
capsule.Segment = *mSegment;
capsule.Radius = mSphere->Radius;
Vector3<Real> relVelocity = velocity1 - velocity0;
Real relSpeed = relVelocity.Normalize();
Segment3<Real> path;
path.Extent = ((Real)0.5)*tmax*relSpeed;
path.Direction = relVelocity; // unit-length vector
path.Center = mSphere->Center + path.Extent*path.Direction;
return IntrSegment3Capsule3<Real>(path, capsule).Test();
}
//----------------------------------------------------------------------------
template <typename Real>
bool IntrSegment3Sphere3<Real>::Find (Real tmax,
const Vector3<Real>& velocity0, const Vector3<Real>& velocity1)
{
// Check if initially intersecting.
if (Find())
{
mContactTime = (Real)0;
mIntersectionType = IT_OTHER;
return true;
}
// Substract the segment velocity from the sphere velocity so that
// the calculations are based in the coordinate system of the segment.
// In this system, the line is of course stationary. The sphere spans
// a capsule, but instead we will "grow" the segment by the sphere radius
// and shrink the sphere to its center. The problem is now to detect
// the first time the moving center intersects the capsule formed by
// the line segment and sphere radius.
Capsule3<Real> capsule;
capsule.Segment = *mSegment;
capsule.Radius = mSphere->Radius;
Vector3<Real> relVelocity = velocity1 - velocity0;
Real relSpeed = relVelocity.Normalize();
Segment3<Real> path;
path.Extent = ((Real)0.5)*tmax*relSpeed;
path.Direction = relVelocity; // unit-length vector
path.Center = mSphere->Center + path.Extent*path.Direction;
IntrSegment3Capsule3<Real> intr(path, capsule);
if (!intr.Find())
{
mIntersectionType = IT_EMPTY;
return false;
}
// We now know the sphere will intersect the segment. This can happen
// either at a segment end point or at a segment interior point. We
// need to determine which.
mContactTime = (intr.GetParameter(0) + path.Extent)/relSpeed;
mQuantity = 1;
mIntersectionType = IT_POINT;
Vector3<Real> MCenter = mSphere->Center + mContactTime*velocity1;
Vector3<Real> MOrigin = mSegment->Center + mContactTime*velocity0;
Real origin = mSegment->Direction.Dot(MOrigin);
Real negEnd = origin - mSegment->Extent;
Real posEnd = origin + mSegment->Extent;
Real center = mSegment->Direction.Dot(MCenter);
if (center < negEnd)
{
// Intersection at segment end point P-e*D.
mPoint[0] = MOrigin - mSegment->Extent*mSegment->Direction;
}
else if (center > posEnd)
{
// Intersection at segment end point P+e*D.
mPoint[0] = MOrigin + mSegment->Extent*mSegment->Direction;
}
else
{
// Intersection with interior point on edge. Use the projection
// along direction axis to find which point that is.
mPoint[0] = MOrigin + (center - origin)*mSegment->Direction;
}
return true;
}
//----------------------------------------------------------------------------
template <typename Real>
int IntrSegment3Sphere3<Real>::GetQuantity () const
{
return mQuantity;
}
//----------------------------------------------------------------------------
template <typename Real>
const Vector3<Real>& IntrSegment3Sphere3<Real>::GetPoint (int i) const
{
return mPoint[i];
}
//----------------------------------------------------------------------------
template <typename Real>
Real IntrSegment3Sphere3<Real>::GetSegmentParameter (int i) const
{
return mSegmentParameter[i];
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class IntrSegment3Sphere3<float>;
template WM5_MATHEMATICS_ITEM
class IntrSegment3Sphere3<double>;
//----------------------------------------------------------------------------
}
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