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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 "Wm5ContCapsule3.h"
#include "Wm5ApprLineFit3.h"
#include "Wm5DistPoint3Line3.h"
#include "Wm5DistPoint3Segment3.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Capsule3<Real> ContCapsule (int numPoints, const Vector3<Real>* points)
{
Line3<Real> line = OrthogonalLineFit3<Real>(numPoints, points);
Real maxRadiusSqr = (Real)0;
int i;
for (i = 0; i < numPoints; ++i)
{
Real rSqr = DistPoint3Line3<Real>(points[i], line).GetSquared();
if (rSqr > maxRadiusSqr)
{
maxRadiusSqr = rSqr;
}
}
Vector3<Real> U, V, W = line.Direction;
Vector3<Real>::GenerateComplementBasis(U, V, W);
Real minValue = Math<Real>::MAX_REAL;
Real maxValue = -Math<Real>::MAX_REAL;
for (i = 0; i < numPoints; ++i)
{
Vector3<Real> diff = points[i] - line.Origin;
Real uDotDiff = U.Dot(diff);
Real vDotDiff = V.Dot(diff);
Real wDotDiff = W.Dot(diff);
Real discr = maxRadiusSqr - (uDotDiff*uDotDiff + vDotDiff*vDotDiff);
Real radical = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
Real test = wDotDiff + radical;
if (test < minValue)
{
minValue = test;
}
test = wDotDiff - radical;
if (test > maxValue)
{
maxValue = test;
}
}
Capsule3<Real> capsule;
capsule.Radius = Math<Real>::Sqrt(maxRadiusSqr);
capsule.Segment.Center = line.Origin +
(((Real)0.5)*(minValue + maxValue))*line.Direction;
capsule.Segment.Direction = line.Direction;
if (maxValue > minValue)
{
// Container is a capsule.
capsule.Segment.Extent = ((Real)0.5)*(maxValue - minValue);
}
else
{
// Container is a sphere.
capsule.Segment.Extent = (Real)0;
}
capsule.Segment.ComputeEndPoints();
return capsule;
}
//----------------------------------------------------------------------------
template <typename Real>
bool InCapsule (const Vector3<Real>& point, const Capsule3<Real>& capsule)
{
Real distance = DistPoint3Segment3<Real>(point, capsule.Segment).Get();
return distance <= capsule.Radius;
}
//----------------------------------------------------------------------------
template <typename Real>
bool InCapsule (const Sphere3<Real>& sphere, const Capsule3<Real>& capsule)
{
Real rDiff = capsule.Radius - sphere.Radius;
if (rDiff >= (Real)0)
{
Real distance = DistPoint3Segment3<Real>(sphere.Center,
capsule.Segment).Get();
return distance <= rDiff;
}
return false;
}
//----------------------------------------------------------------------------
template <typename Real>
bool InCapsule (const Capsule3<Real>& testCapsule,
const Capsule3<Real>& capsule)
{
Sphere3<Real> spherePosEnd(testCapsule.Segment.P1, testCapsule.Radius);
Sphere3<Real> sphereNegEnd(testCapsule.Segment.P0, testCapsule.Radius);
return InCapsule<Real>(spherePosEnd, capsule)
&& InCapsule<Real>(sphereNegEnd, capsule);
}
//----------------------------------------------------------------------------
template <typename Real>
Capsule3<Real> MergeCapsules (const Capsule3<Real>& capsule0,
const Capsule3<Real>& capsule1)
{
if (InCapsule<Real>(capsule0, capsule1))
{
return capsule1;
}
if (InCapsule<Real>(capsule1, capsule0))
{
return capsule0;
}
const Vector3<Real>& P0 = capsule0.Segment.Center;
const Vector3<Real>& P1 = capsule1.Segment.Center;
const Vector3<Real>& D0 = capsule0.Segment.Direction;
const Vector3<Real>& D1 = capsule1.Segment.Direction;
// Axis of final capsule.
Line3<Real> line;
// Axis center is average of input axis centers.
line.Origin = ((Real)0.5)*(P0 + P1);
// Axis unit direction is average of input axis unit directions.
if (D0.Dot(D1) >= (Real)0)
{
line.Direction = D0 + D1;
}
else
{
line.Direction = D0 - D1;
}
line.Direction.Normalize();
// Cylinder with axis 'line' must contain the spheres centered at the
// endpoints of the input capsules.
Vector3<Real> posEnd0 = capsule0.Segment.P1;
Real radius = DistPoint3Line3<Real>(posEnd0, line).Get() +
capsule0.Radius;
Vector3<Real> negEnd0 = capsule0.Segment.P0;
Real tmp = DistPoint3Line3<Real>(negEnd0, line).Get() + capsule0.Radius;
if (tmp > radius)
{
radius = tmp;
}
Vector3<Real> posEnd1 = capsule1.Segment.P1;
tmp = DistPoint3Line3<Real>(posEnd1, line).Get() + capsule1.Radius;
if (tmp > radius)
{
radius = tmp;
}
Vector3<Real> negEnd1 = capsule1.Segment.P0;
tmp = DistPoint3Line3<Real>(negEnd1, line).Get() + capsule1.Radius;
if (tmp > radius)
{
radius = tmp;
}
// Process sphere <posEnd0,r0>.
Real rDiff = radius - capsule0.Radius;
Real rDiffSqr = rDiff*rDiff;
Vector3<Real> diff = line.Origin - posEnd0;
Real k0 = diff.SquaredLength() - rDiffSqr;
Real k1 = diff.Dot(line.Direction);
Real discr = k1*k1 - k0; // assert: k1*k1-k0 >= 0
Real root = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
Real tPos = -k1 - root;
Real tNeg = -k1 + root;
// Process sphere <negEnd0,r0>.
diff = line.Origin - negEnd0;
k0 = diff.SquaredLength() - rDiffSqr;
k1 = diff.Dot(line.Direction);
discr = k1*k1 - k0; // assert: k1*k1-k0 >= 0
root = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
tmp = -k1 - root;
if (tmp > tPos)
{
tPos = tmp;
}
tmp = -k1 + root;
if (tmp < tNeg)
{
tNeg = tmp;
}
// Process sphere <posEnd1,r1>.
rDiff = radius - capsule1.Radius;
rDiffSqr = rDiff*rDiff;
diff = line.Origin - posEnd1;
k0 = diff.SquaredLength() - rDiffSqr;
k1 = diff.Dot(line.Direction);
discr = k1*k1 - k0; // assert: k1*k1-k0 >= 0
root = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
tmp = -k1 - root;
if (tmp > tPos)
{
tPos = tmp;
}
tmp = -k1 + root;
if (tmp < tNeg)
{
tNeg = tmp;
}
// Process sphere <negEnd1,r1>.
diff = line.Origin - negEnd1;
k0 = diff.SquaredLength() - rDiffSqr;
k1 = diff.Dot(line.Direction);
discr = k1*k1 - k0; // assert: K1*K1-K0 >= 0
root = Math<Real>::Sqrt(Math<Real>::FAbs(discr));
tmp = -k1 - root;
if (tmp > tPos)
{
tPos = tmp;
}
tmp = -k1 + root;
if (tmp < tNeg)
{
tNeg = tmp;
}
Capsule3<Real> capsule;
capsule.Radius = radius;
capsule.Segment.Center = line.Origin +
((Real)0.5)*(tPos + tNeg)*line.Direction;
capsule.Segment.Direction = line.Direction;
capsule.Segment.ComputeEndPoints();
if (tPos > tNeg)
{
// Container is a capsule.
capsule.Segment.Extent = ((Real)0.5)*(tPos - tNeg);
}
else
{
// Container is a sphere.
capsule.Segment.Extent = (Real)0;
}
return capsule;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Capsule3<float> ContCapsule<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
bool InCapsule<float> (const Vector3<float>&, const Capsule3<float>&);
template WM5_MATHEMATICS_ITEM
bool InCapsule<float> (const Sphere3<float>&, const Capsule3<float>&);
template WM5_MATHEMATICS_ITEM
bool InCapsule<float> (const Capsule3<float>&, const Capsule3<float>&);
template WM5_MATHEMATICS_ITEM
Capsule3<float> MergeCapsules<float> (const Capsule3<float>&,
const Capsule3<float>&);
template WM5_MATHEMATICS_ITEM
Capsule3<double> ContCapsule<double> (int, const Vector3<double>*);
template WM5_MATHEMATICS_ITEM
bool InCapsule<double> (const Vector3<double>&, const Capsule3<double>&);
template WM5_MATHEMATICS_ITEM
bool InCapsule<double> (const Sphere3<double>&, const Capsule3<double>&);
template WM5_MATHEMATICS_ITEM
bool InCapsule<double> (const Capsule3<double>&, const Capsule3<double>&);
template WM5_MATHEMATICS_ITEM
Capsule3<double> MergeCapsules<double> (const Capsule3<double>&,
const Capsule3<double>&);
//----------------------------------------------------------------------------
}
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