//----------------------------------------------------------------------------
bool Mgc::FindIntersection (const Plane& rkPlane0, const Plane& rkPlane1,
Line3& rkLine)
{
// If Cross(N0,N1) is zero, then either planes are parallel and separated
// or the same plane. In both cases, 'false' is returned. Otherwise,
// the intersection line is
//
// L(t) = t*Cross(N0,N1) + c0*N0 + c1*N1
//
// for some coefficients c0 and c1 and for t any real number (the line
// parameter). Taking dot products with the normals,
//
// d0 = Dot(N0,L) = c0*Dot(N0,N0) + c1*Dot(N0,N1)
// d1 = Dot(N1,L) = c0*Dot(N0,N1) + c1*Dot(N1,N1)
//
// which are two equations in two unknowns. The solution is
//
// c0 = (Dot(N1,N1)*d0 - Dot(N0,N1)*d1)/det
// c1 = (Dot(N0,N0)*d1 - Dot(N0,N1)*d0)/det
//
// where det = Dot(N0,N0)*Dot(N1,N1)-Dot(N0,N1)^2.
Real fN00 = rkPlane0.Normal().SquaredLength();
Real fN01 = rkPlane0.Normal().Dot(rkPlane1.Normal());
Real fN11 = rkPlane1.Normal().SquaredLength();
Real fDet = fN00*fN11 - fN01*fN01;
if ( Math::FAbs(fDet) < gs_fEpsilon )
return false;
Real fInvDet = 1.0f/fDet;
Real fC0 = (fN11*rkPlane0.Constant() - fN01*rkPlane1.Constant())*fInvDet;
Real fC1 = (fN00*rkPlane1.Constant() - fN01*rkPlane0.Constant())*fInvDet;
rkLine.Direction() = rkPlane0.Normal().Cross(rkPlane1.Normal());
rkLine.Origin() = fC0*rkPlane0.Normal() + fC1*rkPlane1.Normal();
return true;
}
//----------------------------------------------------------------------------
bool Mgc::Culled (const Plane& rkPlane, const Sphere& rkSphere,
bool bUnitNormal)
{
Vector3 kNormal = rkPlane.Normal();
Real fConstant = rkPlane.Constant();
if ( !bUnitNormal )
{
Real fLength = kNormal.Unitize();
fConstant /= fLength;
}
Real fTmp = kNormal.Dot(rkSphere.Center()) - fConstant;
return fTmp <= -rkSphere.Radius();
}
//----------------------------------------------------------------------------
bool Mgc::TestIntersection (const Plane& rkPlane, const Sphere& rkSphere,
bool bUnitNormal)
{
Vector3 kNormal = rkPlane.Normal();
Real fConstant = rkPlane.Constant();
if ( !bUnitNormal )
{
Real fLength = kNormal.Unitize();
fConstant /= fLength;
}
Real fPseudoDistance = kNormal.Dot(rkSphere.Center()) - fConstant;
return Math::FAbs(fPseudoDistance) <= rkSphere.Radius();
}
//----------------------------------------------------------------------------
bool Mgc::Culled (const Plane& rkPlane, const Ellipsoid& rkEllipsoid,
bool bUnitNormal)
{
Vector3 kNormal = rkPlane.Normal();
Real fConstant = rkPlane.Constant();
if ( !bUnitNormal )
{
Real fLength = kNormal.Unitize();
fConstant /= fLength;
}
Real fDiscr = kNormal.Dot(rkEllipsoid.InverseA()*kNormal);
Real fRoot = Math::Sqrt(Math::FAbs(fDiscr));
Real fSDist = kNormal.Dot(rkEllipsoid.Center()) - fConstant;
return fSDist <= -fRoot;
}
//----------------------------------------------------------------------------
bool Mgc::Culled (const Plane& rkPlane, const Lozenge& rkLozenge,
bool bUnitNormal)
{
Vector3 kNormal = rkPlane.Normal();
Real fConstant = rkPlane.Constant();
if ( !bUnitNormal )
{
Real fLength = kNormal.Unitize();
fConstant /= fLength;
}
Real fTmp00 = kNormal.Dot(rkLozenge.Origin()) - fConstant;
if ( fTmp00 < 0.0f )
{
Real fDotNE0 = kNormal.Dot(rkLozenge.Edge0());
Real fTmp10 = fTmp00 + fDotNE0;
if ( fTmp10 < 0.0f )
{
Real fDotNE1 = kNormal.Dot(rkLozenge.Edge1());
Real fTmp01 = fTmp00 + fDotNE1;
if ( fTmp01 < 0.0f )
{
Real fTmp11 = fTmp10 + fDotNE1;
if ( fTmp11 < 0.0f )
{
// all four lozenge corners on negative side of plane
if ( fTmp00 <= fTmp10 )
{
if ( fTmp00 <= fTmp01 )
return fTmp00 <= -rkLozenge.Radius();
else
return fTmp01 <= -rkLozenge.Radius();
}
else
{
if ( fTmp10 <= fTmp11 )
return fTmp10 <= -rkLozenge.Radius();
else
return fTmp11 <= -rkLozenge.Radius();
}
}
}
}
}
return false;
}
//----------------------------------------------------------------------------
bool Mgc::TestIntersection (const Plane& rkPlane, const Lozenge& rkLozenge,
bool bUnitNormal)
{
Vector3 kNormal = rkPlane.Normal();
Real fConstant = rkPlane.Constant();
if ( !bUnitNormal )
{
Real fLength = kNormal.Unitize();
fConstant /= fLength;
}
Vector3 kC10 = rkLozenge.Origin() + rkLozenge.Edge0();
Vector3 kC01 = rkLozenge.Origin() + rkLozenge.Edge1();
Vector3 kC11 = kC10 + rkLozenge.Edge1();
Real fTmp00 = kNormal.Dot(rkLozenge.Origin()) - fConstant;
Real fTmp10 = kNormal.Dot(kC10) - fConstant;
if ( fTmp00*fTmp10 <= 0.0f )
{
// two lozenge ends on opposite sides of the plane
return true;
}
Real fTmp01 = kNormal.Dot(kC01) - fConstant;
if ( fTmp00*fTmp01 <= 0.0f )
{
// two lozenge ends on opposite sides of the plane
return true;
}
Real fTmp11 = kNormal.Dot(kC11) - fConstant;
if ( fTmp10*fTmp11 <= 0.0f )
{
// two lozenge ends on opposite sides of the plane
return true;
}
return Math::FAbs(fTmp00) <= rkLozenge.Radius()
|| Math::FAbs(fTmp10) <= rkLozenge.Radius()
|| Math::FAbs(fTmp01) <= rkLozenge.Radius()
|| Math::FAbs(fTmp11) <= rkLozenge.Radius();
}
//----------------------------------------------------------------------------
void Mgc::PerspProjEllipsoid (const GeneralEllipsoid& rkEllipsoid,
const Vector3& rkEye, const Plane& rkPlane, GeneralEllipse& rkEllipse)
{
// compute matrix M
Vector3 kAE = rkEllipsoid.m_kA*rkEye;
Real fEAE = rkEye.Dot(kAE);
Real fBE = rkEllipsoid.m_kB.Dot(rkEye);
Real fTmp = 4.0f*(fEAE + fBE + rkEllipsoid.m_fC);
Vector3 kTmp = rkEllipsoid.m_kB + 2.0f*kAE;
Matrix3 kMat;
kMat[0][0] = kTmp.x*kTmp.x - fTmp*rkEllipsoid.m_kA[0][0];
kMat[0][1] = kTmp.x*kTmp.y - fTmp*rkEllipsoid.m_kA[0][1];
kMat[0][2] = kTmp.x*kTmp.z - fTmp*rkEllipsoid.m_kA[0][2];
kMat[1][1] = kTmp.y*kTmp.y - fTmp*rkEllipsoid.m_kA[1][1];
kMat[1][2] = kTmp.y*kTmp.z - fTmp*rkEllipsoid.m_kA[1][2];
kMat[2][2] = kTmp.z*kTmp.z - fTmp*rkEllipsoid.m_kA[2][2];
kMat[1][0] = kMat[0][1];
kMat[2][0] = kMat[0][2];
kMat[2][1] = kMat[1][2];
// Normalize N and construct U and V so that {U,V,N} forms a
// right-handed, orthonormal basis.
Vector3 kU, kV, kN = rkPlane.Normal();
Vector3::GenerateOrthonormalBasis(kU,kV,kN,false);
// compute coefficients for projected ellipse
Vector3 kMU = kMat*kU, kMV = kMat*kV, kMN = kMat*kN;
Real fDmNE = rkPlane.Constant() - kN.Dot(rkEye);
rkEllipse.m_kA[0][0] = kU.Dot(kMU);
rkEllipse.m_kA[0][1] = kU.Dot(kMV);
rkEllipse.m_kA[1][1] = kV.Dot(kMV);
rkEllipse.m_kA[1][0] = rkEllipse.m_kA[0][1];
rkEllipse.m_kB.x = 2.0f*fDmNE*(kU.Dot(kMN));
rkEllipse.m_kB.y = 2.0f*fDmNE*(kV.Dot(kMN));
rkEllipse.m_fC = fDmNE*fDmNE*(kN.Dot(kMN));
}