Quaternion2 Quaternion2::DecomposeRotation2(const VectorR3 vB) const {
//we need to compute v in A's coordinates
VectorR3 vA = this->rotate(vB);
vA.Normalize();
double temp = 0;
//compute the rotation that aligns the vector v in the two coordinate frames (A and T)
VectorR3 rotAxis = vA * vB;
rotAxis.Normalize();
double rotAngle = -safeACOS(vA.Dot(vB));
Quaternion2 TqA = getRotationQuaternion2(rotAngle, rotAxis*(-1));
return TqA * (*this);
}
// Returns a righthanded orthonormal basis to complement vector u
void GetOrtho( const VectorR3& u, VectorR3& v, VectorR3& w)
{
if ( u.x > 0.5 || u.x<-0.5 || u.y > 0.5 || u.y<-0.5 ) {
v.Set ( u.y, -u.x, 0.0 );
}
else {
v.Set ( 0.0, u.z, -u.y);
}
v.Normalize();
w = u;
w *= v;
w.Normalize();
// w.NormalizeFast();
return;
}
// Returns a vector v orthonormal to unit vector u
void GetOrtho( const VectorR3& u, VectorR3& v )
{
if ( u.x > 0.5 || u.x<-0.5 || u.y > 0.5 || u.y<-0.5 ) {
v.Set ( u.y, -u.x, 0.0 );
}
else {
v.Set ( 0.0, u.z, -u.y);
}
v.Normalize();
return;
}
// Returns an intersection if found with distance maxDistance
// viewDir must be a unit vector.
// intersectDistance and visPoint are returned values.
bool ViewableEllipsoid::FindIntersectionNT (
const VectorR3& viewPos, const VectorR3& viewDir, double maxDistance,
double *intersectDistance, VisiblePoint& returnedPoint ) const
{
VectorR3 v = viewPos;
v -= Center;
double pdotuA = v^AxisA;
double pdotuB = v^AxisB;
double pdotuC = v^AxisC;
double udotuA = viewDir^AxisA;
double udotuB = viewDir^AxisB;
double udotuC = viewDir^AxisC;
double C = Square(pdotuA) + Square(pdotuB) + Square(pdotuC) - 1.0;
double B = ( pdotuA*udotuA + pdotuB*udotuB + pdotuC*udotuC );
if ( C>0.0 && B>=0.0 ) {
return false; // Pointing away from the ellipsoid
}
B += B; // Double B to get final factor of 2.
double A = Square(udotuA) + Square(udotuB) + Square(udotuC);
double alpha1, alpha2;
int numRoots = QuadraticSolveRealSafe( A, B, C, &alpha1, &alpha2 );
if ( numRoots==0 ) {
return false;
}
if ( alpha1>0.0 ) {
if ( alpha1>=maxDistance ) {
return false; // Too far away
}
// Found an intersection from outside.
returnedPoint.SetFrontFace();
returnedPoint.SetMaterial( *OuterMaterial );
*intersectDistance = alpha1;
}
else if ( numRoots==2 && alpha2>0.0 && alpha2<maxDistance ) {
// Found an intersection from inside.
returnedPoint.SetBackFace();
returnedPoint.SetMaterial( *InnerMaterial );
*intersectDistance = alpha2;
}
else {
return false; // Both intersections behind us (should never get here)
}
// Calculate intersection position
v=viewDir;
v *= (*intersectDistance);
v += viewPos;
returnedPoint.SetPosition( v ); // Intersection Position
v -= Center; // Now v is the relative position
double vdotuA = v^AxisA;
double vdotuB = v^AxisB;
double vdotuC = v^AxisC;
v = vdotuA*AxisA + vdotuB*AxisB + vdotuC*AxisC;
v.Normalize();
returnedPoint.SetNormal( v );
// Calculate u-v coordinates
ViewableSphere::CalcUV( vdotuB, vdotuC, vdotuA, uvProjectionType,
&returnedPoint.GetUV() );
returnedPoint.SetFaceNumber( 0 );
return true;
}
