// PreCalcInfo takes the vertex values and computes information to
// help with intersections with rays.
void ViewableTriangle::PreCalcInfo()
{
VectorR3 EdgeAB = VertexB - VertexA;
VectorR3 EdgeBC = VertexC - VertexB;
VectorR3 EdgeCA = VertexA - VertexC;
if ( (EdgeAB^EdgeBC) < (EdgeBC^EdgeCA) ) {
Normal = EdgeAB*EdgeBC;
}
else {
Normal = EdgeBC*EdgeCA;
}
double mag = Normal.Norm();
if ( mag>0.0 ) {
Normal /= mag; // Unit vector to triangle's plane
}
PlaneCoef = (Normal^VertexA); // Same coef for all three vertices.
double A = EdgeAB.NormSq();
double B = (EdgeAB^EdgeCA);
double C = EdgeCA.NormSq();
double Dinv = 1.0/(A*C-B*B);
A *= Dinv;
B *= Dinv;
C *= Dinv;
Ubeta = EdgeAB;
Ubeta *= C;
Ubeta.AddScaled( EdgeCA, -B );
Ugamma = EdgeCA;
Ugamma *= -A;
Ugamma.AddScaled( EdgeAB, B );
}
RotationMapR3 VrRotateAlign( const VectorR3& fromVec, const VectorR3& toVec)
{
VectorR3 crossVec = fromVec;
crossVec *= toVec;
double sinetheta = crossVec.Norm(); // Not yet normalized!
if ( sinetheta < 1.0e-40 ) {
return ( RotationMapR3(
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0) );
}
crossVec /= sinetheta; // Normalize the vector
double scale = 1.0/sqrt(fromVec.NormSq()*toVec.NormSq());
sinetheta *= scale;
double cosinetheta = (fromVec^toVec)*scale;
return ( VrRotate( cosinetheta, sinetheta, crossVec) );
}
bool ViewableSphere::CalcPartials( const VisiblePoint& visPoint,
VectorR3& retPartialU, VectorR3& retPartialV ) const
{
retPartialV = visPoint.GetPosition();
retPartialV -= Center;
retPartialU = retPartialV;
retPartialU *= AxisC; // Magnitude = R sin(phi).
retPartialU *= -PI2; // Adjust for [0,1] domain instead of [-pi,pi]
retPartialV *= retPartialU; // Pointing in right direction, magnitude 2 pi R^2 sin(phi)
// Sign and magnitude adjusted below.
double badMagSq = retPartialV.NormSq();
double h;
switch ( uvProjectionType ) {
case 0: // Spherical projection
h = sqrt(badMagSq);
if ( h==0.0 ) {
retPartialV = AxisB;
return false;
}
retPartialV *= (PI*Radius/h); // Convert to domain [0,1] instead of [-pi/2,pi/2].
// Compensate for sign and R^2 magnitude.
break;
case 1:
h = 2.0*(visPoint.GetV()-0.5); // In range [-1,1]
h = sqrt(badMagSq*(1.0 - h*h)); // Derivative of arcsin(h) = 1/sqrt(1-h^2)
if ( h==0 ) {
retPartialV = AxisB;
return false;
}
retPartialV *= PI*Radius/h; // Adjust sign and magnitude
break;
}
return true;
}
