Transform Subtract(const Transform one, const Transform two){
assert(one.parent == two.parent);
return Transform_Create(GLKVector3Subtract(one.position, two.position),
GLKQuaternionSubtract(one.orientation, two.orientation),
// GLKVector4Subtract(one.rotation, two.rotation),
GLKVector3Subtract(one.scale, two.scale),
0);
}
bool IntersectWithEllipsoid( GLKVector3 start, GLKVector3 end, GLKVector3* hit )
{
// transform endpoints into unit sphere basis
start = GLKMatrix4MultiplyAndProjectVector3(kEllipsoidToUnitSphere, start);
end = GLKMatrix4MultiplyAndProjectVector3(kEllipsoidToUnitSphere, end);
// use unit sphere
const double r = 1.;
GLKVector3 diff = GLKVector3Subtract(end, start);
// calculate quadratic components
double a = GLKVector3DotProduct( diff, diff );
double b = GLKVector3DotProduct( GLKVector3MultiplyScalar(diff, 2.0), start );
double c = GLKVector3DotProduct( start, start ) - ( r * r );
// calculate discriminant
double disc = ( b * b ) - ( 4.0 * a * c );
// consider intersection for positive disc only (discard edge cases)
if ( disc > 0.0 ) {
// calculate two solutions
double t1 = ( -b - sqrt(disc) ) / ( 2.0 * a );
double t2 = ( -b + sqrt(disc) ) / ( 2.0 * a );
// calculate points of intersection and normals
if ( t1 > 0.0 && t1 < 1.0 ) {
if ( hit ) {
*hit = GLKVector3Add( start, GLKVector3MultiplyScalar(diff, t1));
*hit = GLKMatrix4MultiplyAndProjectVector3(kUnitSphereToEllipsoid, *hit);
}
return true;
}
if ( t2 > 0.0 && t2 < 1.0 ) {
if ( hit ) {
*hit = GLKVector3Add( start, GLKVector3MultiplyScalar(diff, t2));
*hit = GLKMatrix4MultiplyAndProjectVector3(kUnitSphereToEllipsoid, *hit);
}
return true;
}
}
return false;
}