// Make a rotation Quat which will rotate vec1 to vec2
// Generally take adot product to get the angle between these
// and then use a cross product to get the rotation axis
// Watch out for the two special cases of when the vectors
// are co-incident or opposite in direction.
void ofQuaternion::makeRotate_original( const ofVec3f& from, const ofVec3f& to ) {
const float epsilon = 0.0000001f;
float length1 = from.length();
float length2 = to.length();
// dot product vec1*vec2
float cosangle = from.dot(to) / (length1 * length2);
if ( fabs(cosangle - 1) < epsilon ) {
//osg::notify(osg::INFO)<<"*** Quat::makeRotate(from,to) with near co-linear vectors, epsilon= "<<fabs(cosangle-1)<<std::endl;
// cosangle is close to 1, so the vectors are close to being coincident
// Need to generate an angle of zero with any vector we like
// We'll choose (1,0,0)
makeRotate( 0.0, 0.0, 0.0, 1.0 );
} else
if ( fabs(cosangle + 1.0) < epsilon ) {
// vectors are close to being opposite, so will need to find a
// vector orthongonal to from to rotate about.
ofVec3f tmp;
if (fabs(from.x) < fabs(from.y))
if (fabs(from.x) < fabs(from.z)) tmp.set(1.0, 0.0, 0.0); // use x axis.
else tmp.set(0.0, 0.0, 1.0);
else if (fabs(from.y) < fabs(from.z)) tmp.set(0.0, 1.0, 0.0);
else tmp.set(0.0, 0.0, 1.0);
ofVec3f fromd(from.x, from.y, from.z);
// find orthogonal axis.
ofVec3f axis(fromd.getCrossed(tmp));
axis.normalize();
_v[0] = axis[0]; // sin of half angle of PI is 1.0.
_v[1] = axis[1]; // sin of half angle of PI is 1.0.
_v[2] = axis[2]; // sin of half angle of PI is 1.0.
_v[3] = 0; // cos of half angle of PI is zero.
} else {
// This is the usual situation - take a cross-product of vec1 and vec2
// and that is the axis around which to rotate.
ofVec3f axis(from.getCrossed(to));
float angle = acos( cosangle );
makeRotate( angle, axis );
}
}
void findCoordinateSystem(vector<ofVec3f> &input,ofVec3f &origin,ofVec3f &xVec,ofVec3f &yVec) {
origin = input[0];
xVec = (input[1]-input[0]).getNormalized();
float proj = xVec.dot(input[3]-input[0]);
yVec = (input[3]-(input[0]+xVec*proj)).getNormalized();
}