Maths - Conversion Quaternion to Matrix - Normalization

By: hamouras - hamouras
Quaternion to Matrix with normalization  
2006-08-24 18:10

Hi Matrin. 
 
In the quaternion to matrix page you mention that you need to normalize the quaternion before you convert it. However you can normalize the output matrix instead which is faster since you don't have to use an sqrt. 
 
Since the matrix is created by multiplying pairs of quaternion components (x*y, x*z, etc) you can normalize the matrix by dividing with the square length of the quaternion. Below i have the modified code. Also the same can be done for rotating a vector (since it actually uses the same matrix). 
 
 
public final void quatToMatrix(Quat4d q){ 
double sqw = q.w*q.w; 
double sqx = q.x*q.x; 
double sqy = q.y*q.y; 
double sqz = q.z*q.z; 
// get the invert square length 
double invs = 1 / (sqx + sqy + sqz + sqw); 
 
// rotation matrix is scaled by inverse square length 
m00 = ( sqx - sqy - sqz + sqw) * invs; 
m11 = (-sqx + sqy - sqz + sqw) * invs; 
m22 = (-sqx - sqy + sqz + sqw) * invs; 
 
double tmp1 = q.x*q.y; 
double tmp2 = q.z*q.w; 
m10 = 2.0 * (tmp1 + tmp2) * invs; 
m01 = 2.0 * (tmp1 - tmp2) * invs; 
 
tmp1 = q.x*q.z; 
tmp2 = q.y*q.w; 
m20 = 2.0 * (tmp1 - tmp2) * invs; 
m02 = 2.0 * (tmp1 + tmp2) * invs; 
tmp1 = q.y*q.z; 
tmp2 = q.x*q.w; 
m21 = 2.0 * (tmp1 + tmp2) * invs; 
m12 = 2.0 * (tmp1 - tmp2) * invs;  
}