[eigen] Quaternion toRotationMatrix

[Gabriel <gnuetzi@xxxxxxxxx>]

Hello,


I have the following suggestions for the function toRotationMatrix()   for the QuaternionBase class:

The function is shown here:

http://pastebin.com/QPRANVU6

The documentation says that this function is undefined if a non unit quaternion is used! This is absolutely correct!

The function so far implemented is equation 1.112 in http://snag.gy/J6rDH.jpg  ( tilde is the skew-symetric matrix of a vector  -> cross product)

If we want to use the Eigen function toRotationMatrix()   we need to normalize the quaternion beforehand which is expensive!

A better way is to use equation 1.110 directly in http://snag.gy/J6rDH.jpg, which directly normalizes the quaternion but only needs the square norm of the quaternion "s"
which is much cheaper. Equation 1.110 directly gives a proper rotation matrix! (orthogonal, and det(R)=1)

I would provide the following adaption:

template<bool isQuaternionNormalized = false>
QuaternionBase<...>::toRotationMatrix()

where

toRotationMatrix<true>       -> same function as already implemented (user should use this if quaternion is already normalized)

toRotationMatrix<false>      -> no normalized quaternion is given as argument, use an implementation which uses equation 1.110 in http://snag.gy/J6rDH.jpg

Maybe the default behavior should be "true" so there is no change to the interface for the user who used these functions....


BR Gabriel Nützi