Re: [Algorithms] Direction+Up vector to Axis/angle

[<ro...@do...>]

Max Gilead  wrote:

>Joe Ante wrote:
>
>> > Hello!
>> >
>> > Question: how to convert direction and up vectors to axis/angle
>> > rotation?
>> http://www.magic-software.com/Source/MgcCore3D/MgcMatrix3.cpp
>
>Excuse me maybe stupid question but what should I use from this class?
>It doesn't seem to deal with Axis/Angles except for set/get methods. My
>conversion method (matrix -> a&a) I have included seems to work OK.
>

If you indeed have matrix-> axis angle, then your problem is
essentially solved, because direction and up vector give you directly
two rows (or columns, depending on your matrix convention) of the
rotation matrix, the third row (or column) being their cross product. 

The fact that direction and up vector give you two rows of the matrix
is an instance of what is THE most important defining property of
transformation matrices, which you would learn in any decent course in
linear algebra.

BTW, the derivation of matrix -> axis angle is a bit more
complicated--it is essentially an eigenvalue problem, from a little
more advanced part of the linear algebra course.

>Today I spent another 5 hours trying to figure out how to convert
>this... damn direction/up vector to axis/angle. Help!! Maybe some code
>sample? I'm stuck.
>
>Thanks
>Max