Non orthonal to Orthogonal coordinates system conversion in Python
<p>I have a vector in a non-orthogonal coordinate system spanned by axes a,b,c and their Euler angles alpha(between b&amp;c),beta(between c&amp;a),gamma(between a&amp;b). I want to convert this vector to an orthogonal coordinate system spanned by x,y,z. I assume that axes a and x coincide while conversion.
I can do it mathematically by solving equations for coordinates, but I was wondering if there exists any library in Python to do it efficiently.
(I found a library  - transforms3d. But I couldn't understand its documentation well.)</p>

<p>The best coordinate system transformations function I've knowen in python is this one: <a href="http://www.lfd.uci.edu/~gohlke/code/transformations.py.html" rel="nofollow">http://www.lfd.uci.edu/~gohlke/code/transformations.py.html</a></p>

<p>Take a look at the functions: euler_matrix and euler_from_matrix.
It comes with a self explained comments in the code.</p>

<p>Other libraries that might be relevant is:</p>

<ol>
<li>Shapely - <a href="http://toblerity.org/shapely/manual.html" rel="nofollow">http://toblerity.org/shapely/manual.html</a></li>
<li>Blender - <a href="https://www.blender.org/api/blender_python_api_2_62_0/mathutils.html" rel="nofollow">https://www.blender.org/api/blender_python_api_2_62_0/mathutils.html</a></li>
</ol>

python computational-geometry coordinate-systems coordinate-transformation