transformations

panda3d

# TRANSFORMATIONS¶

BSD licensed set of utilities in python and C

## INSTALLATION¶

Prior to compilation of the C extension the python import gives warning, but functionality is still provided by the pure python implementation:

In [18]: from env.graphics.transformations.transformations import identity_matrix
/usr/local/env/chroma_env/lib/python2.7/site-packages/env/graphics/transformations/transformations.py:1888: UserWarning: failed to import module _transformations
warnings.warn("failed to import module %s" % name)

## Arcball¶

Imagine a virtual ball centered just behind the screen with defined pixel center and radius. Points on the screen can easily be mapped to a position on the virtual ball

Arcball holds a quaternion (representing an orientation) which is updated on the basis of mouse drags as if they manipulate the virtual ball.

In [38]: arcball_map_to_sphere( point=(0,100), center=(200,100), radius=100 )
Out[38]: array([-1.,  0.,  0.])

In [39]: arcball_map_to_sphere( point=(200,200), center=(200,100), radius=100 )
Out[39]: array([ 0., -1.,  0.])

In [40]: arcball_map_to_sphere( point=(200,-200), center=(200,100), radius=100 )
Out[40]: array([ 0.,  1.,  0.])

In [41]: arcball_map_to_sphere( point=(200,100), center=(200,100), radius=100 )
Out[41]: array([ 0.,  0.,  1.])

In [42]: arcball_map_to_sphere( point=(250,100), center=(200,100), radius=100 )
Out[42]: array([ 0.5      ,  0.       ,  0.8660254])

### Axis angle rep¶

Chroma performs rotations using axis and angle, how to get that from the arcball quaternion ?

The below looks invertible:

1231 def quaternion_about_axis(angle, axis):
1232     """Return quaternion for rotation about axis.
1233
1234     >>> q = quaternion_about_axis(0.123, [1, 0, 0])
1235     >>> numpy.allclose(q, [0.99810947, 0.06146124, 0, 0])
1236     True
1237
1238     """
1239     q = numpy.array([0.0, axis[0], axis[1], axis[2]])
1240     qlen = vector_norm(q)
1241     if qlen > _EPS:
1242         q *= math.sin(angle/2.0) / qlen
1243     q[0] = math.cos(angle/2.0)
1244     return q