[vtkusers] colour mapping stress ellipsoids

[Mecit Yaman]

hi,

i am trying to visualize second order tensors using stress ellipsoids with a
different color mapping. the usual colouring is to map a scalar value, e.g.
components, effective stress, trace or other scalars on the surface. i want
to do a colouring where each point/polygon on the ellipsoid will be coloured
differently. the color scheme is defined as follows:

the color along direction n(i) of the ellipsoid is obtained from the angle
between the n(i), direction vector, and the stress vector along n(i). (the
stress vector along a direction can be obtained by multiplying the stress
tensor, T(ij) with the direction vector, n(i)).  Thus:

T(ij) 	tensor
n(i) 	direction vector

stress vector(i) = T(ij) . n(i)

angle between stress vector and direction vector

cos(angle) = stress vector (i) . n(i) / ( |stress vector(i)| | n(i)|)

how does one colour map these angles, which are different for every
direction on an ellipsoid? do I need to change stress ellipsoid into a
polygonal data type? how do I calculate and store the angles in VTK?

i am able to render the icons in Mathematica, and will be happy to share
information with anyone interested.

thanks,

M Yaman
University of Cape Town