Here is one case study:
An impressive animation of the Hopf fibration created by Niles Johnson using only open-source tools, available for all platforms: The Python-based mathematics program Sage was used for determining the fiber parametrizations and keeping track of all the animation data. Sage provides an interface to the ray tracing system Tachyon, which produced the individual frames. These were then stitched into an animation using FFmpeg.FFmpeg.