The Morgan Kaufmann Series in Interactive 3D Technology: Visualizing Quaternions

Appendix G. Quaternion Path Optimization Using Surface Evolver

The Surface Evolver system (Brakke [22]) is a very sophisticated optimization package that has been in active use by the scientific and mathematics community for well over a decade and is still actively maintained by its developer, Ken Brakke, at Susquehanna University. The Surface Evolver can handle a number of issues specifically related to quaternion optimization. The symmetry group option

symmetry_group "central_symmetry"

identifies the quaternion q with –q if desired during the variation to prevent reflected double traversals (such as those depicted in Figure 22.5) from varying independently. The system also supports metrics such as the pull-back metric on the sphere

to compute distances ...