Friday, March 21, 2014

[orbjdcyv] Rotating object

Create a animation of an object rotating such that widely spaced snapshots (in time) uniformly sample the entire space of orientations (views).

I think one way to do it is uniformly pick random orientations and travel the shortest path between them.

Orientation can be decomposed into a point on a sphere and a rotation around the viewing axis.

There remains a tricky question of what speed to travel along the geodesic path.  More likely to work is for the travel time between points to be constant.  I am less sure if constant speed works.

Avoid sudden changes in rotation direction by, instead of traveling on geodesics, constructing splines on the sphere.

Samuel R. Buss and Jay Fillmore. "Spherical Averages and Applications to Spherical Splines and Interpolation." ACM Transactions on Graphics 20 (2001) 95-126. http://math.ucsd.edu/~sbuss/ResearchWeb/spheremean/

However, we technically don't want splines merely on a sphere but this weirder manifold of all possible orientations.

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