Interpolation of triangle hierarchies

We consider interpolation between keyframe hierarchies. We impose a set of weak constraints that allows smooth interpolation between two keyframe hierarchies in an animation or, more generally, allows the interpolation in an n-parameter family of hierarchies. We use hierarchical triangulations obtained by the Rivara element bisection algorithm (M. Rivara, 1984) and impose a weak compatibility constraint on the set of root elements of all keyframe hierarchies. We show that the introduced constraints are rather weak. The strength of our approach is that the interpolation works in the class of conforming triangulations and simplifies the task of finding the intermediate hierarchy, which is the union of the two (or more) keyframe hierarchies involved in the interpolation process. This allows for an efficient generation of the intermediate connectivity and additionally ensures that the intermediate hierarchy is again a conforming hierarchy satisfying the same constraints.