Sfb 288 Differential Geometry and Quantum Physics

Hierarchical Triangulations
Multi-Parameter Families of Geometries

Hierarchical Triangulations are an efficient data structure for numerical algorithms where an adaptive change of discretization is necessary. A special application of hierarchies to time-dependent geometries allows to define interpolation between geometries with varying discretization in time-direction (1-dimensional Interpolation). These interpolation techniques easily generalize to multi-parameter problems (n-dimensional Interpolation), e.g. the study of surface families depending on 1, 2, 3 or more parameters. Here all keyframes may be diffently refined and still allow interpolation.

Author: Axel Friedrich, Konrad Polthier