Development and implementation of numerical algorithm for variational methods and generalized gradient flows for geometric evolution problems of higher order for surface processing in computer graphics

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The main goal of the research project in the research group of Prof. Mathieu Desbrun at the California Institute of Technology (Caltech) in Pasadena, USA, will be the development and implementation of numerical algorithms for evolution problems of the anisotropic Willmore in the context of anisotropic surface fairing and surface restoration. The application includes blending problems, where different surface patches are connected by other surface patches defined as minimizers of the anisotropic Willmore functional. Besides blending problems surface restorations problems are considered. There, a destroyed region of a surface is replaced by a surface patch that restores the surface in a suitable way. In particular one ask for C1-condition at the patch boundary. Since the L2-gradient flow of the anisotropic Willmore functional corresponds to a highly non linear parabolic partial differential equation, this functional is well suited for this kind of restoration problems. Choosing a different metric, e.g. the H^1-metric instead of the L2-metric, generalized gradient flows are considered.