Finite Element Methods for Geometric Modeling and Processing Using General Fourth Order Geometric Flows

A variational formulation of a general form fourth order geometric partial differential equation is derived, and based on which a mixed finite element method is developed. Several surface modeling problems, including surface blending, hole filling and surface mesh refinement with the G continuity, are taken into account. The used geometric partial differential equation is universal, containing several well-known geometric partial differential equations as its special cases. The proposed method is general which can be used to construct surfaces for geometric design as well as simulate the behaviors of various geometric PDEs. Experimental results show that it is simple, efficient and gives very desirable results.