G 1 Spline Surface Construction By Geometric Partial Differential Equations Using Mixed Finite Element Methods ∗

Variational formulations of three fourth order geometric partial differential equations are derived, and based on which mixed finite element methods are presented for constructing G smooth B-spline surfaces. Solutions to several surface modeling problems, including surface fairing, free-form surface design, surface blending and hole filling with G continuity, are handled by this approach. Experimental results show that our method is efficient and gives the desired results. Convergence properties of the proposed method are additionally investigated, which justify that the method is both effective and mathematically correct.