Design of Loop’s Subdivision Surfaces by Fourth-Order Geometric PDEs with $$G^1$$ G 1 Boundary Conditions

Abstract

In this paper, we present a method for constructing Loop's subdivision surface patches with given $$G^1$$ G 1 boundary conditions and a given topology of control polygon, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a function space defined by the extended Loop's subdivision scheme. The method is flexible to the shape of the boundaries, and there is no limitation on the number of boundary curves and on the topology of the control polygon. Several properties for the basis functions of the finite element space are developed.