Variational surface design under normal field guidance

•Two extended energy functionals are proposed for variational surface modeling.•The guiding normal field can be used to control the shapes of the variational surfaces efficiently.•The proposed technique can be used for various modeling purposes like editing, hole filling or transition surface design.

This paper proposes a novel method for shape design of a Bézier surface with given boundary curves. The surface is defined as the minimizer of an extended membrane functional or an extended thin plate functional under the guidance of a specified normal field together with an initial prescribed surface. For given boundary curves and the guiding normal field, the free coefficients of a Bézier surface are obtained by solving a linear system. Unlike previous PDE based surface modeling techniques which construct surfaces just from boundaries, our proposed method can be used to generate smooth and fair surfaces that even follow a specified normal field. Several interesting examples are given to demonstrate the applications of the proposed method in geometric modeling.