Hybrid volume completion with higher-order Bézier elements

Abstract

This paper proposes a methodology to create a hybrid volumetric representation from a 2-manifold without boundaries represented with untrimmed B-spline surfaces. The product consists of trivariate tensor product B-splines near the boundary and unstructured higher-order Bézier tetrahedral elements in the interior of the object with C0 smoothness across their interfaces. The B-spline elements are constructed by offsetting the input surface into its interior. Then, an intermediate interface consisting of Bézier triangles is built to match the inner boundary of the B-spline representation. The rest of the space, bounded by the intermediate interface, is then filled with unstructured Bézier tetrahedral elements. Our approach to constructing stiffness and mass matrices takes into account the dependencies of interior Bézier tetrahedral elements on exterior B-spline elements along their interface, so that C0 smoothness is automatically maintained when performing computer graphics simulations, representing material properties, or performing isogeometric analysis. We apply our methodology on a variety of 3-D objects and demonstrate a fast convergence rate with our 2-D studies.