Hybrid volume completion with higher-order Bezier elements

摘要

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 Bezier tetrahedral elements in the interior of the object with C~0 smoothness across their interfaces. The B-spline elements are constructed by offsetting the input surface into its interior. Then, an intermediate interface consisting of Bezier 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 Bezier tetrahedral elements. Our approach to constructing stiffness and mass matrices takes into account the dependencies of interior Bezier tetrahedral elements on exterior B-spline elements along their interface, so that C~0 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.