Blending using ODE swept surfaces with shape control and C1 continuity

Abstract

Surface blending with tangential continuity is most widely applied in computer-aided design, manufacturing systems, and geometric modeling. In this paper, we propose a new blending method to effectively control the shape of blending surfaces, which can also satisfy the blending constraints of tangent continuity exactly. This new blending method is based on the concept of swept surfaces controlled by a vector-valued fourth order ordinary differential equation (ODE). It creates blending surfaces by sweeping a generator along two trimlines and making the generator exactly satisfy the tangential constraints at the trimlines. The shape of blending surfaces is controlled by manipulating the generator with the solution to a vector-valued fourth order ODE. This new blending methods have the following advantages: (1) exact satisfaction of C1C1 continuous blending boundary constraints, (2) effective shape control of blending surfaces, (3) high computing efficiency due to explicit mathematical representation of blending surfaces, and (4) ability to blend multiple (more than two) primary surfaces.