Blending parametric objects by implicit techniques

Abstract

A blending surface is a transition surface between two intersecting or non-intersecting surfaces which smoothes out peaks, valleys, kinks, creases and so forth. A typical geomernc model of a mechanical part consists of two kinds of surfaces - primaryand secondary. The overall functionality of the model is decided by primarysurfaces whereas secondary surfaces are used to smoothly connect primary surfaces. Blending surfaces can be classified as secondary surfaces. MOTIVATION Blend surfaces can, in general, be classified into implicit and parametric surfaces. The problem of implicit blending is addressed by Bossignac & Requicha ‘84], [Rockwood & Owen ’87] and [Hoffinsn & Hopcroft ‘87]. With the growing trend of incorporatingfree form surfaces into solid modeling systems and due to the fact that these free form surfaces me represented by some kind of parametric surfaces the problem of blending these parametric surfaces becomes important. Various approaches have been taken to find a blend between parametric surfaces; see [Filip ’89], [Choi & Ju ’89] etc. Many of these approaches involve defining “rail curves” on the base surfaces and a set of “profiie curves” between them and finding an interpolating or approximating blend surface between them. Many of these methods suffer from the disadvantage rhatif the base surfaces am somewhat “uneven” the resulting blend may gouge them. This is due the fact that these methods do not take underlying geometry of the base surfaces into account when calculating blend surface. For more discussion on disadvantages of some of the previous parametric blending approaches see [Korparkar ‘91] and [Bien andCheng’91 ]. The implicit blending techniques mentioned above take underlying geometry of the base surfaces into consid