Quartic generalized ball surfaces with shape parameters and its continuity conditions

Abstract

A new geometric model of quartic generalized Ball surfaces with multiple shape parameters is constructed using a class of quartic generalized Ball basis functions. The proposed quartic generalized Ball surfaces not only inherit the outstanding properties of the Ball Surfaces, but also have a good performance on adjusting their shapes by changing shape control parameters. To tackle the problem that the engineering complex surfaces can not be constructed by using a single surface, the continuity conditions of quartic generalized Ball surfaces with shape parameter are investigated. Based on the analysis of the basis functions, the conditions of G1 continuity between two adjacent quartic generalized Ball surfaces are proposed. In addition, some applications in quartic generalized Ball surfaces design are discussed. The modeling examples show that the proposed method is effective and easy to implement, which greatly enhances the ability to constructing complex surface by using quartic generalized Ball surfaces.