Subdivision Algorithm of Quartic Q-Ball Surfaces with Shape Parameters

Abstract

Based on a set of quartic Ball basis functions, the quartic Q-Ball surfaces with shape parameters are proposed, which not only inherits the main properties of classical cubic Ball surfaces, but also have excellent shape adjustability. Then it is introduced some basic properties of the Ball basis function and quartic Q-Ball surfaces. With the aim to solve the problem that local adjustment of complex surface shape in modeling design, the coefficient subdivision algorithm of quartic Q-Ball surfaces are investigated. It is not only deduced the coefficient subdivision algorithm for the quartic Q-Ball surfaces, gave the specific subdivision steps, but also geometric modeling examples. The modeling examples show that the proposed algorithm is effective and easy to implement, which greatly enhances the ability to adjusting the local shape of the Q-Ball surfaces. In addition, surfaces subdivision and local shape adjustment have wide range of applications in shape design and shape adjustment of complex surface in engineering.