Metaball势函数的若干性质研究

对曲面实施基于Metaball的变形时,体现变形约束的势函数起着决定性的作用.分析研究了现有几种常用势函数的形式、特性、含义,以及其导数的性质、最大最小取值、连续性等,并将它们相互比较;在性质研究的基础上,改进这些现有势函数,建立了基本球形函数、普遍指数函数、椭球形函数与超椭球形函数等新势函数,以适应不同的应用背景,拓展基于Metaball的曲面变形的适用范围并丰富其表现力;提出了多个势函数组合作用时的层次控制方法.

Character study of Metaball field functions

While a curve surface is deformed by metaball based method, the field function embodies the deformation constraint and plays a crucial role. The primitive shape of the constraint is defined by the field function. So, we studied the forms, characters and signification of several existing field function formulae, as well as the features, the maximal and minimum values, continuity of their differential coefficients. By comparison and analysis of these properties, some delightful instances are discovered. On the foundation of property study, we ameliorated these field functions, and established several new field functions, such as basic spherical function, general exponent function, ellipsoid and super ellipsoid functions. The new field functions proved to be a clever generalization over the old ones. They can adapt to various application background. Consequently, the applicable scope of metaball based curve surface deformation is extended, and the expressive force is enriched. In order to use several kinds of field function simultaneously, a hierarchical control method is advanced by assigning the function type, group, and quality attribute to the keys.