定义在三维曲面域上的四维曲面插值

4-D SURFACES DEFINED ON 3-D DOMAIN SURFACES

本文对定义在三维曲面域上的四维曲面的构造进行了系统的分析。提出了对三维曲面域上的离散点集进行三角剖分的算法,基于Shepard思想构造了定义在三维曲面域上的四维曲面的插值方案,对四维曲面的图形表示进行了分析,建立了曲面上等值线三角形追踪算法,并进行了填充处理。最后,列举了一些实例,展示了该成果的应用前景。文中所有算法均在IBM PC机上实现,算法简单,而且具有通用性,易于在工程中得到应用。

In this paper,the theory for constructing interpolant to 4-D data defined on 3-D domain surfacesis analyzed and a new algotithm for triangulation of scattered data on a 3-D surface is presented.Amodified Shepard′s method to interpalate 4-D data is given,as well with an algorithm for contouring atrivariate interpolant being made.Some examples in the engineering application are given to show thefine view of 4-D surface research in the future.All algorithms given in this paper are proved to be sim-ple and practical and had accomplished on IBM personal computer.