保持物理特征的三维标量场拓扑简化

Topological simplification of 3D scalar fields with physical feature preservation

针对现有三维标量场拓扑简化方法,在简化的同时可能丢失部分有意义的物理特征问题,提出并实现了一种保持物理特征的三维标量场拓扑简化算法,采用为应用定制的物理判据分类标量场区域,将标量场重要特征检出和拓扑简化关联起来。结合Morse理论在次要物理特征所在区域构造Morse-Smale复形,并通过对复形上一系列临界点对的删除,达到简化和平滑函数拓扑特征的目的。实验结果验证了该方法的可行性。

This paper introduces and realizes a topological simplification of 3D scalar fields with physical feature preservation to solve the physical feature loss problem by pre-existing methods.This paper classifies the scalar field region under the application-specified physical criterion,and combines the feature detection of a vector field with its topological simplification.By constructing Morse-Smale complex over the physically less important subregions and proceeding by repeatedly removing a pair of critical points from the complex,the topological feature is simplified and smoothed,this method is based on the morse theory.The experimentation verifies the feasibility of the method.