一种新的抽取等值面的四面体分解方法

Marching Cubes算法是一种从三维数据场中抽取等值面的简单有效的算法。然而，该算法并不能保证抽取出的等值面的拓扑同三维数据场的数据保持一致，即等值面的拓扑存在二义性。解决这个问题的方法是，将三维数数据场中每一个立方体网格单元分解为五个四面体单元，从每一个四面体单元中抽取等值面。但是，在分解过程中由于分解二义义性的存在，等值面的拓扑仍然存在二义性。本文采用24-分解方法解决了这个问题，生成了拓扑正确的等值面。

A New Tetrahedral Decomposition Scheme for Extracting Isosurfaces

Marching Cubes is a simple and popular algorithm for extracting isosurfaces from three dimensional data fields. However, it does not guarantee the surface to be topologically consistent with the data, called topological ambiguity. To solve this problem, each cubic grid cell can be decomposed into five tetrahedral cells in the three dimensional data fields, then isosufaces can be extracted from each tetrahedral cell. But during the course of decomposition, decomposed ambiguity yet results in the topological ambiguity of isosurfaces. In this paper, we solve the problem using the 24 decomposition scheme to generate correct topological isosurfaces.