A Topology Complexity Based Method to Approximate Isosurface with Trilinear Interpolated Triangular Patch

To approximate isosurface with triangular patch, the selection of sample points is pivotal to the topology correctness and approximation accuracy. In the marching cubes method and its variations, the topology of original surface is not taken into account, and only the same kind of isopoints is selected, and thus these methods can't guarantee correct topology of approximated isosurface. In this paper, Morse theory is incorporated into the study of triangular approximation, and a new method based on topology complexity is presented to approximate the isosurface patch inside a cell. According to the topology complexity of the original isosurface, the approximated isosurfaces can be adaptively constructed by triangulating two kinds of isopoints: critical points and the isopoints on cell edges. Because critical points are the key isopoints defining the surface topology, the new method can guarantee correct topology and high accuracy of the approximated isosurface without adding much computation and data. Examples are given for comparing the approximated isosurface generated from the new method with those from other methods.