Contour-Based Polygonization of Regular Grid Terrain Data

Terrain visualization has been an interesting issue for graphics people for long, and there have been a lot of attempts in various ways for more e cient visualization. In most of the works the terrain data was considered as a triangular mesh as it is, or as an implicit surface in which the original shape(topology) of the terrain can be slightly changed. Recently, the Morse Theory, [1, 2], has been involved to make the visualization of volume or surface more robust in modeling various shapes, [3]. However, the Morse theory has a weak point in degeneracy cases which may occur often in actual terrain data. In this paper, we describe a method of polygonization of the terrain data using topologically guarrented contours based on the analysis of critical points. Since the degeneracy is expected in the actual terrain data, a method of overcoming the degeneracy is discussed rst so that the Morse theory can be extended to the visualization of any discrete random scalar eld data. The contours for each elevation level will be generated by the in ation technique in which the topology of the shape can be accurately preserved. The Morse theory and analysys of critical points will also be described brie y.