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Surface Networks: Extension of the Topology and Extraction from Bilinear Surface Patches

Surface networks capture the topological relations between passes of a continuous surface, the paths of steepest descent and ascent starting at the passes, and the pits and peaks where the steepest paths end. This paper extends the topology of the network in three ways. Objects at the edge of the surface model are introduced. Horizontal areas may represent passes, pits, or peaks, and therefore must be detected and explicitly incorporated. And it is observed that there exist topographic configurations where paths of steepest descent and ascent intersect. These configurations and their consequence for the surface network topology are explained. To ensure consistency and completeness of the surface network, a zero-order continuous surface must be specified from the raster data prior to the extraction. The paper presents a method to derive the network elements from a surface composed of bilinear surface patches. The results are illustrated with two examples.