An Algorithm of the Constrained Construction for Terrain Morse Complexes

The correct connection of the topological relationships between critical points (or lines) is the basis of the earth’s surface description, terrain topological simplification, or geomorphic generalization of relief. However, the intersection of valley and ridge line at regular points often occurs in the existing algorithms of constructing terrain Morse complexes. In this paper, a novel universal algorithm of the constrained construction for terrain Morse complexes is presented. In our approach, the separatrix of descending (or ascending) Morse complex is regarded as the constrained boundary of extracting the separatrix of the dual Morse complex, and the terrain feature line starting from end (or start) saddle coincides exactly with the “macro-saddle line”. As a result, the intersections are prevented absolutely and the macro-saddles can be identified to achieve complete decomposition of the whole terrain surface. In the end, an experiment is done to validate the correctness and feasibility of this algorithm.