Coverage And Visibility Problems On Topographic Surfaces

This thesis discusses and defines visibility coverage problems by using visibility information derived from topographic surfaces. Algorithms for extracting visibility information are developed and tested on both randomly generated and real topographic surfaces to solve visibility coverage problems, such as the determination of visible regions for specific viewpoints, the determination of a minimal set of viewpoints to see the entire surface. Problems are also extended to the cases of viewpoints whose heights are allowed to vary.;A triangulated irregular network (TIN) model was selected to represent topographic surfaces in this study. A drop heuristic algorithm for extracting TIN models from grid digital elevation models (DEM) was also developed and presented. Heuristic algorithms are used to solve visibility coverage problems and are compared for their performances. Solutions to visibility coverage problems suggested that peaks and vertices on ridge lines are found to be most likely good candidates as solution viewpoints. Relief variations on topographic surfaces are found to have a positive relationship with the number of viewpoints as well as the cost of building watchtowers required to see the entire surface. Parameters describing topographic surfaces, such as statistics of elevations and slopes of triangles, proportions of peak and ridge points in a set of vertices, the spatial autocorrelation coefficient, and the parameters of variograms are found to have similar relationship