A new approach for a topographic feature-based characterization of digital elevation data
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Discrete distortion in triangulated 3-manifolds
SGP '08 Proceedings of the Symposium on Geometry Processing
Morphology analysis of 3D scalar fields based on morse theory and discrete distortion
Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
The PR-star octree: a spatio-topological data structure for tetrahedral meshes
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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In order to characterize the morphology of a triangulated terrain, we define several discrete estimators that mimic mean and Gaussian curvatures in the discrete case. We start from concentrated curvature, a discrete notion of Gaussian curvature for polyhedral surfaces, defined by Troyanov [7]. Since concentrated curvature does not depend on the local geometric shape of the terrain, we introduce Ccurvature that allows us to obtain discrete counterparts of both Gaussian and mean curvature. Finally, we define distortion, which behaves as an approximation of mean curvature. We apply all such measures to the analysis of the morphology of triangulated terrains.