Extended Gaussian images, mixed volumes, shape reconstruction
SCG '85 Proceedings of the first annual symposium on Computational geometry
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Exploring surface characteristics with interactive Gaussian images: a case study
Proceedings of the conference on Visualization '02
Polyhedral Metrics in Surface Reconstruction
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
Computing Elevation Maxima by Searching the Gauss Sphere
SEA '09 Proceedings of the 8th International Symposium on Experimental Algorithms
Computing elevation maxima by searching the gauss sphere
Journal of Experimental Algorithmics (JEA)
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We design a set of algorithms to construct and visualise unambiguous Gauss maps for a large class of triangulated polyhedral surfaces, including surfaces of non-convex objects and even non-manifold surfaces. The resulting Gauss map describes the surface by distinguishing its domains of positive and negative curvature, referred to as curvature domains. These domains are often only implicitly present in a polyhedral surface and cannot be revealed by means of the angle deficit. We call the collection of curvature domains of a surface the Gauss map signature. Using the concept of the Gauss map signature, we highlight why the angle deficit is sufficient neither to estimate the Gaussian curvature of the underlying smooth surface nor to capture the curvature information of a polyhedral surface. The Gauss map signature provides shape recognition and curvature characterisation of a triangle mesh and can be used further for optimising the mesh or for developing subdivision schemes.