Complex-valued contour meshing
Proceedings of the 7th conference on Visualization '96
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Extracting iso-valued features in 4-dimensional scalar fields
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Partitioning 3D Surface Meshes Using Watershed Segmentation
IEEE Transactions on Visualization and Computer Graphics
Constant-Time Navigation in Four-Dimensional Nested Simplicial Meshes
SMI '04 Proceedings of the Shape Modeling International 2004
Surface Segmentation through Concentrated Curvature
ICIAP '07 Proceedings of the 14th International Conference on Image Analysis and Processing
Topological analysis and characterization of discrete scalar fields
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Morphological analysis of terrains based on discrete curvature and distortion
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
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
Concentrated curvature for mean curvature estimation in triangulated surfaces
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
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We introduce a novel notion, that we call discrete distortion, for a triangulated 3-manifold. Discrete distortion naturally generalizes the notion of concentrated curvature defined for triangulated surfaces and provides a powerful tool to understand the local geometry and topology of 3-manifolds. Discrete distortion can be viewed as a discrete approach to Ricci curvature for singular flat manifolds. We distinguish between two kinds of distortion, namely, vertex distortion, which is associated with the vertices of the tetrahedral mesh decomposing the 3-manifold, and bond distortion, which is associated with the edges of the tetrahedral mesh. We investigate properties of vertex and bond distortions. As an example, we visualize vertex distortion on manifold hypersurfaces in R4 defined by a scalar field on a 3D mesh. distance fields.