TY - GEN A1 - Hildebrandt, Klaus A1 - Polthier, Konrad A1 - Wardetzky, Max T1 - On the Convergence of Metric and Geometric Properties of Polyhedral Surfaces N2 - We provide conditions for convergence of polyhedral surfaces and their discrete geometric properties to smooth surfaces embedded in Euclidian $3$-space. The notion of totally normal convergence is shown to be equivalent to the convergence of either one of the following: surface area, intrinsic metric, and Laplace-Beltrami operators. We further s how that totally normal convergence implies convergence results for shortest geodesics, mean curvature, and solutions to the Dirichlet problem. This work provides the justification for a discrete theory of differential geometric operators defined on polyhedral surfaces based on a variational formulation. T3 - ZIB-Report - 05-24 KW - Discrete Geometry KW - Differential Geometry KW - Numerical Analysis Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8587 ER - TY - GEN A1 - Kälberer, Felix A1 - Polthier, Konrad A1 - Reitebuch, Ulrich A1 - Wardetzky, Max T1 - Compressing Triangle Meshes using Geometric Infomation N2 - We introduce FreeLence, a lossless single-rate connectivity compression algorithm for triangle surface meshes. Based upon a geometry-driven traversal scheme we present two novel and simple concepts: free-valence connectivity encoding and entropy coding based on geometric context. Together these techniques yield significantly smaller rates for connectivity compression than current state of the art approaches - valence-based algorithms and Angle- Analyzer, with an average of $36\%$ improvement over the former and an average of $18\%$ over the latter on benchmark 3D models, combined with the ability to well adapt to the regularity of meshes. We also prove that our algorithm exhibits a smaller worst case entropy for a class of "'well-behaved"' triangle meshes than valence-driven connectivity encoding approaches. T3 - ZIB-Report - 04-26 KW - Mesh Compression KW - Connectivity Encoding KW - Polygonal Meshes KW - Context-based Entropy Coding Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8016 ER - TY - CHAP A1 - Wardetzky, Max ED - I. Bobenko, Alexander ED - Sullivan, John ED - Ziegler, Günter T1 - Convergence of the Cotan formula - an overview T2 - Discrete Differential Geometry Y1 - 2008 U6 - https://doi.org/10.1007/978-3-7643-8621-4 SP - 275 EP - 286 PB - Birkhäuser Basel ER - TY - JOUR A1 - Kälberer, Felix A1 - Polthier, Konrad A1 - Reitebuch, Ulrich A1 - Wardetzky, Max T1 - Free Lence - Coding with free valences JF - Computer Graphics Forum Y1 - 2005 U6 - https://doi.org/10.1111/j.1467-8659.2005.00872.x VL - 24 IS - Issue 3 SP - 469 EP - 478 ER - TY - CHAP A1 - Hildebrandt, Klaus A1 - Polthier, Konrad A1 - Wardetzky, Max T1 - Smooth feature lines on surface meshes T2 - Third Eurographics Symposium on Geometry Processing Y1 - 2005 SP - 85 EP - 90 ER -