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19 th Annual Fall Workshop on Computational Geometry and CRA-W/CDC Workshop on Computational Geometry Dept. of Computer Science ••• November 13-15, 2009 ••• Medford, MA Forward The 19 th Fall Workshop on Computational Geometry was held at Tufts University, Medford, MA, on November 13-14, 2009. It was followed by a one-day tutorial day on Computational Geometry, held November 15, 2009. The first event was sponsored by the National Science Foundation, while the second event was supported by CRA-W/CDC. Supplementary funding was provided by Tufts University. These generous grants made the workshops possible. The Fall Workshop followed the tradition of being an annual forum for the presentation, discussion, and dissemination of new results, as well as free exchange of questions and research challenges. The tutorial day was designed to encourage the success of women and members of underrepresented groups, aiming at helping these people become interested in and knowledgeable about the paradigms and research of Computational Geometry. These proceedings contain the technical papers accepted for presentation at the Fall Workshop, as well as abstracts of the lectures given on the tutorial day. The 35 contributed talks given at the Fall Workshop covered a broad range of topics, from theoretical to practical aspects of Computational Geometry, and related fields, e.g., Discrete Geometry, Computer Graphics, GPU usage, Sensor Networks, Graph Drawing, etc. In addition, the workshop included five invited talks delivered by researchers in academia and industry, and the traditional open-problems session. The eight lectures of the tutorial day were given by experts in Discrete and Computational Geometry, and covered a broad spectrum of the field. A lot of work went into forming this program and producing these proceedings. The program committee of the Fall Workshop reviewed the submissions on a tight schedule. The committee needed to handle an unexpected flood of submissions, and had to make some difficult choices, being unable to accept all of the exciting submissions. We would like to thank all the authors who submitted papers to the workshop. They provided the material that made it possible to assemble such a distinguished technical program. Thanks also go to the speakers in the tutorial day, which made the creation of an attractive program possible. Gill Barequet Technion and Tufts Univerity Program Committee of FWCG’09 • Esther M. Arkin (SUNY Stony Brook) • Gill Barequet (Technion and Tufts University, chair) • Lenore J. Cowen (Tufts University) • R.L. Scot Drysdale (Dartmouth College) • Audrey Lee-St. John (Mt. Holyoke College) • Anna Lubiw (Univ. of Waterloo and MIT) • Joseph S.B. Mitchell (SUNY Stony Brook) • Diane L. Souvaine (Tufts University) • Csaba D. Tóth (Univ. of Calgary and Tufts University) • Godfried T. Toussaint (McGill University and Harvard) Local Organization • Gill Barequet (Technion and Tufts University) • Mashhood Ishaque (Tufts University) • Diane L. Souvaine (Tufts University) • Jeannine L. Vangelist (Tufts University) Technical Support • John Sotherland (Tufts University) Fall Workshop on Computational Geometry (11/13-14) Friday 11/13 9:00 Opening 1st session: Approximation (chair: Anna Lubiw): 9:05 Catalin Constantin, Shawn Brown, and Jack Snoeyink Streaming Simplification of Labeled Meshes Using Quadric Error Metrics 9:20 David M. Mount, Nathan S. Netanyahu, Christine D. Piatko, Ruth Silverman, and Angela Y. Wu A Practical Approximation Algorithm for the LTS Estimator 9:35 Leonidas Guibas, Nikola Milosavljević, and Arik Motskin Connected Dominating Sets on Geometric Graphs with Mobile Nodes 9:50 Gary L. Miller, Todd Phillips, and Donald R. Sheehy Approximating Voronoi Diagrams with Voronoi Diagrams 10:05 Dengpan Zhou and Jie Gao Maintaining Approximate Minimum Steiner Tree and k-center for Mobile Agents in a Sensor Network 10:20 Break 2nd session: Invited Talk (chair: Jack Snoeyink): 10:35 Hanspeter Pfister (Harvard University) The Connectome - Discovering the Wiring Diagram of the Brain 11:20 Break 3rd session: Representations, Data Structures, and Operators (chair: Godfried T. Toussaint): 11:35 Benoît Hudson Succinct Representation of Well-Spaced Point Clouds 11:50 Sorelle A. Friedler and David M. Mount Spatio-temporal Range Searching over Compressed Kinetic Sensor Data 12:05 Danny Z. Chen and Haitao Wang Dynamic Data Structures for Simplicial Thickness Queries 12:20 Timothy M. Chan, David L. Millman, and Jack Snoeyink Discrete Voronoi Diagrams and Post Office Query Structures without the InCircle Predicate 12:35 Short break 12:45 Lunch and Open Problems (chair: Joseph S.B. Mitchell) 13:35 Short break 4th session: Discrete Geometry (chair: Diane L. Souvaine): 13:45 Ronnie Barequet, Gill Barequet, and Günter Rote Formulae and Growth Rates of High-Dimensional Polycubes 14:00 William Steiger, Mario Szegedy, and Jihui Zhao Six-way Equipartitioning by Three Lines in the Plane 14:15 Mohammad Irfan, Justin Iwerks, Joondong Kim, and Joseph S.B. Mitchell Guarding Polyominoes 14:30 Karin Arikushi and Csaba D. Tóth Drawing Graphs with 90° Crossings and at Most 1 or 2 Bends per Edge 14:45 Javier Cano, Csaba D. Tóth, and Jorge Urrutia A Tight Bound For Point Guards in Piece-Wise Convex Art Galleries 15:00 Break 5th session: Invited Talk (chair: Gill Barequet): 15:15 Dan A. Klain (University of Massachusetts Lowell) If You Can Hide Behind It, Can You Hide Inside It? 16:00 Break 6th session: Mesh Generation and Sensor Networks (chair: Csaba D. Tóth): 16:15 Benoît Hudson, Gary L. Miller, Steve Y. Oudot, and Donald R. Sheehy Mesh-Enhanced Persistent Homology 16:30 Gary L. Miller and Todd Phillips Fast Meshing for Acute PLCs 16:45 Rik Sarkar, Wei Zeng, Xiaotian Yin, Jie Gao, Feng Luo, and Xianfeng Gu Greedy Routing with Guaranteed Delivery Using Ricci Flows 17:00 Wei Zeng, Rik Sarkar, Feng Luo, Xianfeng Gu, and Jie Gao Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space 17:15 Break 18:15 Reception at Hyatt Place Saturday 11/14 7th session: Invited Talk (chair: Nancy M. Amato): 9:00 Chris Bishop (State Univ. of NY at Stony Brook) Conformal Mapping in Linear Time 9:45 Break 8th session: Optimization (chair: Lenore J. Cowen): 10:00 Petter Brass Computing the Largest Bounded Intersection of Halfspaces 10:15 Joseph S.B. Mitchell and Eli Packer On Non-crossing (Projected) Spanning Trees of 3D Point Sets 10:30 Steven Bitner, Yam K. Cheung, Atlas F. Cook IV, Ovidiu Daescu, Anastasia Kurdia, and Carola Wenk Visiting Points with a Bevel-Tip Needle 10:45 Esther M. Arkin, Irina Kostitsyna, Joseph S.B. Mitchell, Valentin Polishchuk, and Girishkumar R. Sabhnani The Districting Problem 11:00 Steven Bitner, Yam-Ki Cheung, and Ovidiu Daescu On the Minimum Color Separation Circle 11:15 Esther M. Arkin, Sándor P. Fekete, Joondong Kim, Joseph S.B. Mitchell, Girishkumar R. Sabhnani, and Jingyu Zou The Pencil Packing Problem 11:30 Umut A. Acar, Benoît Hudson, and Duru Türkoglu A Dynamic Algorithm for Well-Spaced Point Sets 11:45 Break 9th session: Invited Talk (chair: Joseph O'Rourke): 12:00 Brigitte Servatius (Worcester Polytechnic Institute) k-Plane Matroids and Whiteley's Flatenning Conjectures 12:45 Lunch break 10th session: Metrics, Spaces, and Embeddings (chair: Esther M. Arkin): 14:00 Afra Zomorodian Fast Construction of the Vietoris-Rips Complex 14:15 Atlas F. Cook IV, Jessica Sherette, and Carola Wenk Computing the Fréchet Distance Between Polyhedral Surfaces with Acyclic Dual Graphs 14:30 Joondong Kim, Joseph S.B. Mitchell, and Jingyu Zou Routing Parallel and Merging Lanes 14:45 Anand Kulkarni and Sandeep Koranne The Gemcutting Approach to the Hirsch Conjecture (and Other Open Problems on Polytopal Graphs) 15:00 P. Thomas Fletcher, John Moeller, Jeff M. Phillips, and Suresh Venkatasubarmanian Computing Hulls In Positive Definite Space 15:15 Break 11th session: Invited Talk (chair: Audrey Lee-St. John): 15:30 Kirk Haller (Dassault Systemes SolidWorks Corporation) Computational Geometry Problems in CAD 16:15 Break 12th session: Graphics and Applications (chair: Joseph S.B. Mitchell): 16:30 Marta Fort, J. Antoni Sellarès, and Nacho Valladares Reporting Flock Patterns via GPU 16:45 Shu Ye and Karen Daniels Triangle-based Prism Mesh Generation on Interconnect Models for Electromagnetic Simulations 17:00 Sarang Joshi, Raj Varma Kommaraju, Jeff M. Phillips, and Suresh Venkatasubramanian Matching Shapes Using the Current Distance 17:15 Christopher S. Stuetzle, Zhongxian Chen, Katrina Perez, Jared Gross, Barbara Cutler, W. Randolph Franklin, and Thomas Zimmie Segmented Height Field and Smoothed Particle Hydrodynamics in Erosion Simulation 17:30 Sergey Bereg Orthogonal Morphing of Orthogonal Drawings 17:45 Adjourn Abstracts of the Fall Workshop on Computational Geometry Streaming Simpli¯cation of Labeled Meshes Using Quadric Error Metrics Catalin Constantin Shawn Brown Jack Snoeyink Department of Computer Science, University of North Carolina at Chapel Hill Abstract We present a streaming simpli¯cation al- 2 Simpli¯cation Policies gorithm for labeled meshes based on edge contrac- tion under the Quadric Error Metric of Garland and A simpli¯cation policy determines to what point an Heckbert. Given as input a spatially-¯nalized stream- edge may contract to, and a priority for eligible ing mesh, whose vertices are labeled (with object ID, contractions|those that leave the mesh data struc- ground vs. building, or some discrimination between ture in a consistent state. Most policies used in global parts of the mesh that is to be preserved during sim- simpli¯cation carry over naturally to the stream- pli¯cation), our algorithm achieves fast, high-quality ing simpli¯cation. We have adopted subset place- simpli¯cation of gigabyte datasets using a small mem- ment [2] for the contraction point and aggregate ver- ory footprint. tex quadrics by addition. Also, we use the constraint quadrics described by Garland et al. to enforce inter- object boundaries as well as true mesh boundaries. 1 Introduction Whereas Global simpli¯cation [2, 4] begins only af- ter the whole mesh has been initialized, Streaming LIDAR collects high density point clouds from vast simpli¯cation runs continuously as we pass through geographic regions.
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