0:05{10:25 Combining Spatial Data Representations for Rapid Visualization and Analysis. Geometric Complexity and Graphics Maintenance of Geometric Representations through Space Decompositions Combining Spatial Data Representations for Rapid Visualization and Analysis Solving the Embedding Problem in

s of Talks Army Research O ce and MSI Stony Brook Workshop on COMPUTATIONAL GEOMETRY October 14{16, 1993 Brownestone Hotel Raleigh, North Carolina Hosted by the Department of Computer Science North Carolina State University Sponsored by the U.S. Army Research O ce, and the Mathematical Sciences Institute, Stony Brook. Organizers: Pankaj Agarwal (pankaj@cs.duke.edu) Esther Arkin (estie@ams.sunysb.edu) Kenneth Clark (clark@adm.csc.ncsu.edu) Rex Dwyer (dwyer@csc.ncsu.edu) Joseph Mitchell (jsbm@ams.sunysb.edu) Steven Skiena (skiena@sbcs.sunysb.edu) 1 Program Thursday, October 14, 1993 8:00{9:00 Breakfast bu et. 9:00{9:45 Geometric Complexity in Graphics. Jarek Rossignac, IBM Research, Yorktown Heights 9:45{10:05 Maintenance of geometric representations through space decompositions. Vadim Shapiro, GM R&D Center 10:05{10:25 Combining spatial data representations for rapid visualization and analysis. Lori L. Scarlatos, Grumman Data Systems / SUNY Stony Brook 10:25{10:45 Break. 10:45{11:05 Solving the embedding problem in Distance Geometry. Peter Schorn, ETH Z urich 11:05{11:25 An O(N2) Heuristic for Steiner Minimal Trees in E3. J. MacGregor Smith, Univ. of Massachussetts, Amherst 11:25{11:45 Finding a Covering Triangulation Whose Maximum Angle is Provably Small. Scott Mitchell, Sandia National Labs 11:45{12:05 E cient Piecewise-Linear Function Approximation Using the Chebychev Metric. Mike Goodrich, Johns Hopkins Univ. 12:05{1:15 Lunch. 1:15{2:00 Dynamic Geometric Optimization. David Eppstein, University of California, Irvine 2:00{2:20 Computing the intersection of simply connected planar subdivisions in linear time and space. Klaus Hinrichs, Westfalische Wilhems-Univ., M unster 2:20{2:40 Why Optics? Y. B. Karasik, Tel Aviv Univ. 2:40{3:00 Object reconstruction from parallel cross sections. Gill Barequet, Tel Aviv Univ. 3:00{3:20 External-Memory Computational Geometry. Darren Vengro , Brown University 3:20{3:40 Break. 3:40{4:25 Geometric Problems in Robotics, Chemistry, and Medicine. Tomas Lozano-Perez, Massachusetts Institute of Technology 4:25{4:45 Fast Computation of the Minimum Symmetric Di erence for Convex Shapes. L. Paul Chew, Cornell Univ. 4:45{5:05 Shortest Paths and Minimum-Link Paths between Convex Polygons in the Presence of Obstacles. Yi-Jen Chiang, Brown Univ. 5:05{5:25 Planar Upward Tree Drawings with Optimal Area. Roberto Tamassia, Brown Univ. 5:25{5:45 A Lower Bound For Fully Dynamic Planarity Testing in Graphs. Monika Rauch, Cornell Univ. 8:00 Reception. 2 Friday, October 15, 1993 8:00{9:00 Breakfast bu et. 9:00{9:45 Virtual Reality Research at Boeing. David Mizell, Boeing, Seattle 9:45{10:05 Real-Time Contact Determination for Geometric Models. Ming Lin, Univ. of California, Berkeley 10:05{10:25 Applications of Geometric Rounding to Polygon and Polyhedron Modeling. V. Milenkovic, Harvard Univ. 10:25{10:45 Break. 10:45{11:05 E cient Bitmap Resemblance. Klara Kedem, Ben Gurion Univ., Israel 11:05{11:25 Biased Finger Trees and Three-Dimensional Layers of Maxima. Kumar Ramaiyer, Johns Hopkins Univ. 11:25{11:45 A Fast Practical New Edge Test for the Greedy Triangulation. Matthew Dickerson, Middlebury College 11:45{12:05 Delaunay triangulation and optimality. Oleg R. Musin, Moscow State Univ. 12:05{1:15 Lunch. 1:15{2:00 Floodlight Problems. Diane Souvaine, Rutgers University and DIMACS 2:00{2:20 Planning Wielding Strategies for Dynamic Tasks. Radha Krishnan, Univ. of Maryland, College Park 2:20{2:40 Robust Algorithms for Surface Intersection. Dinesh Manocha, Univ. of North Carolina, Chapel Hill 2:40{3:00 Optimal Algorithms for Two Weak Visibility Problems in Polygons. Giri Narasimhan, Memphis State Univ. 3:00{3:20 On Line Navigation Through Regions of Variable Densities. H. Wang, Duke Univ. 3:20{3:40 Break. 3:40{4:25 Experience with Exact Arithmetic in Computational Geometry. Steven Fortune, AT& T Bell Labs 4:25 Open Problem Session. 3 Saturday, October 16, 1993 8:00{9:00 Breakfast bu et. 9:00{9:45 Vertical Decompositions of Arrangements. Leonidas Guibas, Stanford University 9:45{10:05 Low Degree Spanning Trees. Samir Khuller, Univ. of Maryland, College Park 10:05{10:25 Parallel Algorithms for Visibility on Polyhedral Terrains. Y. Ansel Teng, Univ. of Maryland, College Park 10:25{10:45 Break. 10:45{11:05 Multiple Containment Methods and Applications in Clothing Manufacture. K. Daniels, Harvard Univ. 11:05{11:25 On Intersections and Separations of Polytopes. Karel Zikan, Boeing, Seattle 11:25{11:45 Symmetries, Symmetry Groups and Robotics. Yanxi Liu, DIMACS 11:45{12:05 Time-Optimal Multiple Search Algorithms on Meshes with Multiple Broadcasting, with Applications. Stephan Olariu, Old Dominion Univ. 12:05{12:25 Higher Isn't (Much) Better { Visibility Experiments and Algorithms for Terrain Databases. Wm. Randolph Franklin, Rensselaer Polytechnic Institute 12:25{1:30 Lunch. 1:30{3:00 Software Demos on campus. 3:00 Excursion. 4 Geometric Complexity and Graphics Paul Borrel, Josh Mittleman, Remi Ronfard, and Jarek Rossignac IBM Research PO Box 704, Yorktown Heights, NY 10598 The presentation will address the generation and exploitation of multi-resolution graphic models for the interactive visualization of complex mechanical or architectural 3D scenes. The scene is imported from mechanical or architectural CAD systems as a list of solids and their instantiation. A solid is a collection of planar faces (which need not form a connected or manifold surface, nor be the boundary of a polyhedron). An instantiation associates a solid with a matrix de ning its position, orientation, and scaling and with a surface de ning the color and graphic re ectance properties. The same solid may be instantiated many times. A typical scene may contain a million faces unevenly distributed between thousands of solid instances. Face complexity ranges from a triangle to faces with thousands of edges organized in dozens or hundreds of loops. Shading performance on most commercially available hardware 3D graphics adapters is a function of (1) the number of vertices (or triangles) that need to be transformed and lit and (2) the number of times a pixels is visited during scan-conversion. The need for interactive (10 frames per second or more) view manipulation limits the active scene complexity (the number of triangles that need to be processed per frame) to lie between 1K and 100K (depending on the adapter). Most techniques for reducing the active scene complexity fall under three categories: visibility, levels-of-detail (LOD), and graphics data access. Visibility techniques attempt to reject, a priori, most of the faces that cannot not be seen on the screen given the current camera parameters. These techniques include: (1) hierarchical pruning against the clipping planes of the viewing frustum, (2) hierarchical back face culling (for orientable shells), and (3) visibility precomputation (which established for each face and for each cell of a partition of space whether the face may or may not be visible from at least one point in the cell). Levels-of-detail techniques automatically construct several (approximating) graphics representations for each solid (with decreasing number of faces and increasing tolerance on the approximation error). The cheaper (less detailed) representations may be used when displaying objects whose geometric details play a relatively minor role in the overall picture (for example, because the objects appear small or are moving rapidly across the screen). Given the available levels of detail, the visibility information, and the desired target frame rates, optimal levels of detail must be selected automatically for each instance, so as to minimize the visual artifacts of the LOD approximation. Due to the size of the dataset, optimal LOD selection must take into account memory management issues. Furthermore, the data structures for modeling polyhedra do not map well into optimal programming interfaces for graphics pipelines. For example, graphics performance optimization for popular graphics libraries requires triangulating the faces and chaining the triangles into strips. The speaker will describe practical solutions to some of these problems and point out di culties and open issues encountered in the development of the BRUSH system for the interactive inspection of complex mechanical and architectural scenes. 5 Maintenance of geometric representations through space decompositions Vadim Shapiro Analytic Process Department General Motors R&D Center Warren, MI 48090-9055 shapiro@gmr.com September 28, 1993 Maintanence of representations in geometric modeling includes problems of representation conversions, optimization, and assuring consistency between several representations. In particular, the ability to transform between distinct geometric representations is the key to success of multiplerepresentation modeling systems. But the existing theory of geometric modeling does not directly address or support construction, conversion, and comparison of geometric representations. A study of classical problems of CSG $ b-rep conversions, CSG optimization, and other representation conversions suggests a natural relationship between a representation scheme and an appropriate decomposition of space. The problem of boundary evalutation given a CSG representation of a solid has been studied by many and is well understood [RV85]. The inverse problem of computing a CSG representation of a solid given its boundary has been addressed only recently [SV91a, SV91b, SV93]. We study the solutions of both problems and identify common computational themes and methods. These and other examples suggest a general approach to maintanence of representations, based on space decompositions [Sha91]. Speci cally, every representation scheme corresponds to unique way to decompose the space into \cells". The union of some of these cells corresponds to a canonical representfation of a point set in that scheme. The type of cells (closed, open, conn