3D Complexity CS 7491
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This 0 page Class Notes was uploaded by Alayna Veum on Monday November 2, 2015. The Class Notes belongs to CS 7491 at Georgia Institute of Technology - Main Campus taught by Staff in Fall. Since its upload, it has received 6 views. For similar materials see /class/234109/cs-7491-georgia-institute-of-technology-main-campus in ComputerScienence at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Thursday February 12 2004 Prashant Thakare ltthakarecc gatechedugt Zongyu Zhang ltgtg786iprismgatechedugt Midterm 2D Compression 3D Compression Thursday February 19 2004 Closed book one page singlesided Cheat Sheet Hausdorff distance Entropy Huffman Arithmetic Encoding Subdivision Quantization Prediction Curve Compression Algorithms Simpli cation Tradeoff between Compression and Simpli cation Triangle Meshes Corner Tables construction operators traversal Formulae T2V44H etc Organizing triangle soups making shells genus handle shells contained cavities Interpolation of samples Construction of meshes by rolling balls Nonmanifold meshes topology Simpli cation Vertex Clustering Edge Collapse Preserve Topology Compression MPEG4 TST VST Edgebreaker Guest Lecture contents not included Discussions Reducing time complexity for nding radius of ball by using a range A na39139ve algorithm for nding radius of a ball that is neither too small nor too big is of order n4 Performance can be signi cantly improved by caching minmax range of radii minimum radius tting the three neighboring vertices maximum touching the nearest fourth vertex for all triangles and calculating the radius at the end ofthe pass Voronoi Delaunay Triangulation partition The Voronoi diagram of a collection of geometric objects is a partition of space into cells each of which consists of the points closer to one particular object than to any others The Delaunay triangulation of a point set is a collection of edges satisfying an quotempty circlequot property for each edge we can nd a circle containing the edges endpoints but not containing any other points The Voronoi diagram is dual to a Delaunay triangulation By using a sweeping line the complexity to construct the Voronoi diagram for a given set of points on a planar surface is ONlogN N is the number of points The corresponding complexity uncon rmed for the 3D points is ONNlogN Do Genusshell specify the topology completely As to two dimensional shape the answer is Yes Three dimensional shape the answer is NO For example two interlocked torii has the same number of genus and shell with two holes in one sphere But topologically they are different Sphere interlocked torii may not work well How is topology de ned Topology is sometimes used to specify the trianglevertex incidence in a model Connectivity is a more appropriate term for this Topology more correctly is used to mean the classi cation of shapes Presentations Maintaining the order of contents should generally be preferred and jumping across should be avoided Generally give an overview talk in detail summarize As a guideline presenting one idea per 15 minutes is a good idea Taking some time to clearly understand the question is important Question can be strategically rephrased in the mean time this clarifies the question buys some time and sometimes makes the answer trivial Predictions Along with compression schemes for connectivity vertex prediction can be used to achieve further compression A simple scheme works well in practice is called parallelogram prediction Touma amp Gotsman V From above V aacba V acaba V bca The prediction scheme works with the assumption that models are smooth and reasonably regular To simplify the decompression of Vertices connectiVity information can be completely decompressed first and then Vertices can be guessed with aVailable information Is parallelogram prediction good enough for scientific models with dense data samples Yes scientific models are generally tessellated B spline surfaces Triangulation of such tessellations is reasonably smooth and regular Can we get regular smooth model by controlling sampling density and radius of ball It depends an irregular distribution of Vertices to start with may not be necessarily be regularized Compression Algorithm Algorithm for compression presented in slides is designed for manifold models It needs to be altered to work with nonmanifold models In particular marking Vertices may not work well as same Vertex may be shared by nonmanifold triangles For example for a sheet triangulated on both the faces marking the Vertex while traVersing one face will giVe incorrect information while processing other face Marking the Vertex to indicate the sheet may also not help as a traVersal might transition between faces making it difficult to distinguish between them One sppmauh cauldbe mnguq marks mfanufmangesmmdmlwmthz vmex 1r am mm xsmarked m vean canbe cansdexedvmted
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