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# Hierarchyless Improvement, Stripification and Pressure of Triangulated Two-Manifolds.

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Hierarchyless Improvement, Stripification and Pressure of Triangulated Two-Manifolds Pablo Diaz-Gutierrez M. Gopi Renato Pajarola College of California, Irvine Presentation
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Hierarchyless Simplification, Stripification and Compression of Triangulated Two-Manifolds Pablo Diaz-Gutierrez M. Gopi Renato Pajarola University of California, Irvine

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Introduction Intersection of and relationship between three cross section issues : Simplification, stripification and network pressure Each issue must be compelled Imposed limitations permit further materialness http://graphics.ics.uci.edu

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Introduction: Three issues Simplification Decimation Vertex grouping Edge giving way Compression Valence-driven Strip/edge-chart based Stripification Alternating straight strips Generalized strip circles http://graphics.ics.uci.edu

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Talk layout Hierarchyless disentanglement Simplification and stripification Connectivity pressure Results Conclusion http://graphics.ics.uci.edu

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Mesh rearrangements Popular methodology: Edge breakdown/vertex split Problem: Dependencies between given way edges Hierarchy of breakdown/split operations Edge breakdown Vertex split http://graphics.ics.uci.edu

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Edge-breakdown conditions Edge-fall A canât be part before Edge-breakdown B A B http://graphics.ics.uci.edu

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Multi-edges Definition Multi-edge : Edge speaking to numerous edges from the first work, after improvement. Edge breakdown Vertex split http://graphics.ics.uci.edu

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Edge-breakdown conditions A Multi-edges B Collapsing multi-edges produces conditions http://graphics.ics.uci.edu

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Multi-edges Avoiding conditions When one edge of a triangle is crumpled, the other two get to be multi-edges. On the off chance that we donât breakdown multi-edges: Only one edge for every triangle is gave way Edge breakdown 6 5 6 5 1 Collapsing edge 1 9 7/8 7 8 4 2 3 http://graphics.ics.uci.edu

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Hierarchyless rearrangements Each triangle has at most one collapsible edge One collapsible accomplice over that edge Problem: Choosing one edge keeps others from crumpling Optimize decision of collapsible edges http://graphics.ics.uci.edu

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Hierarchyless improvement Pose as diagram issue in the double chart of the triangle cross section Choose collapsible edges Graph coordinating Maximal arrangement of collapsible edges (triangle sets) Perfect diagram coordinating No multi-edges caved in!! (No falling conditions) http://graphics.ics.uci.edu

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Simplification case Genus 0 complex 3 associated arrangements Of collapsible edges http://graphics.ics.uci.edu

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Simplification case Multi-edges http://graphics.ics.uci.edu

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Simplification illustration http://graphics.ics.uci.edu

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Simplification sample http://graphics.ics.uci.edu

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Simplification case http://graphics.ics.uci.edu

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Simplification case http://graphics.ics.uci.edu

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Simplification case Equivalent vertices http://graphics.ics.uci.edu

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Simplification case http://graphics.ics.uci.edu

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Simplification case Equivalent vertices http://graphics.ics.uci.edu

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Simplification case http://graphics.ics.uci.edu

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Simplification case 3 joined parts of collapsible edges 3 vertices after complete improvement http://graphics.ics.uci.edu

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Extremal rearrangements All triangles broken down But not all vertices crumpled Collapsible edges sorted out in joined segments Each associated segment crumples to 1 vertex http://graphics.ics.uci.edu

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Extremal disentanglement Goal : Reduce number of vertices in last model By diminishing number of associated segments of collapsible edges Apply two operations : Edge swap (next slide) Matching reassignment Minimum 1 or 2 associated segments when all is said in done, associated segments are trees Might have circles http://graphics.ics.uci.edu

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Extremal disentanglement Connecting collapsible edges Initially, 3 associated segments of collapsible edges Choose an edge to swap Only two associated segments now http://graphics.ics.uci.edu

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Extremal rearrangements 2 joined segments of collapsible edges 2 vertices after complete improvement http://graphics.ics.uci.edu

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Talk layout Hierarchyless disentanglement Simplification and stripification Connectivity pressure Results Conclusion http://graphics.ics.uci.edu

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Simplification and stripification Each triangle has one collapsible edge The other two unite it to a triangle strip circle Removing collapsible edges makes disjoint triangle strip circles http://graphics.ics.uci.edu

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Extremal disentanglement and single-stripification Connected segments of collapsible edges are trees Triangles around them structure circles Fewer collapsible edge segments â less circles: Reduce number of joined segments of coordinated edges. In manifolds , collapsible edges can be assembled in 1 or 2 associated parts: All triangulated manifolds can be made a solitary triangle strip circle . Schematic representation of triangle strips and average tomahawks. http://graphics.ics.uci.edu

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Maintaining strips amid disentanglement Hierarchyless improvement consequently keeps up triangle strips Edge-breakdown abbreviate strips and average tomahawks But donât change topology Letâs see an exampleâ¦ http://graphics.ics.uci.edu

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Maintaining strips amid rearrangements http://graphics.ics.uci.edu

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Maintaining strips amid disentanglement http://graphics.ics.uci.edu

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Maintaining strips amid improvement http://graphics.ics.uci.edu

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Maintaining strips amid rearrangements http://graphics.ics.uci.edu

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Maintaining strips amid improvement http://graphics.ics.uci.edu

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Quality contemplations Quality of rearrangements Choose collapsible edges with the minimum quadric mistake Quality of stripification Application subordinate (i.e. augment strip territory) Assign edge weights Choose weight minimizing arrangement of collapsible edges Diaz-Gutierrez et al. "Constrained strip era and administration for proficient intuitive 3D renderingâ , CGI 2005 0 1 0 3 0 1 0 1 0 http://graphics.ics.uci.edu

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Talk plot Hierarchyless disentanglement Simplification and stripification Connectivity pressure Results Conclusion http://graphics.ics.uci.edu

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Collapsible edges & network pressure Important: topological , not geometric pressure. Some current methods produce triangle strips as repercussion of pressure. A couple pack availability alongside strips. We misuse duality of strips and average tomahawks. Pictures from http://www.gvu.gatech.edu/~jarek/http://graphics.ics.uci.edu

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1 0 1 0 1 0 1 0 Encoding of a strip as a compressing of two trees âHand and Gloveâ pressure Genus-0 triangulated manifolds Encode class 0 network as: Two vertex crossing trees of collapsible edges (â hand and glove â trees) a touch string compresses the trees together along the single strip circle Guaranteed upper bound : 2 bits/face (i.e. 4 bits/vertex) http://graphics.ics.uci.edu

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âHand and Gloveâ pressure Genus-0 triangulated manifolds Predict heading of strip to enhance pressure Slight adjustments to handle: Higher variety Boundaries Quadrilateral manifolds Etc. Extremely easy to code One day for model project http://graphics.ics.uci.edu

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Talk diagram Hierarchyless disentanglement Simplification and stripification Connectivity pressure Results Conclusion http://graphics.ics.uci.edu

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Results: Simplification Models with 1358, 454, 54 and 4 triangles. http://graphics.ics.uci.edu

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Results: Simplification Models with 19778, 7238, 1500 and 778 triangles . Models with 16450, 6450, 2450 and 450 triangles. http://graphics.ics.uci.edu

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Results: Simplification Models with 101924, 33924, 9924 and 1924 triangles. http://graphics.ics.uci.edu

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Results: View-subordinate rearrangements Notice emotional change in improvement http://graphics.ics.uci.edu

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Results: Stripification with hilter kilter disentanglement http://graphics.ics.uci.edu

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Results: Compression bit proportions Bits per vertex acquired with Hand & Glove strategy. Examination with Edgebreaker. The yield of both techniques is packed with a math encoder. http://graphics.ics.uci.edu

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Talk plot Hierarchyless disentanglement Simplification and stripification Connectivity pressure Results Conclusion http://graphics.ics.uci.edu

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Summary and decision This paper establishes a hypothetical framework for joining three critical regions of geometric figuring. By registering and fittingly overseeing arrangements of collapsible edges , we accomplished: Hierarchyless cross section disentanglement Dynamic administration of triangle strip circles Efficient availability pressure http://graphics.ics.uci.edu

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Future work Explore and enhance Hand & Glove network pressure. Plan a lighter information structure for figuring mistakes in perspective ward improvement. Amplify current results on stripification (mostly finished). http://graphics.ics.uci.edu

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Acknowledgments ICS Computer Graphics Lab @ UC Irvine http://graphics.ics.uci.edu http://graphics.ics.uci.edu

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THE END Thanks for your time Questions? Remarks? Proposals? http://graphics.

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