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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

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

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

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

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

Edge-breakdown conditions Edge-fall A canât be part before Edge-breakdown B A B http://graphics.ics.uci.edu

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

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

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 donât 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1 0 1 0 1 0 1 0 Encoding of a strip as a compressing of two trees âHand 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

âHand 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

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

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

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

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

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

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

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

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

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

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

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

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