1. Siggraph Summer Seminar Yin Xu 2011.07.14

2. Geometry processing Simulation Computational geometry Interactive and Anisotropic Geometry Processing Using the Screened Poisson Equation MeshFlow: Interactive Visualization of Mesh Construction Sequences Real-Time Large-Deformation Substructuring On the Velocity of an Implicit Surface LR: Compact Connectivity Representation for Triangle Meshes Contributing Vertices-Based Minkowski Sum of a Non-Convex--Convex Pair of Polyhedra Dinus: Double insertion, nonuniform, stationary subdivision surfaces

3. Geometry processing Simulation Computational geometry Interactive and Anisotropic Geometry Processing Using the Screened Poisson Equation MeshFlow: Interactive Visualization of Mesh Construction Sequences Real-Time Large-Deformation Substructuring On the Velocity of an Implicit Surface LR: Compact Connectivity Representation for Triangle Meshes … …

4. Interactive and Anisotropic Geometry Processing Using the Screened Poisson Equation Ming Chuang Johns Hopkins University Michael Kazhdan Johns Hopkins University

5. Authors Ming Chuang Michael Kazhdan

6. What to Do? Geometry filtering sharpening smoothing

7. Motivation Specific filter is not known Low efficiency hard to predict filtering effects

8. Contribution Localized editing using anisotropic filters Interactive rates Adapt to user-prescribed metric 20 fps extend screened Poisson formulation in image processing by Bhat, 2008

9. Screened Poisson Equation Objective energy: Solution: screened Poisson equation

10. Screened Poisson Equation Objective energy:

11. Anisotropic Filtering spatially varying inner-product on the tangent space of M

12. Anisotropic Filtering Adjusting Riemannian metric to curvature: amplify: large negative curvature large positive curvature preserve: sharp concave creases sharp convex creases

13. Interactive Surface Editing B-spline basis Pre-processing Parallelizing …

14. Specifying Editing Constraints Spatially varying by user interaction

15. MeshFlow: Interactive Visualization of Mesh Construction Sequences Jonathan D. Denning William B. Kerr Fabio Pellacini

16. Author Introdunction

17. What to Do? Interactive system for visualizing mesh construction sequences Help users to learn construction of complex polygon models

18. Mesh Construction Complex task

19. Previous Use Tutorials Video Document long recording time (several hours); hard to get an overview of the whole process. good overview of the whole process; skips many details that are necessary for correct construction

20. MeshFlow Mesh construction sequences Hierarchical clustering of sequences record all the operations during construction; view independent; can be easily played back groups similar operations together at different levels of detail visualize the clustered operations

21. Mesh Construction Sequence Polygonal mesh + tag Tag: operations, camera view, selection

22. Visualizing System Similar with video Visualizing operations with different notations Support LOD view based on clustering

23. Clustering Operations Combine similar operations together Each LOD has different clustering criteria

24. Clustering Operations Combine similar operations together Each LOD has different clustering criteria

25. Different Clusters on Same Level

26. Filtering Focus on construction on local region

27. Limitations Only support polygonal mesh only support clustering expressions sequentially No semantic clustering criteria Future work: NURBS Future work: cluster operations out of order Future work: geometry analysis on models

28. Demo

29. Real-time Large-deformation Substructuring Jernej Barbic Yili Zhao University of Southern California

30. Author Introduction Jernej Barbic Yili Zhao PhD student computer graphics Animation interactive physics Haptics sound and control computer graphics physically-based simulation

31. What to Do? Fast simulation of deformable models Model reduction complex model: hard to deform in real-time

32. Model Reduction High-dimensional equations of motions Project to low-dimensional space Deformation: solving r*r linear system r basis vectors linear combination of basis vectors

33. Low Efficiency of Model Reduction Reduction basis is global in space and time Interactively solving r*r dense linear system first r eigen-vectors of n*n matrix when n is large, r should also be large

34. Key Idea Decompose the model into several subdomains Model reduction on each domain Connect the domains using inertia coupling

35. Model Decomposition Decomposition No cycles in domain graph

36. Model Reduction Pre-processing on each domain determine basis vectors

37. Connection between domains Physical simulation Transform from root domain to subdomains Rigid motion on each domain

38. Algorithm Select root domain Deform from root to leaves Output model reduction on each subdomain

39. Limitations Limited to domain topologies without loops Small amount of non-rigid deformation Parallelizing

40. Demo

41. On the Velocity of an Implicit Surface JOS STAM and RYAN SCHMIDT Autodesk Research

42. Author Introduction JOS STAM RYAN SCHMIDT natural phenomena physics-based simulation rendering surface modeling mesh representations implicit surfaces point-set parameterization pen-and-ink NPR rendering 3D widgets sketch-based interaction

43. What to do? Simulate motion of implicit surfaces

44. Motion of Implicit surface Only the normal component of velocity is unambiguously defined an implicit surface does not have a unique parameterization

45. Velocity of Implicit surface Time evolving implicit surface F: Velocity: Only normal component, no tangential velocity

46. Rendering Implicit Surfaces Generating a new mesh at each frame Updating original mesh at each frame Surface Tracking

47. Given an animated implicit surface Normal velocity is uniquely determined How to determine tangential velocity? zero tangential velocity appropriate tangential velocity

48. Tangential Velocity Require the normal at each point does not vary over time Uniquely determine the tangential velocity specifically derived to preserve rigidity of the normal field normal velocity total velocity

49. Normal Velocity vs. Total Velocity

50. Motion Blur

51. Demo

52. LR: Compact Connectivity Representation for Triangle Meshes Topraj Gurung Georgia Institute of Technology Mark Luffel Georgia Institute of Technology Peter Lindstrom Lawrence Livermore National Laboratory Jarek Rossignac Georgia Institute of Technology

53. Author Introduction Topraj Gurung Peter Lindstrom Mark Luffel Jarek Rossignac

54. What to Do? A simple data structure for representing the connectivity of manifold triangle meshes Save both space and traversal time linear space and time complexity

55. LR Representation Storage-saving modification of the Corner Table (CT) [Rossignac 2001] Laced Ring representation for each triangle stores 3 integer references to its vertices in the V table and 3 references to opposite corners in adjacent triangles in the O table. 1.08 rpt (references per triangle) or about 26.2 bpt (bits per triangle) 75% reduction in total storage

56. LR Representation Nearly-Hamiltonian cycle of primal mesh edges greedy RING-EXPANDER algorithm

57. Triangle Classification Number of edges on the ring

58. LR Representation Store ring vertices T1 and T2 triangles in order of the ring Isolated vertices are stored last most triangles are of type T1 or T2; two of their vertex references (V entries of the CT) are defined implicitly and need not be stored.

59. Limitations Incremental connectivity changes cannot be performed efficiently Input mesh data structure must be CT recommend LR for use in applications where mesh connectivity remains fixed provides constant-time adjacency queries

60. Thank You!