Siggraph Summer Seminar

1. Siggraph Summer Seminar Yin Xu 2011.07.14

2. Interactive and Anisotropic Geometry Processing Using the Screened Poisson Equation MeshFlow: Interactive Visualization of Mesh Construction Sequences • Geometry processing • Simulation • Computational geometry 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. Interactive and Anisotropic Geometry Processing Using the Screened Poisson Equation MeshFlow: Interactive Visualization of Mesh Construction Sequences • Geometry processing • Simulation • Computational geometry 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 anisotropicfilters • Interactive rates • Adapt to user-prescribed metric extend screened Poisson formulation in image processing by Bhat, 2008 20 fps

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 𝛽 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 mesh representations implicit surfaces point-set parameterization pen-and-ink NPR rendering 3D widgets sketch-based interaction natural phenomena physics-based simulation rendering surface modeling

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. Surface Tracking • 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