Siggraph Summer Seminar Yin Xu

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

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 … …

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

Authors Ming Chuang Michael Kazhdan

What to Do? Geometry filtering sharpening smoothing

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

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

Screened Poisson Equation Objective energy: Solution: screened Poisson equation

Screened Poisson Equation Objective energy:

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

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

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

Specifying Editing Constraints Spatially varying by user interaction

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

Author Introdunction

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

Mesh Construction Complex task

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

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

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

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

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

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

Different Clusters on Same Level

Filtering Focus on construction on local region

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

Demo

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

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

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

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

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

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

Model Decomposition Decomposition No cycles in domain graph

Model Reduction Pre-processing on each domain determine basis vectors

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

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

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

Demo

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

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

What to do? Simulate motion of implicit surfaces

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

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

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

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

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

Normal Velocity vs. Total Velocity

Motion Blur

Demo

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

Author Introduction Topraj Gurung Peter Lindstrom Mark Luffel Jarek Rossignac

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

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 rpt (references per triangle) or about 26.2 bpt (bits per triangle) 75% reduction in total storage

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

Triangle Classification Number of edges on the ring

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.

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

Thank You!