Point Based Methods

CREATED: 200701021627 Author: Leonidas J. Guibas

** Point based methods

• physical simulation ** phyxels (sparse) ** surfels (dense)
• good for highly dynamic situations - mesh does not get in the way

** Dealing with point clouds

• given point cloud, connect nearby (dist < $\epsilon$ points to get topology
• Q: How to set $\epsilon$ to get the actual topology?
• for a range of epsilon, observe birth/death of topological features, persistent features are part of the shape
• persistent bar codes captures topology and geometry of point clouse
• use local properties such as neighbourhood, curvature to produce a series of filtration to get bar code
• topology is coarse but robust
• use tangent space to get geometry
• increase curvature of tangent to get closer approximations to the actual shape
• stability, efficiency can be obtained by using a derived set of points

** Simulations

• point based elasticity from continuum mechanics
• Q: How to derive global properties, displacement field form local properties of points
• Phyxels (dense), surfels (dense but not involve in physics, contribute to appearance)
• Add new simulation nodes, when crack passes through to improve accuracy
• No mesh restructuring required for simulation of cracks

** Proximity

• interactions between points are short range
• geometric spanner - stable combinatorial structure which captures proximity across time
• space graph such that shortest path ~ euclidean distance
• maintain this property as graph changes
• replace geometric queries (who is near) by graph search

** Summary

• particles interact with neighbours
• resampling
• topological features are created and destroyed
• maintain some combinatorial structure behind the scenes to make things fast