Melvin's digital garden

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

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