Point Based Methods

CREATED: 200701021627 Author: Leonidas J. Guibas

** Point based methods

** 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