### Summary

This paper gives an overview of the particle level set method and a particle level set library developed at UCLA. Level sets are a useful tool for representing a surface implicitly for the purposes of simulation and visualization. They have the nice property that for any point in space, the level set function will provide the distance to the surface being represented, and thus the exact location of the surface (where the function is 0). This leads to the nice property that any level set will produce a valid surface. Mesh representations of surfaces, for example, can run in to problems with self intersection or cracking.

However, A problem arises with coarse-grid level sets during advection in which sharp edges end up being smoothed out causing the level set to lose volume. The particle level set addresses this problem by adding several particles in a band around the implicit surface. These particles are advected along with the level set and used to correct the level set after advection.

### Problem

Level sets provide a useful tool for visualization and simulation of surfaces, but are prone to unintentional smoothing caused by numerical error and coarse grid sizes.

### Contributions

1. Particle level set method for correcting errors during the advection of a level set.

2. A C++ library for performing level set computation.