Distance Fields in Monte Carlo Geometry Processing

We propose to use discrete signed distance rep- resentations in Monte Carlo geometry processing simulations. In particular, we investigate the ap- plication of algebraic and geometric generaliza- tions of traditional signed distance fields. These are means to unify signed distance and closest point queries that are required by the walk-on- spheres algorithmic framework. We apply these to plane shapes enclosed by parametric polynomial boundaries. Our tests quantify the performance- accuracy trade-off compared to brute force closest point queries on test shapes.