Revisiting adaptively sampled distance fields

Implicit surfaces are a powerful shape description for many applications in computer graphics. An implicit surface is defined by a function f:R³→R as the set of points satisfying f(p)=0. Implicit representation becomes more effective when f is a signed distance function, i.e., when |f| gives the distance to the closest point on the surface and f is negative inside the object and positive outside the object bounded by the surface. The distance function to an arbitrary surface does not have a simple analytic description, and we must resort to approximations. One simple solution is to use a volumetric representation, constructed by sampling f uniformly, but such models are very large and their resolution is limited by the sampling rate. Frisken et al. (2000) proposed adaptively sampled distance fields (ADFs) as a way to overcome these problems. The authors revisit the ADFs and make two contributions to the original framework. First, we analyse the ADF representation and discuss some possible improvements. Second, we show how to compute ADFs more efficiently