Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

We discuss adaptive enumeration and rendering methods for implicit surfaces , using octrees computed with aane arithmetic, a new tool for range analysis. AAne arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster. We also describe applications of aane arithmetic to intersection and ray tracing of implicit surfaces.