Multiresolution Molecular Shapes

We introduce a multiresolution representation scheme for variable levels of detail of molecular shapes (shapes synthesized as sets of balls). In particular, we consider in our model the exact boundary computation of the the basic union of balls for CPK model and solvent accessible surface as well as the more complex rolling ball solvent contact surface and molecular skin. Our decimation/refinement scheme supports the creation of a hierarchical structure which provides the flexibility to trade run-time traversal speed for storage size and adaptiveness. In our approach we also track the topology of the molecular body at any adaptive level of resolution. Moreover we are able to guarantee a consistent embedding (no self intersections) of any decimated molecular surfaces. The fast traversal version of our data-structure is a classical hierarchy that stores an explicit representation of all the triangles at all levels of resolution and a DAG of dependencies between them. The more adaptive version is a light-weighted tree of points that requires the computation, at traversal time, of the sequences of flips induced by vertex insertion and removal operations. We consider several error norms to evaluate the quality of any adaptive level of detail including support for the estimation of conservative bounds of the exact Hausdorff distance. While the decimation scheme, the hierarchical structure and the error estimates are defined in any dimension, we show practical results for a 2D implementation.