EASAL (Efficient Atlasing, Analysis and Search of Molecular Assembly Landscapes)

We leverage a mix of classical concepts such as stratifications of semialgebraic sets, and recent theoretical results concerning configuration spaces with a convex parametrization. These lead to a key observation that most regions of assembly and packing configuration spaces indeed have a convex parametrization. In this they differ starkly by from configuration spaces used for folding, or structure determination, for example. This observation leads to (1) a novel, efficient and intuitive representation of configuration spaces which we call the Atlas; (2) an efficient algorithm for generating the Atlas and sampling the configuration space. The latter uses recent algorithms for efficiently realizing geometric constraint systems.