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Discovering molecules: Pass planning through a gap

We present a new algorithm for a molecular pass planning
through a circle. Our algorithm can solve the given problem
with the significant improvement of accuracy for arbitrary
shaped molecules in comparison with the method using a minimal
bounding sphere. This accuracy is gained by eliminating the
overestimation of the substrate size by the bounding volume
approaches. Our approach is particularly beneficial in cases
where the bounding volume fits poorly to the substrate geometry
as is the case with oblong shaped substrates. We are using a
sampling-based version of the motion path planning and the
Delaunay triangulation to arrange the substrate for the space
search. The successor configurations are then computed
incrementally from the already known configurations until we
find a connected path of the substrate through a circle or we
can claim that such path does not exist.