Computing the exact arrangement of circles on a sphere, with applications in structural biology
Résumé
Given a collection of circles in a sphere, we adapt the Bentley-Ottmann algorithm to the spherical setting to compute the {\em exact} arrangement of the circles. Assuming the circles are induced by balls, we also extend the algorithm to report the balls covering each face of the arrangement. The algorithm consists of sweeping the sphere by a meridian, which is non trivial because of the degenerate cases and the algebraic specification of event points. The paper focuses on the construction of the arrangement, the predicates and algebraic questions being developed in a companion paper. This construction is motivated by the calculation of parameters describing multi-body contacts in structural biology, so as to go beyond the classical exposed and buried surface areas. As an illustration, statistics featuring spectacular changes wrt traditional observations on protein - protein complexes are provided.
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