Reducing feasible contacts between polyhedral models to red–blue intersections on the sphere

Abstract

Orientation-related problems in geometric design can be naturally expressed on the spherical surface S 2. A wide subset of such problems can be solved directly on the sphere by adapting well-known planar data structures and algorithms. This paper shows that the detection of feasible contacts between two translating polyhedral models can be formulated as a problem of this type. First, a dual spherical representation of polyhedra is introduced, which reduces the contact detection above to finding intersections between two sets of spherical polygons. Next, the red–blue blocks plane sweep algorithm is adapted to obtain both edge intersections and point-in-polygon inclusions in the spherical setting. An experimental comparison of this algorithm against a naı̈ve one shows an increasing advantage of the former as the complexity of the setting grows. The obtained edge–edge and vertex–face polyhedral contacts provide the relevant feature pairs to be tested for interference, leading to considerable savings in collision detection between polyhedral models, as shown in the experimental test performed.