Bending and kissing: Computing self-contact configurations of planar loops with revolute joints

In recent work, we introduced the notion of a construction tree of simplices for a linkage L under distance constraints, and showed that the deformation space DSpace(L) of such an L (i.e., its configuration space CSpace(L) modulo rigid motions of ambient space respecting all system specifications) carries geometrically-defined simplex-based parameters that endow it with a ldquopractically piecewise-convexrdquo structure. Here we present parametrizations of contact deformations of planar loops with revolute joints. We show that the bending and kissing loci, which include the self-contact subspace DSContact (generally as a strict subset) can be efficiently described by triangle-based parameters. These results further demonstrate the effectiveness of the simplex-based approach.