Extremal Point Tracking on Smooth Surfaces

Kinematic and dynamic simulations of colliding and sliding bodies have traditionally been based on triangulated object representations, which lead to numerical inaccuracies due to wrong surface normals and inaccurate surface representations. Moreover, contact layers are needed to be able to do efficient simulations. For simulating tight fitting assembly operations, this is particularly critical as the size of numerical inaccuracies and the contact layer are similar to the size of the slack during insertion. Simulations using mathematical surface representations such as planes, cylinders, ellipsoids and B-splines are becoming increasingly popular, and are not suffering from these flaws. It is typically more expensive to find contact points, but once they are found, the contact points can be tracked efficiently if the extrema is unique (singularity free). In this paper, we extend this tracking method for efficiently handling, and also tracking in (near)-singular situations. We outline how this can be done and illustrate it on two cases with singularities.