Finding Thin Points in an Abstract Cellular Complex

Abstract

This research describes an algorithm to find “thin points'” in a solid represented as an Abstract Cellular Complex. The algorithm is mostly iterative, adding one face at a time to a set of previously selected faces, and choosing the selections that produce the loops with the shortest lengths for the next iteration. The output from the algorithm is a set of loops that indicate the thinnest portions of the solid. As implemented, the algorithm allows a threshold to be set to limit the number of loops that are selected in each iteration. The results indicate that, while it does occasionally produce errors, the algorithm is mostly accurate, and a lower threshold increases its speed, without negatively affecting its accuracy.