Hausdorff and Minimal Distances between Parametric Freeforms in R{sup}2 and R{sup}3

摘要

We present algorithms to derive the precise Hausdorff distance and/or the minimal distance between two freeform shapes, either curves or surfaces, in R{sup}2 or R{sup}3. The events at which the Hausdorff/minimal distance can occur are identified and means to efficiently compute these events are presented. Examples are also shown and the extension to arbitrary dimensions is briefly discussed.