Hausdorff and Minimal Distancesbetween Parametric Freeforms in R~2 and R~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~2 or R~3. The events at which the Haus-dorff/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.