Approximating the Minimum-Bounding Box of a 3D Model with Minimum Spans for Flush Edges

Abstract

In this paper, a method for determining the approximated minimum-bounding box is presented. This method can only be used in the model that has finite vertices. A concept of the minimum span is introduced to determine one length of the bounding box according to a flush edge. After calculating a minimum span, the minimum-area rectangle of the projection is required to be one candidate of minimum-bounding boxes. In many applications, the volume of the bounding box is requested as small as possible. This paper provides an additional property to keep both one length and one rectangle of the bounding box are as small as possible.