Block model conversion using binary space partitioning trees

Abstract

This paper presents an efficient block model conversion algorithm that converts a general polyhedron into a set of discrete blocks. Block model conversion is an important problem in three-dimensional orebody modeling where solid shells representing orebody zones must be discretized so that geostatistical or conventional ore reserve estimation methods can be used to estimate grades of individual blocks. However, the problem has not received adequate treatment. The core of the conversion task is repeated applications of a point-in-polyhedron test using a ray casting technique. Naive implementation of this test procedure is too slow for general polyhedra consisting of hundreds of faces. To speed up the process, an efficient space subdivision scheme is employed, which is known as a Binary Space Partitioning Tree. The resulting algorithm is not only efficient, but also robust, and has been incorporated into a three-dimensional mine modeling, visualization and information system developed by the author.