Orebody modelling by optimal surface reconstruction

Abstract

The general problem of automatically constructing a three-dimensional orebody shape from irregularly spaced points (provided by drill-hole intersections) on the outer surface of the orebody is discussed, and two methods, Dijkstra’s algorithm and the centre-of-gravity algorithm, are proposed for its solution. The threedimensional shape is constructed as a set of triangular tiles. The problem is reduced to construction of a sequence of partial approximations, each of which connects planar contours on two adjacent planes. An improvement to the centre-of-gravity algorithm previously published by one of the authors is presented and Dijkstra’s algorithm is proposed as an optimal alternative. Dijkstra’s algorithm is used effectively in graph theory to find the shortest path through a directed graph with weighted arcs. The proposal here is to adapt the algorithm to three-dimensional orebody reconstruction from planar shapes by defining the arcs as the sides of the triangular tiles and setting the weight of the arc to a cost function equal to the area of the triangle represented by the tile. The methods are illustrated by simple examples and demonstrated on a complex, real orebody.