Extreme points of a large 3D point set along multiple directions

In reverse engineering CAD modeling, a facet model is usually constructed from a large point cloud data which are obtained from a surface scanning process. The number of points in the point cloud data may range from hundred thousands to several millions depending on the user-defined precision. As a result, the facet model becomes very ‘large’ in terms of number of facets or vertices. The computational effort required to manipulate such a large set of data becomes enormous. This effort is significant even for some simple operations, e.g. rotating, scaling and translation. In this paper, an algorithm is proposed to determine the extreme points in a large 3D point set along multiple directions. This algorithm uses a cylindrical grid approximation technique to give both approximate solution and exact solution. This algorithm can be used to accelerate the computational process of some geometric problems on a large model, e.g., the minimum bounding box of a facet model [Comput Aid Des 20 (1988) 506; Comput Struct 79I (2001) 1433; Int J Comput Inform Sci 14 (1985) 183] and the ‘fitness’ problem of a model into a bounded volume [Comput Aid Des 20 (1988) 506].