A new general triangulation method for planar contours

Abstract

The problem of approximating the surface spanning a given set of 3D points as a polyhedron of triangular faces (“triangulation”) is a significant one, and has many applications in the fields of computer graphics and computer vision. In this paper, several solutions to this problem are reviewed. These solutions can be grouped into two classes, and particular emphasis is given to the class of surfaces spanned by parallel planar contours. For a contour pair P 0 ,P 1 ,...P m−1 and Q 0 ,Q 1 ,...Q n−1 , a graph theoretic approach can be used to arrive at a class of solutions, each requiring exactly m+n steps to triangulate the pair. Existing methods (both rigorous and heuristic) for extracting a particular solution from this group are reviewed, and a new heuristic based on inter-contour coherence is proposed. This heuristic is being used in the field of Ultrasonic Non-destructive Evaluation to produce images of flaws in pressure vessels, and its performance is shown to compare favorably with methods of greater computational complexity. It is believed that this heuristic can also be used with success in industrial vision systems where similar contours are obtained using a laser range finder.