A triangulation algorithm from arbitrary shaped multiple planar contours

Abstract

Conventional triangulation algorithms from planar contours suffer from some limitations. For instance, incorrect results can be obtained when the contours are not convex, or when the contours in two successive slices are very different. In the same way, the presence of multiple contours in a slice leads to ambiguities in defining the appropriate links. The purpose of this paper is to define a general triangulation procedure that provides a solution to these problems. We first describe a simple heuristic triangulation algorithm which is extended to nonconvex contours. It uses an original decomposition of an arbitrary contour into elementary convex subcontours. Then the problem of linking one contour in a slice to several contours in an adjacent slice is examined. To this end, a new and unique interpolated contour is generated between the two slices, and the link is created using the previously defined procedure. Next, a solution to the general case of linking multiple contours in each slice is proposed. Finally, the algorithm is applied to the reconstitution of the external surface of a complex shaped object: a human vertebra.