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.

Online reconstruction of 3D objects from arbitrary cross-sections

“…The first generation of work on the topic of reconstruction from contours (e.g., Batnitzky et al [1981], Fix and Ladner [1998], Fuchs et al [1977], Ganapathy and Dennehy [1982], , , Keppel [1975], Sloan and Painter [1988], Wang and Aggarwal [1986], and Welzl and Wolfers [1994]) studied the problem of interpolation between parallel cross-sections of a single object. Some (e.g., Choi and Park [1994], Christiansen and Sederberg [1978], Ekoule et al [1991], Meyers et al [1991], Shantz [1981], and Zyda et al [1987]) even restrict the problem to scenarios where only a single contour is present in every input slice.…”

A Virtual-Reality Training System for Knee Arthroscopic Surgery

“…Surface mesh is created from the series of 2D contours using the 3D reconstruction algorithm. We use the method proposed by Ganapathy [10] to construct the surface mesh. Since each contour of a single slice can be identified by its two neighboring tissues, there is no correspondence problem in our case.…”

Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches

“…The above definition follows the notation in [43]. In this paper, to simplify the algorithm, every polygonal face in M is subdivided into triangles by the Constrained Delaunay Triangulation (CDT) [44] of a planar contour. If the contour of a polygonal face is not coplanar, we project the vertices of this face onto its least-square plane to apply the CDT.…”