ved. Among the five flavors [15] of sequential 2D Delaunay triangulation algorithms, incremental insertion methods (e.g., [8]) are most popular mainly because they are potentially dynamic, simple to implement and easy to be generalized to higher dimensions. However, normally they are not regarded as among the fastest methods. The basic principle of constructing Delaunay triangulation (DT) by in...

In this paper we describe a method for directly generating triangle strips from unstructured point clouds based on onion peeling triangulation (OPT). It is an iterative reconstruction of the convex hulls of point clouds in the 2D plane, and it uses pairs of subsequent layers to establish triangle strips. We compare the obtained triangulations with the results of Delaunay triangulations in terms...

Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest area triangle in the triangulation. There exists a dynamic programming algorithm that computes ...

For any closed compact 2-manifold, there is a finite number of minimal (irreducible) triangulation. Thus, we may obtain any triangulation of a surface by splitting vertices of a minimal triangulation of the surface. The number of vertices in these minimal triangulations is linear in the genus of the underlying surface.

Computing the Delaunay triangulation of n points requires usually a minimum of (n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time.

We present new results concerning the Delaunay triangulation of the set of points of pieces of digital straight lines. More precisely, we show how the triangulation topology follows the arithmetic decomposition of the line slope as well as its combinatorial decomposition (splitting formula). A byproduct is a linear time algorithm for computing the Delaunay triangulation and the Voronoi diagram ...

The traditional image matching algorithms adopt more complex strategies when dealing with mismatch caused by a lot of noise. In this paper, a simple, intuitive and effective noise processing algorithm is proposed based on Delaunay triangulation in computational geometry. The algorithm extracts feature points using SIFT method, respectively establishes Delaunay triangulation in multi-spectral an...

We consider bounding the cardinality of an arbitrary triangulation with smallest angle We show that if the local feature size i e distance between disjoint vertices or edges of the triangulation is within a con stant factor of the local feature size of the input then N O M where N is the cardinality of the triangulation and M is the cardinality of any other triangulation with smallest angle at ...

A triangulation of points in , or a tetrahedronization of points in , is used in many applications. It is not necessary to fulfill the Delaunay criteria in all cases. For large data (more then 5 ∙ 10 points), parallel methods are used for the purpose of decreasing time complexity. A new approach for fast and effective parallel CPU and GPU triangulation, or tetrahedronization, of large data sets...

Hand-held laser scanners are used massively in industry for reverse engineering and quality measurements. In this process, it is difficult for the human operator to scan the target object completely and uniformly. Therefore, an interactive triangulation of the scanned points can assist the operator in this task. Our method computes a triangulation of the point stream generated by the laser scan...