The paper presents a new robust method for finding points of intersection of line segments in the plane. In this method the subdivision of the plane based on the Delaunay triangulation plays the main role. First, the Delaunay triangulation spanning the end points of line segments is constructed. Next, for line segments that are not realized by Delaunay edges, midpoints are inserted recursively ...

The edge-flip technique can be used for transforming any existing triangular mesh into one that satisfies the Delaunay condition. Although several implementations for generating Delaunay triangulations are known, to the best of our knowledge no full parallel GPU-based implementation just dedicated to transform any existent triangulation into a Delaunay triangulation has been reported yet. In th...

In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enforcing boundary conformity—ensuring that triangulation edges cover the boundaries (both interior an...

Let S be a finite set of points in the Euclidean plane, and let E be the complete graph whose point-set is S. Chew, in 1986, proved a lower bound of π/2 on the stretch factor of the Delaunay triangulation of S (with respect to E), and conjectured that this bound is tight. Dobkin, Friedman, and Supowit, in 1987, showed that the stretch factor of the Delaunay triangulation of S is at most π( √ 5 ...

Facial features determination is essential in many applications such as personal identification, 3D face modeling and model based video coding. Fast and accurate facial feature extraction is still a filed to be explored. In this paper, an automatic extracting algorithm is developed to locate “key points” of facial features. The Delaunay Triangulation/Voronoi Diagram technique well known in comp...