A new algorithm for constructing Delaunay polyline is represented in this paper. It is used in parallel Delaunay triangulation. The represented algorithm works in two steps. At first, Convex Hull of ...all points is de termined. After that, the algorithm starts moving from the most left point of the convex hull in the positive x direction. The search of the closest points is used in this task. The algorithm searches for triples of points which circumcircle is empty. The most right point of such circumcircle is taken and added to Delaunay polyline. The algorithm moves to this point and a search for the empty circumcircle is repeated until convex hull is reached again. The algorithm is fast, uses low amount of memory, and works at best on uniform distribution of input points.
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