#
Delaunay Triangulation Using a Uniform Grid

Cheng-Ling Lin, WPI CS Department

## Introduction

This paper presents an algorithm for computing the Delaunay
triangulation of 2D points. With a given number of randomly generated 2D
points, this algorithm can generate Delaunay triangles to connect all
points with linear time complexity.

One of the application of Delaunay triangulation is Finite Element
Analysis (FEA). After FEA computation, the coordinations of mesh may be
very different with original coordinations. Delaunay triangulation can
help to re-construct the relations between coordinations.

## Description

The steps of this algorithm is:

- Preprocessing the data.
Divide the whole point distributed area into grids with around the
same number of grids and points. Based on the coordination of points,
put all points into corresponsing grids.

- Forming a triangle
Find the point somewhere near by the middle to start, finding its
nearest to form a edge. Scan the right side of this edge, finding the
point which has the largest angle between that point and two end of the
edge. Then scanning the are of circle which passing the ends of edge and
the point, if there is point inside the circle, use that point to form
another circle and scan again until no point inside circle.

- Putting the triangles together
Find out all Delaunay triangle based on above algorithm. While
looking for triangles, putting all new edges of found triangles into a
queue and remove the edges which used by two triangle or knwon is a
boundary edge out from the queue. repeat the process until the queue
is empty, then the triangulation is finished.

## Conclusion

The algorithm is very easy for implementation, but there is no extension
for 3D points.

## Reference

Paper from IEEE Computer Graphics and Applications 1993-05,
by Tsung-Pao Fang and Les A. piegl of University of South Florida.

*cllin@cs.WPI.EDU *