Abstract: A rapid and efficient method for triangulating random points is based on a "circular" triangulation strategy that allows the deletion of data points from the data set during triangulation. In one embodiment, data is initially preprocessed by sorting and is put into a sparse matrix, while in another embodiment, data is preprocessed directly into a uniform grid prior to the triangulation strategy. A circular queue is used to govern the triangulation process and allows dynamic update of the internal matrix or grid data structure. A substantial decrease in complexity is provided by the triangulation strategy as the number of points to be searched for triangle points decreases as the triangles are created. The method is stable and fast and is not sensitive to difficult cases such as collinear or nearly collinear points.