The partitioning of a single space or map region into triangles or triangular regions has proved to be very useful in numerous diverse applications of geographic information systems. Triangulated irregular networks (TINs) have been successfully used in applications in elevation modeling and representation, in network analysis and routing problems, in land use and hydrologic studies, in roadway design and landscape visualization, in nearest-neighbor search and zoning problems, and in many other searching, sorting, and spatial data organization problems.