The Practical Generation and Use of Geographic Triangular Element Data Structures

Most computer contour mapping of irregularly spaced data points is performed using an intermediate rectangular grid. An alternative method is proposed whereby a map area is automatically divided into suitable triangular domains with a data point at each vertex. Surface estimation and contour plotting are then performed independently for each triangle using a measured or bestfit plane associated with each data point. The approach requires the utilization of three non-original aspects: (1) the derivation of a local homogeneous "area" coordinate system for any arbitrary triangle; (2) the construction of a data-structure linking each triangular domain with its three neighbouring triangles and three associated data points, and (3) the use of a "conforming" triangular finite-element interpolating function. Use of the first two of these concepts permits the economic generation and optimization of a triangular mesh from a set of data points. Optimization criteria used to define the "best" triangular partition are described in some detail, along with computer timing for this step. Merging of adjacent or overlapping data sets is readily performed by initial connection followed by re-optimization. The method may be extended to higher dimensions. Polygon encoding may be performed using triangular elements with chain structures, thus simplifying topological error detection. Use of the first and third concepts permits the interpolation of a smooth surface over the whole map area even though each triangular element is estimated and plotted independently. The requirements for a suitable interpolating function are discussed, and an interpolant is suggested that preserves elevation and slope at each data point as well as elevation and slope continuity between domains. Contour line resolution is then a function of local data point density.