Examination of a constant-area quadrilateral grid in representation of global digital elevation models

Abstract

The WGS84 ellipsoid is tessellated using quadrilaterals of roughly the same size. This tiling is of general interest to global geographical information systems, but it has special relevance to global digital elevation models based on block averages. The simple relation between the tiling presented and the latitude/longitude reference system makes the tiling easy to implement, and the quadrilateral property of the cells offers regular subdivision like quadtrees. An error analysis gives a strict bound on the difference between cell averages calculated in plane and ellipsoidal coordinates. The mathematical results from this investigation are general and can be applied in error analysis related to other types of quadrilateral meshes. The grid can be easily subdivided into quadtree blocks. The error estimate makes it possible to combine the quadtree structure with standard two-dimensional wavelet representations.

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