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<p><strong>Abstract.</strong> A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construction of spherical Delaunay and Voronoi tessellations. The algorithms aredoi:10.5194/gmd-6-1353-2013 fatcat:koaytvybgvhrzlbkfq4qjbydtm