Space-Filling Curves

Volume 9 of the series Texts in Computational Science and Engineering pp 129-142


Refinement Trees and Space-Filling Curves

  • Michael BaderAffiliated withDepartment of Informatics, Technische Universität München

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In Sect. 1.1, we introduced quadtrees and corresponding refinement trees, as shown in Fig. 9.1, as efficient data structures for geometric modelling. We have even considered a sequential order on the respective grid cells, which we now recognise as equivalent to a Hilbert curve. In this chapter, we will add the respective details to this idea – we will discuss a highly memory-efficient bitstream data structure to store quadtree and octree structures, extend the idea to general spacetrees, and, above all, introduce how to generate and compute sequential orderings of the grid cells based on space-filling curves.