Hierarchical RLE level set

Abstract

This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set ) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000×3000×3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the H-RLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage.

A fast level set framework for large three-dimensional topography simulations

“…Recently, the hierarchical run-length encoded (HRLE) level set data structure was developed [13]. This data structure efficiently stores the level set values of a subset of all grid points in lexicographical order.…”

“…We implemented exactly the same data structure as described in [13], where a detailed description of the HRLE data structure can be found.…”

“…The HRLE data structure can be setup by inserting all defined grid points (i, j, k) in lexicographical order (with reversed significance (k, j, i) to be consistent with [13]) together with their level set values. Undefined runs are automatically created if grid points are skipped.…”

“…In order to obtain linear scaling algorithms, in spite of neighbor access, stencils of iterators can be used and moved simultaneously over the whole data structure [13]. For this purpose our iterator allows the definition of an offset.…”

“…9 and resolved on a grid with lateral dimensions 1500 × 1500. The etching rate is set proportional to the incoming flux (13). Fig.…”