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In [[computer science]] a [[level set]] [[data structure]] is designed to represent discretely [[Sampling (statistics)|sampled]] dynamic level sets functions.
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===Octree===
The [[octree]] level set method, introduced by Strain in 1999<ref name=Strain>Strain, J. 1999. "Tree methods for moving interfaces." ''[[Journal of Computational Physics]]''. 151(2)616–648.</ref> and refined by Losasso, Gibou and Fedkiw,<ref name=Losasso>Losasso, F., Gibou, F., & Fedkiw, R. 2004. [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.459.1489&rep=rep1&type=pdf Simulating water and smoke with an octree data structure]. [[ACM Transactions on Graphics]]. 23(3)457–462.</ref> and more recently by Min and Gibou<ref name=MinGibou>Min, C. & Gibou, F. 2007. A second order accurate level set method on non-graded adaptive cartesian grids. [[Journal of Computational Physics]]. 225(1)300–321.</ref> uses a tree of nested cubes of which the leaf nodes contain signed distance values. Octree level sets currently require uniform refinement along the interface (i.e. the narrow band) in order to obtain sufficient precision. This representation is efficient in terms of storage, <math>O(n^2),</math> and relatively efficient in terms of access queries, <math>O(\log\, n).</math> An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group<ref name=CASL>
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