Level-set method: Difference between revisions

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{{Short description|Conceptual framework used in numerical analysis of surfaces and shapes}}

{{Tone|date=FebruaryDecember 2024|section2023}}

[[File:Levelset-mean-curvature-spiral.ogv|thumb|Video of spiral being propagated by level sets ([[curvature flow]]) in 2D. Left image shows zero-level solution. Right image shows the level-set scalar field.]]

'''Level-set methods''' ('''LSM''') constitute a conceptual framework for using [[level set]]s as a tool for the [[numerical analysis]] of [[Surface (topology)|surface]]s and [[shape]]s. Invented in 1988 by Osher and Sethian, the key advantage of LSM is its ability to perform numerical computations involving [[curve]]s and surfaces on a fixed [[Cartesian grid]] without having to [[Parametric surface|parameterize]] these objects (this is called the ''Eulerian approach'').<ref>{{Citation |last1 = Osher |first1 = S. |last2 = Sethian |first2 = J. A.| title = Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations| journal = J. Comput. Phys.| volume = 79 |issue = 1 |year = 1988 |pages = 12&ndash;49 |url = http://math.berkeley.edu/~sethian/Papers/sethian.osher.88.pdf |doi=10.1016/0021-9991(88)90002-2|bibcode = 1988JCoPh..79...12O |hdl = 10338.dmlcz/144762 |citeseerx = 10.1.1.46.1266|s2cid = 205007680 }}</ref> Importantly, LSM makes it easier to follow shapes with sharp corners or that change [[topology]], for example, when a shape splits in two, develops holes, or the reverse of these operations. These characteristics make LSM an effective method for modeling time-varying objects, like inflation of an [[airbag]], or a drop of oil floating in water.

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[[Image:level set method.png|thumb|right|400px|An illustration of the level-set method]]