Level-set method: Difference between revisions

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

{{Tone|date=DecemberFebruary 20232024|section}}

[[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.]]

Lumbung was started by Andri Saputra in 2010. Andri studied architecture at the Udayana University between 2004-2008. Upon graduation, he worked with three architecture consultants in Bali to develop experience and knowledge in both western and local architectural practices. Then he also worked and traveled with senior foreign architects from France and Australia for the next 3 years. Afterward, Andri Saputra decided to establish his first architectural firm in 2010, Studio Lumbung Architect. Lumbung Architect is based in Bali and it has around 60 staff employed. They currently have completed projects throughout Bali, Jakarta, Nigeria, and the Bahamas. By recruiting the professional team in his field which includes a team of architects, structural engineers, quantity surveyors, mechanical, electrical, and plumbing engineers, Lumbung Architect strives to provide an excellent solution for the client’s need.

'''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.

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