Magnetism and Minimal Surfaces -- a Different Tool for Surface Design

dc.contributor.authorGruber, Franzen_US
dc.contributor.authorGlaeser, Georgen_US
dc.contributor.editorDouglas W. Cunningham and Gary Meyer and Laszlo Neumannen_US
dc.date.accessioned2013-10-22T07:39:41Z
dc.date.available2013-10-22T07:39:41Z
dc.date.issued2007en_US
dc.description.abstractThe design of free form surfaces is usually based on NURBS and it works well to quickly get shapes that a designer intends to create. Such surfaces then have desired properties like given border lines and C1 or C2 continuity along lines where several surfaces touch. Our approach is to create surfaces with certain physical properties that designers often need. Given a closed or not closed border line, can we then find an elastic surface (comparable with a rubber surface) with the property requiring that in each point the tension is equally distributed? This is simplified spoken the condition for a minimal surface. Our solution does not use any differential equations but rather the following idea: We start from a patch that may be planar or part of a cylinder or any easy to define surface. This patch is tesselated in such a way that the vertices have roughly equal distances. Each point is considered to be magnetic. Now we start a converging real-time-iteration that allows the points to move according to the rules of magnetism. Border lines or parts of them may be fixed and manipulated. The corresponding algorithm is adapted from earlier algorithms by Fruchterman et al. The result is an approximation to a minimal surface that is defined by the fixed border lines. The advantage of such a surface design is twofold: First, the problem is hard to solve exactly by means of differential equations, and second the algorithm works interactively in real time. This means that the designer can change shapes almost as quickly as with conventional free form surfaces. Finally, the surface is already suitably triangulated.en_US
dc.description.seriesinformationComputational Aesthetics in Graphics, Visualization, and Imagingen_US
dc.identifier.isbn978-3-905673-43-2en_US
dc.identifier.issn1816-0859en_US
dc.identifier.urihttps://doi.org/10.2312/COMPAESTH/COMPAESTH07/081-088en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Minimal surfaces, Fair surface design, Force directed placement, Calculus of variations;en_US
dc.titleMagnetism and Minimal Surfaces -- a Different Tool for Surface Designen_US
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