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Finite volume distance field and its application to medial axis transforms
Author(s) -
Xia Hao,
Tucker Paul G.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2762
Subject(s) - medial axis , eikonal equation , mathematics , fast marching method , voronoi diagram , computation , context (archaeology) , representation (politics) , finite volume method , level set (data structures) , differential equation , field (mathematics) , algorithm , mathematical optimization , mathematical analysis , computer science , geometry , artificial intelligence , pure mathematics , physics , paleontology , politics , political science , mechanics , law , biology
Accurate and efficient computation of the nearest wall distance d (or level set) is important for many areas of computational science/engineering. Differential equation‐based distance/level set algorithms, such as the hyperbolic‐natured Eikonal equation, have demonstrated valuable computational efficiency. Here, in the context, as an ‘auxiliary’ equation to the main flow equations, the Eikonal equation is solved efficiently with two different finite volume approaches (the cell‐vertex and cell‐centered). The application of the distance solution is studied for various geometries. Moreover, a procedure using the differential field to obtain the medial axis transform (MAT) for different geometries is presented. The latter provides a skeleton representation of geometric models that has many useful analysis properties. As an alternative to other methods, the current d ‐MAT procedure bypasses difficulties that are usually encountered by pure geometric methods (e.g. the Voronoi approach), especially in three dimensions, and provides better accuracy than pure thinning methods. It is also shown that the d ‐MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Copyright © 2009 John Wiley & Sons, Ltd.