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Finite volume distance field and its application to medial axis transforms

journal contribution
posted on 2023-06-08, 14:31 authored by Hao Xia, Paul G Tucker
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.

History

Publication status

  • Published

Journal

International Journal for Numerical Methods in Engineering

ISSN

0029-5981

Publisher

John Wiley and Sons

Issue

1

Volume

82

Page range

114-134

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2013-03-04

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