Finite volume distance field and its application to medial axis transforms

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Xia, Hao and Tucker, Paul G (2010) Finite volume distance field and its application to medial axis transforms. International Journal for Numerical Methods in Engineering, 82 (1). pp. 114-134. ISSN 0029-5981

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Abstract

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.

Item Type: Article
Keywords: finite volume; wall distance; Eikonal equation; α-shape; medial axis transform
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Subjects: T Technology > TA Engineering (General). Civil engineering (General) > TA0349 Mechanics of engineering. Applied mechanics
T Technology > TL Motor vehicles. Aeronautics. Astronautics > TL0500 Aeronautics. Aeronautical engineering
Depositing User: Hao Xia
Date Deposited: 04 Mar 2013 08:46
Last Modified: 04 Mar 2013 08:46
URI: http://sro.sussex.ac.uk/id/eprint/43843

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