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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 732365, 9 pages
http://dx.doi.org/10.1155/2012/732365
Research Article

Polygon Morphing and Its Application in Orebody Modeling

Department of Mathematics, Hacettepe University, Beytepe, 06800 Ankara, Turkey

Received 2 December 2011; Revised 15 February 2012; Accepted 27 February 2012

Academic Editor: P. Liatsis

Copyright © 2012 Hacer İlhan and Haşmet Gürçay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Three different polygon morphing methods are examined. The first one is based on the utilization of the trimmed skeleton of the symmetric difference of the source and target polygons as an intermediate polygon. The second one reduces the problem to the problem of morphing compatible planar triangulations and utilizes the representation of planar triangulations as a matrix constructed using barycentric coordinates of the planar triangulation's vertices relative to their neighbors. The third and last one describes the polygon by the parametric curve representation based on estimated Fourier parameters and thus transfers the morphing process to Fourier parametric space. The different features and comparative results of these methods are shown by the tests with different examples. These methods are used for generating a set of polygonal sections from two nonplanar polygonal sections which are nearly planar in 3D before constructing a three-dimensional object from these nonplanar sections.