Abstract
For a given convex polygon with inner angle no less than \(\frac{2}{3}\pi\) and boundary edge bounded by [l, αl] for 1≤ α ≤ 1.4, where l is a given standard bar’s length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by [βl,2l], where β is a given constant and meets \(0 < \beta <\frac{1}{2}\), and (ii) the number of non-standard bars in the triangulation is minimum. This problem is motivated by practical applications and has not been studied previously. In this paper, we present a heuristic to solve the above problem, which is based on the heuristic to generate a triangular mesh with more number of standard bars and shorter maximal edge length, and a process to make the length of each edge lower bounded. Our procedure is simple and easily implemented for this problem, and we prove that it has good performance guaranteed.
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© 2005 Springer-Verlag Berlin Heidelberg
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Xu, Y., Dai, W., Katoh, N., Ohsaki, M. (2005). Triangulating a Convex Polygon with Small Number of Non-standard Bars. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_49
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DOI: https://doi.org/10.1007/11533719_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
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