Abstract
Given a polygonal path P with vertices p 1, p 2,...,p n and a real number t ≥ 1, a path \(Q = (p_{i_1},p_{i_2},...,p_{i_k})\) is a t-distance-preserving approximation of P if 1 = i 1 < i 2 < ... < i k = n and each straight-line edge (\(p_{i_j}, p_{i_{j+1}}\)) of Q approximates the distance between \(p_{i_j}\) and \(p_{i_{j+1}}\) along the path P within a factor of t. We present exact and approximation algorithms that compute such a path Q that minimizes k (when given t) or t (when given k). We also present some experimental results.
Gudmundsson was supported by NWO, Smid was supported by NSERC.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, H., Blömer, J., Godau, M., Wagener, H.: Approximation of convex polygons. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 703–716. Springer, Heidelberg (1990)
Barequet, G., Goodrich, M.T., Chen, D.Z., Daescu, O., Snoeyink, J.: Efficiently approximating polygonal paths in three and higher dimensions. In: Proceedings 14th Annual ACM Symposium on Computational Geometry, pp. 317–326 (1998)
Callahan, P.B., Kosaraju, S.R.: A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields. Journal of the ACM 42, 67–90 (1995)
Chan, W.S., Chin, F.: Approximation of polygonal curves with minimum number of line segments or minimum error. International Journal of Computational Geometry & Applications 6, 59–77 (1996)
Chen, D.Z., Daescu, O.: Space-efficient algorithms for approximating polygonal curves in two-dimensional space. International Journal of Computational Geometry & Applications 13, 95–111 (2003)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Goodrich, M.T.: Efficient piecewise-linear function approximation using the uniform metric. Discrete & Computational Geometry 14, 445–462 (1995)
Guibas, L.J., Hershberger, J.E., Mitchell, J.S.B., Snoeyink, J.S.: Approximating polygons and subdivisions with minimum link paths. International Journal of Computational Geometry & Applications 3, 383–415 (1993)
Imai, H., Iri, M.: Computational-geometric methods for polygonal approximations of a curve. Computer Vision, Graphics and Image Processing 36, 31–41 (1986)
Imai, H., Iri, M.: Polygonal approximations of a curve-formulations and algorithms. In: Toussaint, G.T. (ed.) Computational Morphology, pp. 71–86. North-Holland, Amsterdam (1988)
Melkman, A., O’Rourke, J.: On polygonal chain approximation. In: Toussaint, G.T. (ed.) Computational Morphology, pp. 87–95. North-Holland, Amsterdam (1988)
Varadarajan, K.R.: Approximating monotone polygonal curves using the uniform metric. In: Proceedings 12th Annual ACM Symposium on Computational Geometry, pp. 311–318 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gudmundsson, J., Narasimhan, G., Smid, M. (2003). Distance-Preserving Approximations of Polygonal Paths. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-24597-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20680-4
Online ISBN: 978-3-540-24597-1
eBook Packages: Springer Book Archive