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On minimum-area hulls

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Algorithms — ESA '96 (ESA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1136))

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Abstract

We study some minimum-area hull problems that generalize the notion of convex hull to star-shaped and monotone hulls. Specifically, we consider the minimum-area star-shaped hull problem: Given an n-vertex simple polygon P, find a minimum-area, star-shaped polygon P * containing P. We also consider the case in which P * is required to be monotone (the minimum-area monotone hull problem).

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References

  1. E. M. Arkin, Y-J. Chiang, M. Held, J. S. B. Mitchell, V. Sacristan, S. S. Skiena, and T-C. Yang. On minimum-area hulls. Manuscript, 1996. Available on http://ams.sunysb.edu/∼jsbm/jsbm.html

    Google Scholar 

  2. E. M. Arkin, S. Khuller, and J. S. B. Mitchell. Geometric knapsack problems. Algorithmica, 10:399–427, 1993.

    Google Scholar 

  3. M. J. Atallah. Computing the convex hull of line intersections. J. Algorithms, 7:285–288, 1986.

    Google Scholar 

  4. J. S. Chang. Polygon optimization problems. Report 240, Comput. Sci. Div., New York Univ., New York, NY, 1986.

    Google Scholar 

  5. J. S. Chang and C. K. Yap. A polynomial solution for the potato-peeling problem. Discrete Comput. Geom., 1:155–182, 1986.

    Google Scholar 

  6. B. Chazelle, H. Edelsbrunner, M. Grigni, L. Guibas, J. Hershberger, M. Sharir, and J. Snoeyink. Ray shooting in polygons using geodesic triangulations. In Proc. 18th JCALP'91, vol. 510, Springer LNCS, pages 661–673.

    Google Scholar 

  7. B. Chazelle and L. J. Guibas. Visibility and intersection problems in plane geometry. Discrete Comput. Geom., 4:551–581, 1989.

    Google Scholar 

  8. K. Daniels. The restrict/evaluate/subdivide paradigm for translational containment. In Fifth MSI Stony Brook Workshop on Computational Geometry, 1995.

    Google Scholar 

  9. K. Daniels and V. Milenkovic. Personal communication, 1995.

    Google Scholar 

  10. K. Daniels and V.J. Milenkovic. Multiple translational containment. Part I: An approximation algorithm. Algorithmica, to appear.

    Google Scholar 

  11. D. Eppstein, M. Overmars, G. Rote, and G. Woeginger. Finding minimum area k-gons. Discrete Comput. Geom., 7:45–58, 1992.

    Google Scholar 

  12. J. Erickson and R. Seidel. Better lower bounds on detecting affine and spherical degeneracies. In Proc. FOCS'1993, pages 528–536.

    Google Scholar 

  13. R. Fleischer, K. Mehlhorn, G. Rote, E. Welzl, and C. K. Yap. Simultaneous inner and outer approximation of shapes. Algorithmica, 8:365–389, 1992.

    Google Scholar 

  14. A. Gajentaan and M. H. Overmars. On a class of O(n 2) problems in computational geometry. Comput. Geom. Theory Appl., 5:165–185, 1995.

    Google Scholar 

  15. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 2:209–233, 1987.

    Article  Google Scholar 

  16. Z. Li. Compaction algorithms for non-convex polygons and their applications. Ph.d. Thesis, Harvard University, Division of Applied Sciences, 1994.

    Google Scholar 

  17. Z. Li and V. Milenkovic. A compaction algorithm for non-convex polygons and its application. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 153–162, 1993.

    Google Scholar 

  18. V. Milenkovic, K. Daniels, and Z. Li. Automatic marker making. In Proc. 3rd Canad. Conf. Comput. Geom., pages 243–246, 1991.

    Google Scholar 

  19. V. Milenkovic, K. Daniels, and Z. Li. Placement and compaction of nonconvex polygons for clothing manufacture. In Proc. 4th Canad. Conf. Comput. Geom., pages 236–243, 1992.

    Google Scholar 

  20. D. M. Mount and R. Silverman. Packing and covering the plane with translates of a convex polygon. J. Algorithms, 11:564–580, 1990.

    Google Scholar 

  21. F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, NY, 1985.

    Google Scholar 

  22. G. T. Toussaint and H. ElGindy, A counterexample to an algorithm for computing monotone hulls of simple polygons. Pattern Recogn. Lett., 1:219–222, 1983.

    Google Scholar 

  23. G. T. Toussaint. A linear-time algorithm for solving the strong hidden-line problem in a simple polygon. Pattern Recogn. Lett., 4:449–451, 1986.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Applied Mathematics and Statistics, SUNY, 11794-3600, Stony Brook, NY, USA

    Esther M. Arkin, Yi-Jen Chiang & Joseph S. B. Mitchell

  2. Institut für Computerwissenschaften, Universität Salzburg, Jakob-Haringer Str. 2, A-5020, Salzburg, Austria

    Martin Held

  3. Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028, Barcelona, Spain

    Vera Sacristan

  4. Computer Science, SUNY, 11794-4400, Stony Brook, NY

    Steven S. Skiena

  5. Computer Science, Kyungsung University, 110, DaeYeon-dong, Nam-gu, 608-736, Pusan, Korea

    Tae-Cheon Yang

Authors
  1. Esther M. Arkin
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  2. Yi-Jen Chiang
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  3. Martin Held
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  4. Joseph S. B. Mitchell
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  5. Vera Sacristan
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  6. Steven S. Skiena
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  7. Tae-Cheon Yang
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Editor information

Josep Diaz Maria Serna

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© 1996 Springer-Verlag Berlin Heidelberg

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Arkin, E.M. et al. (1996). On minimum-area hulls. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_66

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  • DOI: https://doi.org/10.1007/3-540-61680-2_66

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61680-1

  • Online ISBN: 978-3-540-70667-0

  • eBook Packages: Springer Book Archive

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