Fast Algorithm for Finding Maximum Distance with Space Subdivision in E2

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9218)


Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum distance of two points in E2. This algorithm is based on a polar subdivision followed by division of remaining points into uniform grid. The main idea of the algorithm is to eliminate as many input points as possible before finding the maximum distance. The proposed algorithm gives the significant speed up compared to the standard algorithm.


Maximum distance Polar space subdivision Uniform 2D grid Points reduction 


  1. 1.
    Clarkson, K.L., Shor, P.W.: Applications of random sampling in computational geometry, II. Discrete Comput. Geom. 4(1), 387–421 (1989)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Dobkin, D.P., Snyder, L.: On a general method for maximizing and minimizing among certain geometric problems. In: Proceedings of the 20th Annual Symposium on the Foundations of Computer Science, pp. 9–17 (1979)Google Scholar
  3. 3.
    Fasshauer, G.E.: Meshfree Approximation Methods with MATLAB. World Scientific Publishing Co., Inc., Singapore (2007)CrossRefMATHGoogle Scholar
  4. 4.
    Hilyard, J., Teilhet, S.: C# Cookbook. O’Reilly Media Inc., Sebastopol (2006)Google Scholar
  5. 5.
    Liu, G., Chen, C.: A new algorithm for computing the convex hull of a planar point set. J. Zhejiang Univ. Sci. A 8(8), 1210–1217 (2007)CrossRefMATHGoogle Scholar
  6. 6.
    Mehta, D.P., Sahni, S.: Handbook of Data Structures and Applications. CRC Press, Boca Raton (2004)CrossRefGoogle Scholar
  7. 7.
    O’Rourke, J.: Computational Geometry in C. Cambridge University Press, Cambridge (1998)CrossRefMATHGoogle Scholar
  8. 8.
    Skala, V.: Fast Oexpected (N) algorithm for finding exact maximum distance in E2 instead of O (N2) or O (N lgN). In: AIP Conference Proceedings, no. 1558, pp. 2496–2499 (2013)Google Scholar
  9. 9.
    Snyder, W.E., Tang, D.A.: Finding the extrema of a region. IEEE Trans. Pattern Anal. Mach. Intell. 2(3), 266–269 (1980)CrossRefGoogle Scholar
  10. 10.
    Vince, J.: Geometric Algebra for Computer Graphics. Springer, Berlin (2008)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Applied SciencesUniversity of West BohemiaPlzenCzech Republic

Personalised recommendations