Computing and Reducing Slope Complexes

  • Walter G. KropatschEmail author
  • Rocio M. Casablanca
  • Darshan Batavia
  • Rocio Gonzalez-Diaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11382)


In this paper we provide a new characterization of cell decomposition (called slope complex) of a given 2-dimensional continuous surface. Each patch (cell) in the decomposition must satisfy that there exists a monotonic path for any two points in the cell. We prove that any triangulation of such surface is a slope complex and explain how to obtain new slope complexes with a smaller number of slope regions decomposing the surface. We give the minimal number of slope regions by counting certain bounding edges of a triangulation of the surface obtained from its critical points.



This research has been partially supported by MINECO, FEDER/UE under grant MTM2015-67072-P. We thank the anonymous reviewers for their valuable comments.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Walter G. Kropatsch
    • 1
    Email author
  • Rocio M. Casablanca
    • 2
  • Darshan Batavia
    • 1
  • Rocio Gonzalez-Diaz
    • 2
  1. 1. Pattern Recognition and Image Processing Group 193/03TU WienViennaAustria
  2. 2.University of SevilleSevilleSpain

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