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Pole Dancing: 3D Morphs for Tree Drawings

  • Elena ArsenevaEmail author
  • Prosenjit Bose
  • Pilar Cano
  • Anthony D’Angelo
  • Vida Dujmović
  • Fabrizio Frati
  • Stefan Langerman
  • Alessandra Tappini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with \(O(\log n)\) steps, while for the latter \(\varTheta (n)\) steps are always sufficient and sometimes necessary.

Notes

Acknowledgments

We thank Therese Biedl for pointing out Remark 2. The research for this paper started during the Intensive Research Program in Discrete, Combinatorial and Computational Geometry, which took place in Barcelona, April-June 2018. We thank Vera Sacristán and Rodrigo Silveira for a wonderful organization and all the participants for interesting discussions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Elena Arseneva
    • 1
    Email author
  • Prosenjit Bose
    • 2
  • Pilar Cano
    • 2
    • 3
  • Anthony D’Angelo
    • 2
  • Vida Dujmović
    • 4
  • Fabrizio Frati
    • 5
  • Stefan Langerman
    • 6
  • Alessandra Tappini
    • 7
  1. 1.St. Petersburg State University (SPbU)Saint PetersburgRussia
  2. 2.Carleton UniversityOttawaCanada
  3. 3.Universitat Politècnica de CatalunyaBarcelonaSpain
  4. 4.University of OttawaOttawaCanada
  5. 5.Roma Tre UniversityRomeItaly
  6. 6.Université libre de Bruxelles (ULB)BrusselsBelgium
  7. 7.Università degli Studi di PerugiaPerugiaItaly

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