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Pole dancing: 3D morphs for tree drawings

par Arseneva, Elena;Bose, Prosenjit ;Cano, Pilar;D’Angelo, Anthony;Dujmović, Vida V.;Frati, Fabrizio;Langerman, Stefan ;Tappini, Alessandra
Référence Lecture notes in computer science, 11282 LNCS, page (371-384)
Publication Publié, 2018

Article révisé par les pairs

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Résumé :

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 Θ(n) steps are always sufficient and sometimes necessary.