Research output per year
Research output per year
Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, Giordano Da Lozzo, Vincenzo Roselli
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
We consider the problem of morphing between contact representations of a plane graph. In a contact representation of a plane graph, vertices are realized by internally disjoint elements from a family of connected geometric objects. Two such elements touch if and only if their corresponding vertices are adjacent. These touchings also induce the same embedding as in the graph. In a morph between two contact representations we insist that at each time step (continuously throughout the morph) we have a contact representation of the same type. We focus on the case when the geometric objects are triangles that are the lower-right half of axis-parallel rectangles. Such RT-representations exist for every plane graph and right triangles are one of the simplest families of shapes supporting this property. Thus, they provide a natural case to study regarding morphs of contact representations of plane graphs. We study piecewise linear morphs, where each step is a linear morph moving the endpoints of each triangle at constant speed along straight-line trajectories. We provide a polynomial-time algorithm that decides whether there is a piecewise linear morph between two RT-representations of a plane triangulation, and, if so, computes a morph with a quadratic number of linear morphs. As a direct consequence, we obtain that for 4-connected plane triangulations there is a morph between every pair of RT-representations where the “top-most” triangle in both representations corresponds to the same vertex. This shows that the realization space of such RT-representations of any 4-connected plane triangulation forms a connected set.
Original language | English |
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Title of host publication | 35th International Symposium on Computational Geometry (SoCG 2019) |
Editors | Gill Barequet, Yusu Wang |
Place of Publication | Dagstuhl, Germany |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Pages | 10:1-10:16 |
Volume | 129 |
ISBN (Print) | 978-3-95977-104-7 |
DOIs | |
Publication status | Published - 2019 |
Externally published | Yes |
Series | Leibniz International Proceedings in Informatics (LIPIcs) |
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Volume | 129 |
ISSN | 1868-8969 |
Research output: Contribution to journal › Article › Academic › peer-review