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Density of straight-line 1-planar graph drawings
Information Processing Letters, 2013 A 1-planar drawing of a graph is such that each edge is crossed at most once. In 1997, Pach and Toth showed that any 1-planar drawing with n vertices has at most 4n-8 edges and that this bound is tight for n>=12. We show that, in fact, 1-planar drawings with n vertices have at most 4n-9 edges, if we require that the edges are straight-line segments. We
Walter Didimo
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Line-drawing interpretation: straight lines and conic sections
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1988Line drawings of man-made scenes often exhibit instances of straight lines and conic sections, i.e. ellipses, parabolas, and hyperbolas. Constraints imposed on the scene by such instances are investigated, under the assumption of general viewpoint, i.e.
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On the Area Requirements of Straight-Line Orthogonal Drawings of Ternary Trees
, 2018 We prove that every n-node ternary tree has a planar straight-line orthogonal drawing in \(O(n^{1.576})\) area, improving upon the previously best known \(O(n^{1.631})\) bound. Further, we present an upper bound, the outcomes of an experimental evaluation, and a conjecture on the area requirements of planar straight-line orthogonal drawings of complete
Barbara Covella +2 more
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On the area requirements of planar straight-line orthogonal drawings of ternary trees
Theoretical Computer Science, 2021 In this paper, we study the area requirements of planar straight-line orthogonal drawings of ternary trees. We prove that every ternary tree admits such a drawing in sub-quadratic area. Further, we present upper bounds, the outcomes of an experimental
Fabrizio Frati, Maurizio Patrignani
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From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-Line Drawings and Morphs
Lecture Notes in Computer Science, 2021 The algorithm of Tutte for constructing convex planar straight-line drawings and the algorithm of Floater and Gotsman for constructing planar straight-line morphs are among the most popular graph drawing algorithms.
Fabrizio Frati, Giuseppe Di Battista
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Finding straight lines in drawings
Proceedings of the Fourth International Conference on Document Analysis and Recognition, 2002We have developed an efficient method to extract straight lines at any orientation from a line drawing. The method works by extracting the horizontal and vertical lines using the FAST method, detecting the angles of the other lines and applying the FAST method again while the image is rotated to each corresponding angle. The method is efficient because
Juan F. Arias +2 more
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An Algorithm for Straight-Line Drawing of Planar Graphs
Algorithmica, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Harel, Meir Sardas
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