Related papers: Morphing Rectangular Duals
A rectangular dual of a graph $G$ is a contact representation of $G$ by axis-aligned rectangles such that (i)~no four rectangles share a point and (ii)~the union of all rectangles is a rectangle. The partial representation extension problem…
We consider the problem of morphing between contact representations of a plane graph. In an $\mathcal F$-contact representation of a plane graph $G$, vertices are realized by internally disjoint elements from a family $\mathcal F$ of…
A rectangular dual of a plane graph $G$ is a contact representation of $G$ by interior-disjoint rectangles such that (i) no four rectangles share a point, and (ii) the union of all rectangles is a rectangle. In this paper, we study…
A morph between two straight-line planar drawings of the same graph is a continuous transformation from the first to the second drawing such that planarity is preserved at all times. Each step of the morph moves each vertex at constant…
A plane graph is said to be a rectangular graph if each of its edges can be oriented horizontal or vertical, its internal regions are four-sided and it has a rectangular enclosure. If dual of a planar graph is a rectangular graph, then the…
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. If…
A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their…
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. Only…
We describe an algorithm that morphs between two planar orthogonal drawings $\Gamma_I$ and $\Gamma_O$ of a connected graph $G$, while preserving planarity and orthogonality. Necessarily $\Gamma_I$ and $\Gamma_O$ share the same combinatorial…
We prove that, given two topologically-equivalent upward planar straight-line drawings of an $n$-vertex directed graph $G$, there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and…
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an $n$-vertex planar graph and two planar straight-line drawings of the graph…
Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…
We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound. Further, we prove…
In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an $n$-vertex planar graph, there exists a…
We consider quadrangles of perimeter $2$ in the plane with marked directed edge. To such quadrangle $Q$ a two-dimensional plane $\Pi\in\mathbb{R}^4$ with orthonormal base is corresponded. Orthogonal plane $\Pi^\bot$ defines a plane…
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
A plane graph is rectilinear planar if it admits an embedding-preserving straight-line drawing where each edge is either horizontal or vertical. We prove that rectilinear planarity testing can be solved in optimal $O(n)$ time for any plane…
We consider the problem of morphing between two planar drawings of the same triangulated graph, maintaining straight-line planarity. A paper in SODA 2013 gave a morph that consists of $O(n^2)$ steps where each step is a linear morph that…
A rectangular drawing of a planar graph $G$ is a planar drawing of $G$ in which vertices are mapped to grid points, edges are mapped to horizontal and vertical straight-line segments, and faces are drawn as rectangles. Sometimes this latter…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…