1,461 research outputs found
Optimal Morphs of Convex Drawings
We give an algorithm to compute a morph between any two convex drawings of
the same plane graph. The morph preserves the convexity of the drawing at any
time instant and moves each vertex along a piecewise linear curve with linear
complexity. The linear bound is asymptotically optimal in the worst case.Comment: To appear in SoCG 201
Convexity-Increasing Morphs of Planar Graphs
We study the problem of convexifying drawings of planar graphs. Given any
planar straight-line drawing of an internally 3-connected graph, we show how to
morph the drawing to one with strictly convex faces while maintaining planarity
at all times. Our morph is convexity-increasing, meaning that once an angle is
convex, it remains convex. We give an efficient algorithm that constructs such
a morph as a composition of a linear number of steps where each step either
moves vertices along horizontal lines or moves vertices along vertical lines.
Moreover, we show that a linear number of steps is worst-case optimal.
To obtain our result, we use a well-known technique by Hong and Nagamochi for
finding redrawings with convex faces while preserving y-coordinates. Using a
variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and
Nagamochi's result which comes with a better running time. This is of
independent interest, as Hong and Nagamochi's technique serves as a building
block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201
Morphing Planar Graph Drawings Optimally
We provide an algorithm for computing a planar morph between any two planar
straight-line drawings of any -vertex plane graph in morphing steps,
thus improving upon the previously best known upper bound. Further, we
prove that our algorithm is optimal, that is, we show that there exist two
planar straight-line drawings and of an -vertex plane
graph such that any planar morph between and requires
morphing steps
Pole Dancing: 3D Morphs for Tree Drawings
We study the question whether a crossing-free 3D morph between two
straight-line drawings of an -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 steps, while for the latter steps
are always sufficient and sometimes necessary.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
On contractible edges in convex decompositions
Let be a convex decomposition of a set of points in
general position in the plane. If consists of more than one polygon, then
either contains a deletable edge or contains a contractible edge
A Note on Plus-Contacts, Rectangular Duals, and Box-Orthogonal Drawings
A plus-contact representation of a planar graph is called -balanced if
for every plus shape , the number of other plus shapes incident to each
arm of is at most , where is the maximum degree
of . Although small values of have been achieved for a few subclasses of
planar graphs (e.g., - and -trees), it is unknown whether -balanced
representations with exist for arbitrary planar graphs.
In this paper we compute -balanced plus-contact representations for
all planar graphs that admit a rectangular dual. Our result implies that any
graph with a rectangular dual has a 1-bend box-orthogonal drawings such that
for each vertex , the box representing is a square of side length
.Comment: A poster related to this research appeared at the 25th International
Symposium on Graph Drawing & Network Visualization (GD 2017
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