Given an n-vertex graph and two straight-line planar drawings of the graph that have the same faces and the same outer face, we show that there is a morph (i.e., a continuous transformation) between the two drawings that preserves straight-line planarity and consists of O(n) steps, which we prove is optimal in the worst case. Each step is a unidirectional linear morph, which means that every ve...

Recently, some advanced algorithms for straight line drawings of planar graphs have been introduced. However, these algorithms produce drawings with many small angles. Their drawings are not aesthetically nice. Our goal is to resolve these problems by a beautifier. We consider the angles of planar straight line drawings. In a first phase we compute maximal angles by repeatedly solving a linear ...

Wilson loops which are small deviations from straight, infinite lines, called wavy lines, are considered in the context of the AdS/CFT correspondence. A single wavy line and the connected correlation function of a straight and wavy line are considered. It is argued that, to leading order in “waviness”, the functional form of the loop is universal and the coefficient, which is a function of the ...

We introduce forest straight-line programs (FSLPs) as a compressed representation of unranked ordered node-labelled trees. FSLPs are based on the operations of forest algebra and generalize tree straight-line programs. We compare the succinctness of FSLPs with two other compression schemes for unranked trees: top dags and tree straight-line programs of first-child/next sibling encodings. Effici...

In this paper, we arithmetically describe the convex hull of a digital straight segment by three recurrence relations. This characterization gives new insights into the combinatorial structure of digital straight segments of arbitrary length and intercept. It also leads to two on-line algorithms that computes a part of the convex hull of a given digital straight segment. They both run in consta...

It is shown that every disconnected vertex-colored plane straight line graph with no isolated vertices can be augmented (by adding edges) into a connected plane straight line graph such that the new edges respect the coloring and the degree of every vertex increases by at most two. The upper bound for the increase of vertex degrees is best possible: there are input graphs that require the addit...

We present a simple algorithm for computing straight skeletons of planar straight-line graphs. We exploit the relation between motorcycle graphs and straight skeletons, and introduce a wavefront-propagation algorithm that circumvents the expensive search for the next split event. Our algorithm maintains the simplicity of the triangulation-based algorithm by Aichholzer and Aurenhammer but has a ...

Straight line motion is one of the most fundamental target motions. Its modeling has been well studied for unconstrained targets, e.g., air targets. However, the existing straight line motion models can not be directly used for the constrained case on straight line tracks, which has wide application, e.g., in ground target tracking. In this paper, modeling of the constrained target motion on a ...

This technical brief presents a refined slabbing method, originally used for free-flying robots, for finding efficient paths for nonholonomic robots. Our method takes kinematic constraints and reversal maneuvers into account. We create orientation levels for each orientation configuration of the robot. The slopes of slabbing lines in each orientation level match the orientation of a robot in th...

Recently developed manipulator control languages typically specify motions as sequences ofpoints through which a tool afixed to the end of the manipulator is to pass. The effectiveness of such motion specijication formalisms is greatly increased if the tool moves in a straight line between the user-specijied points. This paper describes two methods for achieving such straight line motions. The ...