We prove that any AVL tree admits a linear-area straight-line strictly-upward planar grid drawing, that is, a drawing in which (a) each edge is mapped into a single straight-line segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates. © 1998 Elsevier Science B.V.

We study the practical computation of mitered and beveled offset curves of planar straight-line graphs (PSLGs), i.e., of arbitrary collections of straight-line segments in the plane that do not intersect except possibly at common end points. The line segments can, but need not, form polygons. Similar to Voronoi-based offsetting, we propose to compute a straight skeleton of the input PSLG as a p...

Decisions based on basic geometric entities can only be optimal, if their uncertainty is propagated trough the entire reasoning chain. This concerns the construction of new entities from given ones, the testing of geometric relations between geometric entities, and the parameter estimation of geometric entities based on spatial relations which have been found to hold. Basic feature extraction p...

Many optimizations are easier or more effective for straight-line code (basic blocks). Straight-line code in Forth is limited mainly by calls and returns. Inlining eliminates calls and returns, which in turn makes the basic blocks longer, and increases the effectiveness of other optimizations. In this paper we present a first prototype implementation of ininlining for Gforth.

For every n ∈ N, there is a straight-line drawing Dn of a planar graph on n vertices such that in any crossing-free straight-line drawing of the graph, at most O(n) vertices lie at the same position as in Dn. This improves on an earlier bound of O( √ n) by Goaoc et al. [6].

Geometric straight-line programs [5, 8] can be used to model geometric constructions and their implicit ambiguities. In this paper we discuss the complexity of deciding whether two instances of the same geometric straight-line program are connected by a continuous path, the Complex Reachability Problem.

This paper presents an efficient method of obtaining a straight-line motion in the tool configuration space using an articulated robot between two specified points. The simulation results & the implementation results show the effectiveness of the method. Keywords—Bounded deviation algorithm, Straight line motion, Tool configuration space, Joint space, TCV.

Fast constant factor approximation algorithms are devised for a problem of intersecting a set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0, where the set of segments forms a straight line drawing G = (V,E) of a planar graph without edge crossings. Exploiting its tough connection with the geometric Hitting Set problem we give (

We give a new proof of the NP-hardness of deciding the existence of real roots of an integer univariate polynomial encoded by a straight line program based on certain properties of the Tchebychev polynomials. These techniques allow us to prove some new NP-hardness results related to real root approximation for polynomials given by straight line programs.

Geometric straight-line programs [6, 10] can be used to model geometric constructions and their implicit ambiguities. In this paper we discuss the complexity of deciding whether two instances of the same geometric straight-line program are connected by a continuous path, the Complex Reachability Problem.