Smallest rectilinear paths are rectilinear paths with a minimum number of bends and with a minimum length, simultaneously. In this paper, given two pairs of terminals within a rectilinear polygon, we derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear p...

Let G be a graph on n vertices; let S be a set of n points in general position (no three of them collinear) in the plane. A rectilinear drawing of G is a drawing of G in the plane that satisfies the following. Its vertices are points in general position and its edges are drawn as straight line segments. The number of crossings of a rectilinear drawing is the number of pairs of its edges that cr...

The application of convolution potential voh.ammetry to questions of metal complexation is described. Theoretical relations are derived to show that the stability constants may be directly related to the shift in the peak potential of the semiderivative wave, provided the complexes are labile. Equations are also given for inert and quasilabile complexes. Stability constants for the PbCI, and Cd...

Title of Document: DESIGN AND ANALYSIS OF EXAGGERATED RECTILINEAR GAIT-BASED SNAKE-INSPIRED ROBOTS James Kendrick Hopkins Doctor of Philosophy, 2014 Dissertation directed by: Professor S. K. Gupta Department of Mechanical Engineering Snake-inspired locomotion is much more maneuverable compared to conventional locomotion concepts and it enables a robot to navigate through rough terrain. A rectil...

We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set P of h pairwise-disjoint rectilinear polygonal obstacles with a total of n vertices in the plane, a minimumlink rectilinear path between two points is a rectilinear path that avoids all obstacles with ...

Scheinerman and Wilf [SW94] assert that “an important open problem in the study of graph embeddings is to determine the rectilinear crossing number of the complete graph Kn.” A rectilinear drawing of Kn is an arrangement of n vertices in the plane, every pair of which is connected by an edge that is a line segment. We assume that no three vertices are collinear, and that no three edges intersec...