An orthogonal drawing of a plane graph G is a drawing of G in which each edge is drawn as a sequence of alternate horizontal and vertical line segments. In this paper we give a linear-time algorithm to find an orthogonal drawing of a given 3-connected cubic plane graph with the minimum number of bends. The best known algorithm takes time O(nT/4o~/I'd'~) for any plane graph of n vertices.

An orthogonal drawing of a plane graph G is a drawing of G in which each edge is drawn as a sequence of alternate horizontal and vertical line segments. In this paper we give a linear-time algorithm to find an orthogonal drawing of a given 3-connected cubic plane graph with the minimum number of bends. The best previously known algorithm takes time O(n √ log n) for any plane graph with n vertices.

An IC-plane graph is a topological graph where every edge is crossed at most once and no two crossed edges share a vertex. We show that every IC-plane graph has a visibility drawing where every vertex is of the form { , , , }, and every edge is either a horizontal or vertical segment. As a byproduct of our drawing technique, we prove that every IC-plane graph has a RAC drawing in quadratic area...

We consider a viscous incompressible fluid filling an infinite horizontal domain bounded at the bottom by a plane wall and at the top by a rough wall. The latter is assumed to consist of a plane wall covered with periodically distributed asperities which size depends on a small parameter ε > 0. The assumption of sharp asperities is made, that is the height of the asperities does not vanish as ε...

objectives: differential diagnosis of bifid mandibular condyle (bmc) is important, since it may play a role in temporomandibular joint (tmj) dysfunctions and joint symptoms. in addition, radiographic appearance of bmc may mimic tumors and/or fractures. the aim of this study was to evaluate the prevalence and orientation of bmc based on cone beam computed tomography (cbct) scans.   materials and...

Localization of sound source in the horizontal plane employs the evaluation of interaural time and intensity differences. The precision of the evaluating system depends on a number of parameters: frequency, overall intensity and deviation of the source from the medial plane. A preliminary psychophysical experiment was conducted to explore the intensity dependence of just noticeable time and int...

Contents List of Tables viii List of Figures ix Abstract xi 1 Introduction 1Each pixel shows the computation work of a scanline. Scanlines for a slice progress from left to right on the horizontal axis. Slices of a frame are top to bottom on the vertical axis.. 2.13 Ray intersections with volume (a) Viewing plane is aligned with the XY plane (b) Viewing plane is at an angle from the XY

Many species navigate in three dimensions and are required to maintain accurate orientation while moving in an Earth vertical plane. Here we explored how head direction (HD) cells in the rat anterodorsal thalamus responded when rats locomoted along a 360° spiral track that was positioned vertically within the room at the N, S, E, or W location. Animals were introduced into the vertical plane ei...

OBJECTIVE The purpose of this study was to determine the accuracy and reliability of Frankfort horizontal plane identification using displays of multi-planar reconstructed MRI images, and propose it as a sufficiently stable and standardized reference plane for craniofacial structures. MATERIALS AND METHODS MRI images of 43 subjects were obtained from the longitudinal population based cohort s...

Kinematic data on primate head and neck posture were collected by filming 29 primate species during locomotion. These were used to test whether head and neck posture are significant influences on basicranial flexion and whether the Frankfurt plane can legitimately be employed in paleoanthropological studies. Three kinematic measurements were recorded as angles relative to the gravity vector, th...