The Clifford algebra for the group of rigid body motions is described. Linear elements, that is points, lines and planes are identified as homogeneous elements in the algebra. In each case the action of the group of rigid motions on the linear elements is found. The relationships between these linear elements are found in terms of operations in the algebra. That is, incidence relations, the con...

Widely used statistical graphs (such as line graphs and bar graphs) are usually accompanied by graphical entities other than the graph proper. Those graphical cues, such as point marks and arrows serve for communicative purposes by bringing certain aspects to the foreground over the others. The present study discusses the results of an experimental investigation, in which the participants produ...

A novel and efficient quasi-Monte Carlo method for estimating the surface area of digitized 3D objects in the volumetric representation is presented. It operates directly on the original digitized objects without any surface reconstruction procedure. Based on the Cauchy–Crofton formula from integral geometry, the method estimates the surface area of a volumetric object by counting the number of...

For a number of common configurations of points (lines) in the plane, we develop data structures in which insertions and deletions of points (or lines, respectively) can be processed rapidly, without sacrificing much of the efficiency of query answering which known static structures for these configurations attain. As a main result we establish a fully dynamic maintenance algorithm for convex h...

Given a set of i (i = 1; 2; : : :; k) orientations (angles) in the plane, one can deene a distance function which induces a metric in the plane, called the orientation metric 3]. In the special case where all the angles are equal, we call the metric a uniform orientation metric 2]. Speciically, if there are orientations, forming angles ii ; 0 i ?1, with the x-axis, where 2 is an integer, we cal...

The ‘FitPitch’ computer program allows characterisation of preferred orientation of planar microstructures in a rock from the orientations of their intersection-lines on different sections. Measured pitch or strike angles of such intersection-lines are fitted to the theoretical intersection-lines of a single model-plane, or a combination of two or three model-planes. The degree of fit is quanti...

We show that for m points and n lines in R2, the number of distinct distances between the points and the lines is Ω(m1/5n3/5), as long as m1/2 ≤ n ≤ m2. We also prove that for any m points in the plane, not all on a line, the number of distances between these points and the lines that they span is Ω(m4/3). The problem of bounding the number of distinct point-line distances can be reduced to the...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D function of light over the domain of directed lines. These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-p...