In this paper, a tri-reflector compact antenna test range (CATR) consisting of main parabolic reflector with square aperture 3 m in side length and two sub-reflectors rotationally standard quadric surfaces working terahertz is proposed. By using the equivalent paraboloid theory cross-polarization elimination conditions then combining appropriate shaped feed, low good quiet zone (QZ) performance...

This paper uses ALIS data to compare academic performance in two subjects often viewed as relatively close substitutes for one another at A-level. The important role of GCSE achievement is confirmed for both subjects. There is evidence of strong gender effects and variation in outcomes across Examination Boards. A counterfactual exercise suggests that if the sample of Business Studies candidate...

We study the problem of polygonal line simpliication. The objective is to seek a polygonal line of smaller size that approximates the original one well. We present an algorithm that is based on edge contraction. An edge contraction merges two adjacent vertices into a new vertex and this new vertex will be made the new endpoint of the uncontracted edges incident to the two vertices merged. Thus,...

During the summer between my junior and senior year, I was extremely lucky to be one of the 80 rising seniors who were admitted to the Research Science Institute (RSI) held at MIT. My mentor was Ryan Reich, a graduate student from Harvard University. Before the program, I was contacted by my mentor and was given a couple of project ideas. I could either do a project on tropical geometry or do a...

A scheme for combining auto-calibration and scene constraints in the “structure-from-motion” problem is proposed. This scheme focuses on the recovery of the absolute quadric using auto-calibration while imposing orthogonal scene plane constraints. First, an initial estimate of the absolute quadric is obtained using a linear method. A nonlinear constrained optimization step is then applied to re...

Existing methods to create contour files generate a polygonal approximation of the contours instead of an exact representation. This paper presents a method to generate exact contours from Constructive Solid Geometry (CSG) representations. The method preserves the accuracy of the contour files provided the primitives used to generate the CSG tree are polygonal or quadric objects. Due to the inc...

It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space P3 and all real points of the so-called Plücker quadric Ψ. Moreover one can identify each point of the Plücker quadric’s ambient space with a linear complex of lines in P3. Within this paper we give an alternative interpretation for the points of P5 as lines of an Euclidean 4-space E4, ...

This paper addresses the problem of reconstructing textureless objects of quadric like shape. It is known that a quadric can be uniquely recovered from its apparent contours in three views. But, in the case of only two views the reconstruction is a one parameter family of quadrics. Polarization imaging provides additional geometric information compared to simple intensity based imaging. The pol...

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, set of solutions is called the curvature diagram or W-diagram surface. Making use notion geometric linear momentum plane curve, we propose new approach to study rotational in Euclidean 3-space. Our contribution consists reducing any type condition on surface first-order differential equation generatrix curve...