Deconstructing Approximate Offsets

We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If it does, we also seek a preferably simple-looking solution P; then, P's offset constitutes an accurate, vertex-reduced, and smoothened approximation of Q. We give an O(n log n)-time exact decision algorithm that handles any polygonal shape, assuming the real-RAM model of computation. A variant of the algorithm, which we have implemented using CGAL, is based on rational arithmetic and answers the same deconstruction problem up to an uncertainty parameter \delta; its running time additionally depends on \delta. If the input shape is found to be approximable, this algorithm also computes an approximate solution for the problem. It also allows us to solve parameter-optimization problems induced by the offset-deconstruction problem. For convex shapes, the complexity of the exact decision algorithm drops to O(n), which is also the time required to compute a solution P with at most one more vertex than a vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011, submitted to DC

Proprietary software tools as learning aids

Proprietary software tools, though not designed for educational use, have considerable educational potential. This paper describes, as case studies, the use of proprietary graphics- and audio-editing tools in two distance-taught courses produced by the Department of Information and Communication Technologies at the UK Open University – Europe's largest distance teaching institution. The paper examines the potential advantages and disadvantages of this type of software relative to conventional educational software in terms of constructivist learning theory, and describes how students use the software in the courses concerned. The paper concludes by suggesting further developments of this approach

An explicit multi-time-stepping algorithm for aerodynamic flows

An explicit multi-time-stepping algorithm with applications to aerodynamic flows is presented. In the algorithm, in different parts of the computational domain different time steps are taken, and the flow is synchronized at the so-called synchronization levels. The algorithm is validated for aerodynamic turbulent flows. For two-dimensional flows speedups in the order of five with respect to single time stepping are obtained.

Input description for Jameson's three-dimensional transonic airfoil analysis program

The input parameters are presented for a computer program which performs calculations for inviscid isentropic transonic flow over three dimensional airfoils with straight leading edges. The free stream Mach number is restricted only by the isentropic assumption. Weak shock waves are automatically located where they occur in the flow. The finite difference form of the full equation for the velocity potential is solved by the method of relaxation, after the flow exterior to the airfoil is mapped to the upper half plane

PIV measurements of the effect of pulsed blowing jet on a NACA0012 wing model

Wingtip vortices are present in taking off, and landing operations and their presence in airport runways must be reduced. To that end, several strategies have been considered in the last decades, being the active control one possible technical solution. To compute the effectiveness of active control that corresponds to pulsed low-blowing-ratio transverse jet for the reduction of the wingtip vortex strength, we carry out 2D-PIV measurements in a towing tank for chord-based Reynolds numbers 15000 and 20000. We consider two cases: (i) no active control Rjet=0 and (ii) pulsating radial jet of blowing-ratio Rjet smaller than 1.7 (or momentum coefficient lower than 0.12) and different Strouhal numbers ranging from 0.27 to 0.94. Our observations show that the best reduction of wingtip vortex strength takes place at the lowest Strouhal number tested. We use the maximum azimuthal velocity and vorticity together with the circulation to quantify this decrease in the vortex strength. Besides, we define the spatial evolution of a disturbance parameter which allow us to detect again the optimal frequency that leads to vortex destruction.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Dual differential interferometer

A dual two-beam differential interferometer that measures both the amplitude and orientation of propagating, broadband surface acoustic waves is disclosed. Four beams are focused on a surface. The four reflected beams are separated into two pairs. The two pairs are detected to produce two signals that are used to compute amplitude and orientation