Designing digital technologies and learning activities for different geometries

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and co-ordinate geometries in two and three dimensions, and non-Euclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry

Writing Reusable Digital Geometry Algorithms in a Generic Image Processing Framework

Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and algorithms. We propose an image processing framework focused on the Generic Programming paradigm in which an algorithm on the paper can be turned into a single code, written once and usable with various input types. This approach enables users to design and implement new methods at a lower cost, try cross-domain experiments and help generalize resultsComment: Workshop on Applications of Discrete Geometry and Mathematical Morphology, Istanb : France (2010

Influence of camera distortions on satellite image registration and change detection applications

Applications such as change detection and digital elevation model extraction from optical images require a rigorous modeling of the acquisition geometry. We show that the unrecorded satellite jitter during image acquisition, and the uncertainties on the CCD arrays geometry are the current major limiting factors for applications requiring high accuracy. These artifacts are identified and quantified on several optical satellites, i.e., SPOT, ASTER, QuickBird, and HiRISE

DGD Gallery: Storage, sharing, and publication of digital research data

We describe a project, called the "Discretization in Geometry and Dynamics Gallery", or DGD Gallery for short, whose goal is to store geometric data and to make it publicly available. The DGD Gallery offers an online web service for the storage, sharing, and publication of digital research data.Comment: 19 pages, 8 figures, to appear in "Advances in Discrete Differential Geometry", ed. A. I. Bobenko, Springer, 201

Digital program analyzes supersonic flow field within bell-shaped rocket nozzles

Digital computer program computes and analyzes supersonic flow field in axisymmetric rocket nozzle for specified gas properties, nozzle geometry, and input or starting line. Method of characteristics is used for solution of set of hyperbolic partial differential equations

Computer program calculates steady-state temperature distribution within plane or axisymmetric solids

Digital computer program, using the finite element analysis technique, determines the steady-state temperature within plan or axisymmetric solids composed of many different materials of various geometry. Program output is used to plot isotherms and provide data enabling the performance of stress analysis or heat transfer calculations upon the bodies