This archive is open for any geometer to publish new geometric models, or to browse this site for material to be used in education and research. These geometry models cover a broad range of mathematical topics from geometry, topology, and to some extent from numerics.
Kig is a program for exploring geometric constructions.
It is meant as a better replacement for such free programs as KGeo, KSeg and Dr. Geo and commercial programs like Cabri.
Eukleides is a Euclidean geometry drawing language. Two softwares are related to it. First, eukleides, a compiler which allows to typeset geometric figures within a (La)TeX document. This program is also useful to convert such figures in EPS format or in various other vector graphic formats. Second, xeukleides, a GUI front-end which makes possible to create interactive geometric figures. This program is also useful to edit and tune some Eukleides code.
EDEN is the Engine for DEfinitive Notations. It is the primary software tool of the Empirical Modelling research group. We build models with it, using a variety of definitive notations that it implements.
Abstract
The Earth Mover's Distance (EMD) between two weighted point sets (point distributions) is a distance measure commonly used in computer vision for color-based image retrieval and shape matching. It measures the minimum amount of work needed to transform one set into the other one by weight transportation. We study the following shape matching problem: Given two weighted point sets A and B in the plane, compute a rigid motion of A that minimizes its Earth Mover's Distance to B. No algorithm is known that computes an exact solution to this problem. We present simple FPTASs and polynomial-time (2+ε)-approximation algorithms for the minimum Euclidean EMD between A and B under translations and rigid motions. Earth Movers Distance
recc. by https://news.ycombinator.com/item?id=9623707 : "I have been working ten years professionally developing a CAD program, and if I could time travel and give my ten years younger self a single tip it would be to use a proper geometrical kernel (like CGAL) rather than doing anything with floating point."
This manual has been available on this site since about 1996, with improvements taking place frequently. The current version has been published as a book of about 350 pages by Cambridge University Press. By agreement with the Press, however, it will remain posted on this web site. Many improvements in the current version over previous ones are due to the (anonymous) referees of the Press, whom I wish to thank heartily. I also wish to thank Lauren Cowles, of the New York office of the Press, for much help with preparing the original version for publication. The paper edition appears also in Duotone red and black. For information on obtaining the paper edition, take a look at the Cambridge Press catalogue.