140 research outputs found
Approximation by planar elastic curves
We give an algorithm for approximating a given plane curve segment by a
planar elastic curve. The method depends on an analytic representation of the
space of elastic curve segments, together with a geometric method for obtaining
a good initial guess for the approximating curve. A gradient-driven
optimization is then used to find the approximating elastic curve.Comment: 18 pages, 10 figures. Version2: new section 5 added (conclusions and
discussions
B\'ezier curves that are close to elastica
We study the problem of identifying those cubic B\'ezier curves that are
close in the L2 norm to planar elastic curves. The problem arises in design
situations where the manufacturing process produces elastic curves; these are
difficult to work with in a digital environment. We seek a sub-class of special
B\'ezier curves as a proxy. We identify an easily computable quantity, which we
call the lambda-residual, that accurately predicts a small L2 distance. We then
identify geometric criteria on the control polygon that guarantee that a
B\'ezier curve has lambda-residual below 0.4, which effectively implies that
the curve is within 1 percent of its arc-length to an elastic curve in the L2
norm. Finally we give two projection algorithms that take an input B\'ezier
curve and adjust its length and shape, whilst keeping the end-points and
end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure
Graph colouring for office blocks
The increasing prevalence of WLAN (wireless networks) introduces the potential of electronic information leakage from one company's territory in an office block, to others due to the long-ranged nature of such communications. BAE Systems have developed a system ('stealthy wallpaper') which can block a single frequency range from being transmitted through a treated wall or ceiling to the neighbour. The problem posed to the Study Group was to investigate the maximum number of frequencies ensure the building is secure. The Study group found that this upper bound does not exist, so they were asked to find what are "good design-rules" so that an upper limit exists
Monge surfaces and planar geodesic foliations
A Monge surface is a surface obtained by sweeping a generating plane curve
along a trajectory that is orthogonal to the moving plane containing the curve.
Locally, they are characterized as being foliated by a family of planar
geodesic lines of curvature. We call surfaces with the latter property PGF
surfaces, and investigate the global properties of these two naturally defined
objects. The only compact orientable PGF surfaces are tori; these are globally
Monge surfaces, and they have a simple characterization in terms of the
directrix. We show how to produce many examples of Monge tori and Klein
bottles, as well as tori that do not have a closed directrix.Comment: 12 pages 5 figure
Measuring glucose content in the aqueous humor
Many diabetics must measure their blood glucose levels regularly to maintain good health. In principle, one way of measuring the glucose concentration in the human body would be by measuring optically the glucose content of the aqueous humor in the eye. Lein Applied Diagnostics wish to assess whether this is feasible by a linear confocal scan with an LED source, or by supplementing such a system with other measurements
Husdyrbruget i 1938, med særligt Henblik paa Kvægbruget og Kvægavlen.
Husdyrbruget i 1938, med særligt Henblik paa Kvægbruget og Kvægavlen
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