1,517 research outputs found
Wire mesh design
We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods
Practical quality control tools for curves and surfaces
Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects
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
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