35 research outputs found
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
On the use of Artificial Neural Networks in Topology Optimisation
The question of how methods from the field of artificial intelligence can
help improve the conventional frameworks for topology optimisation has received
increasing attention over the last few years. Motivated by the capabilities of
neural networks in image analysis, different model-variations aimed at
obtaining iteration-free topology optimisation have been proposed with varying
success. Other works focused on speed-up through replacing expensive optimisers
and state solvers, or reducing the design-space have been attempted, but have
not yet received the same attention. The portfolio of articles presenting
different applications has as such become extensive, but few real breakthroughs
have yet been celebrated. An overall trend in the literature is the strong
faith in the "magic" of artificial intelligence and thus misunderstandings
about the capabilities of such methods. The aim of this article is therefore to
present a critical review of the current state of research in this field. To
this end, an overview of the different model-applications is presented, and
efforts are made to identify reasons for the overall lack of convincing
success. A thorough analysis identifies and differentiates between problematic
and promising aspects of existing models. The resulting findings are used to
detail recommendations believed to encourage avenues of potential scientific
progress for further research within the field.Comment: 36 pages, 7 figures (13 figures counting sub-figures), accepted for
publication in Structural and Multidisciplinary Optimizatio