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

Generative theatre of totality

Generative art can be used for creating complex multisensory and multimedia experiences within predetermined aesthetic parameters, characteristic of the performing arts and remarkably suitable to address Moholy-Nagy's Theatre of Totality vision. In generative artworks the artist will usually take on the role of an experience framework designer, and the system evolves freely within that framework and its defined aesthetic boundaries. Most generative art impacts visual arts, music and literature, but there does not seem to be any relevant work exploring the cross-medium potential, and one could confidently state that most generative art outcomes are abstract and visual, or audio. It is the goal of this article to propose a model for the creation of generative performances within the Theatre of Totality's scope, derived from stochastic Lindenmayer systems, where mapping techniques are proposed to address the seven variables addressed by Moholy-Nagy: light, space, plane, form, motion, sound and man ("man" is replaced in this article with "human", except where quoting from the author), with all the inherent complexities