Bézier curves that are close to elastica

10/25/2017

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by   David Brander, et al.

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We study the problem of identifying those cubic Bézier curves that are close in the L2 norm to planar elastic curves. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. Using this, we identify geometric criteria on the control polygon that guarantee that a Bézier curve is within 1 percent of its arc-length to an elastic curve. Finally we give two projection algorithms that take an input Bézier curve and adjust its length, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.