分野別セミナー

Abstract:
Euler's elastica are natural curves that appeared in design before the introduction of computers, because these curves are the natural shape for the wooden splines that were used in drafting. Although they have natural aesthetic properties, they were abandoned when computers were introduced because polynomial splines are much easier to deal with mathematically. Motivated by new fabrication processes, we have studied the practical problem of designing with elastic curves and splines on a computer. We show in [1] that the problems of non-uniqueness and instability, inherent in the nonlinear mathematics of elastic splines, can be solved by introducing a suitable proxy curve to represent the elastica. In this talk, I will describe this work, as well as some remaining issues.

[1] Bézier curves that are close to elastica.
D. Brander, J.A. Bærentzen, A. Fisker and J. Gravesen, Computer-Aided Design, 104, (2018), 36--44.

[2] Approximation by planar elastic curves.
D. Brander, J. Gravesen and T. Nørbjerg. Adv. Comput. Math. DOI: 10.1007/s10444-016-9474-z