Seminar
Designing with elastic curves

Hold Date 
20181019 15:00～20181019 16:00 


Place 
Lecture Room L W1C502, West Zone 1, Ito campus, Kyushu University 


Object person 



Speaker 
David Brander (Technical University of Denmark) 

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 nonuniqueness 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, ComputerAided Design, 104, (2018), 3644.
[2] Approximation by planar elastic curves.
D. Brander, J. Gravesen and T. Nørbjerg. Adv. Comput. Math. DOI: 10.1007/s104440169474z