ISSN 2079-3537      


Scientific Visualization, 2019, volume 11, number 3, pages 17 - 26, DOI: 10.26583/sv.11.3.02

Agile Finite Difference Approach to Euler Elastica Visualization

Authors: E.V. Popov1,A, T.P. Popova2,B

A Nizhegorodsky State Architectural and Civil Engineering University

B National Research University Higher School of Economics

1 ORCID: 0000-0002-3058-2369,

2 ORCID: 0000-0002-1351-222X,



This paper describes the finite difference approach (FDM) to visualization of the structure called Euler elastica in 1691 by Jacob Bernoulli. This shape is popular in some manufacturing applications: for example, in structures made from thin, flexible strips of wood or plastic. The shape of each strip, between two endpoints, is called elastica. Another application concerns thin metal bended strips for architectural decorated framework that looks aesthetically pleasing. Also an important application of Euler elastica is the technology of forming various patterns for decorating architectural spaces. Usually the analytic solution of this problem is based on the variational method, elliptic integral theory and so on. The visualization approach described in this paper is very compact and agile. In the case considered, the approach concerns bending of the elastica with a fixed left endpoint and a free right endpoint. Bending is provided by specifying the tangent angles of both endpoints. There are some numerical examples of Euler elastica in the paper.


Keywords: Euler elastica, Finite difference method, elastic rod, HTML5/Javascript languages.