To the theory of optimal splines

摘要

On June 18, 2008 at the Plenary Meeting of the International Conference “Differential Equations and Topology” dedicated to the 100th anniversary of Pontryagin, the report [1] was submitted by Isaev and Leitmann. This report in a summary form included a section dedicated to the research of scientists of TsAGI in the field of automation of full life-cycle (i.e. engineering-design-manufacturing, or CAE/CAD/CAM, or CALS-technologies) of wind tunnel models [2]. Within this framework, methods of geometric modeling [3], [4] were intensively developed, new classes of optimal splines have been built, including the Pontryagin splines and the Chebyshev splines [5], [6], [7], [8]. This paper reviews some results on the Pontryagin splines. We also give some results on the Lurie splines, that arise in the problem of interpolation of a cylindrical type surface given by the family of table coplanar planes.