On the geometry and the deformation of shapes represented by piecewise continuous Bézier curves with application to shape optimization

Abstract

In this work, we develop a framework based on piecewise Bézier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape optimization problem to a finite dimensional problem of integration of a special type of vector field. We show a practical problem where this approach leads to efficient algorithms. © 2013 Springer-Verlag.