On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bézier Curves with Application to Shape Optimization

Olivier Ruatta (1)

1 XLIM-DMI - DMI

In this work, we develop a framework based on piecewise B ézier 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 fi nite dimensional problem of integration of a special type of vector eld. We show a practical problem where this approach leads to effi cient algorithms.

Mots clés: Shapes representation; shape optimization; free forms

Domaines: Géométrie différentielle [math.DG]; Optimisation et contrôle [math.OC]

Olivier Ruatta. On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bézier Curves with Application to Shape Optimization. Geometric Science of Information, Aug 2013, Paris, France. pp.112-119, ⟨10.1007/978-3-642-40020-9⟩. ⟨hal-00908903⟩