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In this work, we develop a framework based on piecewize B\'ezier curves toplane shapes deformation and we apply it to shape optimization problems. Wedescribe a general setting and some general result to reduce the study of ashape optimization problem to a finite dimensional problem of integration of aspecial type of vector field. We show a practical problem where this approachleads to efficient algorithms.

On the geometry and the deformation of shape represented by a piecewise continuous B\'ezier curve with application to shape optimization