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Theses

Dualité géométrique et relations de correspondance entre courbes primales et duales

Abstract : This thesis is a basic study dealing with the transformation of geometric duality between points and hyperplans. Then an essential step is to establish a rigourous definition of geometric duality as well as its properties and characteristics. This notion of duality can be generalised for every geometric form described by a family of points or hyperplans. Therefore, a dual curve of a parametric curve is defined as the envelop of a family of lines . These dual curves are then analysed in order to find the relationship between primal curves and their dual curves. Indeed, interpolation and convexity relationship are established and some examples of Bézier dual curves are illustrated. A complete study establishes a relationship between the singularities of primal and dual curves. Finally, a generalisation of the geometric duality using a symetric matrix allowes to associate with any parametric curve a family of curves depending on the considered symmetric matrix.
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Hafsa Deddi. Dualité géométrique et relations de correspondance entre courbes primales et duales. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1997. Français. ⟨tel-00004935⟩

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