Curve And Surface Fractal Approximation Model And Applications

This thesis studies modeling and the simple application of the fractal approximation of curves and surfaces. The modeling of curves and surfaces constitutes an important research area in several application domains (medical imaging, multimedia data representation, computer aided geometry design). Up to now, a wide variety of representation methods have been proposed for the approximation of curves and surfaces. Basically, they can be classified into three categories: mesh representation, parametric representation and implicit representation. For a simple and fast visualization of curves and surfaces, the model widely used is the mesh representation. Parametric representation is suitable to a CAD use. Implicit model can be chosen like superquadrics. Unfortunately, these models do not recover rough curves and surfaces. In order to propose an efficient solution to approximating smooth or rough curves and surfaces. This thesis gives the fractal approximation models. We also give the satisfactory application of models in morphing.Firstly, we introduce the traditional modeling of curves and surfaces. Furthermore we point out the necessity of proposing the fractal approximation of curves and surfaces.In the aspect of the fractal approximation of curves, projected IFS(PIFS) model by Eric Guerin is introduced. In addition, we propose rational projected IFS (RPIFS) model which enlarges the denotation ability of PIFS model. We also give the properties and the convergence of the two models.In the aspect of the fractal approximation of surfaces. We propose the improved quadrangular projected IFS (QPIFS) model and quadrangular rational projected IFS (QRPIFS) model. Considering the necessary of the representation of triangle surfaces, we propose triangle projected IFS (TPIFS) model, triangle rationalprojected IFS (TRPIFS) model, and the properties and the convergence of thesemodels.Finally, we introduce the satisfactory application of these models in morphing.