The Research Of Methods About Shape Modification Of Curves And Surfaces

With the development of CAGD, designing perfect curves and the easy operation of the curves' inter-designing are becoming more and more important in the economy, science and technology. Many researchers do a lot of jobs in designing curves and surfaces as well as modify them.To keep pace with the era and the development of the situation and to meet the practical needs on designing, it is necessary to modify curves and surfaces. This thesis studies different modification methods on different curves and surfaces, and puts emphasis on modification of NURBS curves and surfaces as well as two parameter curves. Apply the constrained optimization method to the General Bezier curves with parameter and given derivative vectors. Considering the limitation of endpoints and passing through the given points, we conclude a modification method, including solving curve passing through many given points and have the limitation of given derivative vectors on endpoints.Methods and theory in this thesis are based on the quality of different curves and surfaces. This method plays an important role in the interactive design of curves and surfaces, and we also hope to apply suitable operation to this method.