Two Basic Propositions On Modeling Of Curves And Surfaces

There are totally seven chapters in this thesis.In the first chapter, the concept of polynomial tree is proposed in order to present a concrete thread of thought for the structure of basis The second chapter mainly deals with the transplantation of polynomial trees. It is expected that many kinds of basis will be generated through this transplantation. As an example, the properties and algorithms of Bezier-Wang-Ball basis is offered, the properties of the curve generated by this basis is fairly good. In the third chapter, the basis proposed by J.Delgado is improved. The original basis does not satisfy the boundary tangent property. On the contrary, the improved basis on the one hand can ensure the tangency and one the other hand can keep the linearity of its complexity of time. In the fourth chapter, the exponential basis is presented on the basis of the knowledge of probability. The curve generated by this function shows good properties and enjoys the linearity of its complexity of time. The concept of point set Bezier curves is put forward in the sixth chapter. Starting from the improvement of interval and disk Bezier curves, these curves overcome some defects of interval Bezier curves. In the last chapter, the concept of matricial Bezier curves is proposed. These curves can be applied in the mathematical model for the research on the movement of robot arm.