Surface Blending Theory And Technology Studies

In CAD/CAM modeling system, with the development of Surface modeling, more theory was proposed. In actual surface designing, it is very difficult to draw a complex surface only with a simple surface. Then it is a question How to do that the generated surface by several surfaces looks more smooth in visual .So people proposea new theory to research these questions - Surface Blending.Blending surfaces are used to join two or more primary surfaces smoothly and are extensively used in computer graphics, computer animation and computer-aided design. Their function is to satisfy aesthetic, functional or certain manufacturing requirements.Our works in this paper:(1) Knot insertion and Knot refinement is more common Algorithms in CAGD.In this paper we introduce the concept and the application scope of Knot insertion and Knot refinement. And we also give out the difference between Knot insertion and Knot refinement. Also we give some examples to demonstrate the application of these algorithms.(2) Using the algorithm of the Knot refinement, we get the conditions of G~1/ G~2 continuity of the B-Spline surface.(3) PDE is the most widely used method for blending surfaces. In this paper we introduce the concept of PDE, and discuss the compound function and its resolution method.(4) Using fourth-order PDE with three vector-valued parameters, we generate a new surface with C~1 continuity between two primary surfaces, and using sixth-order PDE with four vector-valued parameters, we get another new surface with C~2 continuity. At last, we give some examples to demonstrate the application of our method.