Researches And Application In Lower Order Blending Of Curve And Surfaces

In industrial design, curve and surface design requirements are very strict. Especially, in some high-technology areas. Some products are not only prefect function but also for its smoothly shape design. We know that some complex surfaces do not give a precise function expression, while we deal with the actual curve and surfaces design in CAGD modeling system. So, we encountered a problem that how to generate a surfaces and ultimately through this surface to link other surfaces. Lastly, giving a satisfactory result for people in the sensory. Many scholars thought about this issue from mathematical view. In order to meet the requirements for continuity and smoothness of complex surfaces. Given a rigorous mathematical definition and theoretical basis. They study these theories from different views and applied different methods. These theories are called surface blending.In practical application, surface blending is widely used in surface modeling design. We calculated the blending conditions to meet a variety of surfaces by Computer Graphic Design, computer software language, many algorithms of Numerical Analysis, knowledge of Advanced Algebra.This paper mainly discuss curve and surfaces from the following four areas and Introduce some blending methods.The main work of this paper is as follows.Firstly,this section introduced the interpolation techniques.Especially,Polynomial Interpolation and Cubic B-spline curve function, then combined with Cubic B-spline and Node Interpolation. At the end of this part, results are presented through a simple example.Secondly, this section introduced knowledge of the curve and surfaces blending,compared some existing surfaces blending technology to summary the advantages and disadvantages.then choose research directions of this paper.Thirdly, this section introduced that assumed the conditions of control surfaces are presence. From Algebraic geometry point of view and knowledge of ideal, then transformed into seek homogeneous linear equations by Groebner-bases. Studying four different implicitly algebraic surfaces to meet the low smooth blending necessary and sufficient condition and obtain four theorems, to fill the blank about two implicitly algebraic surfaces of low splicing research.Lastly, for example as one theorem is verified and proved the rationality and feasibility of the method, then given the implicitly expressions of blending surfaces, with Grapher software gives splicing renderings. At the end of this part shows the effect of splicing from different views, then given intuitively the study results by graphic, and explain the question that we should be noted in the course of studies.The end of this paper, we given the summary and outlook for the full text and proposed further research orientation.