Research On Construction Of Parametric Blending Surface Via B-spline Curve

In engineering design and geometric modeling process, how to construct a blending surface among several curves or surfaces is an important problem in the CAGD, which is to construct a blending surface that smoothly joins two or more given curves or surfaces. That is, for given two or several surfaces and those blending borders, how to construct a blending surface which contacts original surfaces as high order continuity as possible. Because it has strong practicability in automobile, airplane, shipping and other industrial manufacturing field, so it become an important academic branch of computer aided geometric design (CAGD).This paper summary, analysis, research some methods which other researchers construct blending surface,and find as many construction of blending surface methods, surface can be classified into two types: one of the implicit surfaces, another is parametric surfaces .In comparing the two types of surfaces one notes that parametric surfaces are generally easier to draw, subdivided and bound, or easier to adjust the shape of blending surface whereas an implicit surface is easily determine the continuity between the blending surface and the original surface, make it can easily achieve satisfactory continuity. If we choose one kind of form and another form advantages is abate. So it is an important research fields to combine with the two forms advantage. This requires that we research the construction methods to satisfy some continuity but also to satisfy the flexible adjustment.Through the comparative analysis, this paper put forward a new method. Because the blending surface is constructed with a collection of space curves, which are defined by points on the blending boundaries of primary surfaces and the points on the given adjustment curves. The iso-parametric curves are B-Spline curves, which interpolate the blending boundaries. So we call it B-spline curves constructing method. And the constructing method that smoothly joining two or more surfaces with G 1 continuity. Because the blending surface has a parametric form, so its shape is easy to be controlled by adjusting the parameters and adjustment curves. In the end of this paper several numerical examples are presented to show the feasibility and validity of our method.