The Construction Of Blending Surface Between Two Trimmed B-spline Surfaces

On the surface modeling of CAD,we can't realize a geometry entity with a single piece of parametric surface sometimes because of it's complexity. The geometric entity is proposed to be divided into some parts and then to be connected accounding to a certain smoothness condition. The construction of blending surface is one of critical techniques in modeling technology of CAD . It's also the hot spot and difficulty there. Its' purpose is that a blending surface is generated between the correlative surfaces. Currently.there are several methods as follows:(1)RADII blending:(2)PDE ; (3)energy optimization. These methods can solve the surface blending in a certain extent,but they also have some shortages. For example .they can't satisfy some shape restrictions ;the shape of blending surface is hard to control; the method of energy optimization is a new popular method except a little more calculation.In this paper ,two algorithms are provided for constructing blending surface. The blending surface is able to reach a better smoothness requirement. The method of B-spline is the popular one in surface modeling. So we consider the B-spline surface as the base surface and operate method on it. The trimming curve we considered is parameter curve in parameter field of base surface.The first method :constructing blending surface based on discrete method. According to industry standard, trimming curve in parameter space is transformed into polygon within error band. A B-spline curve,boundary curve, is constructed by interpolating the points on the base surface mapped from vertexs of the polygon . Another B-spline curve,tangent curve, is constructed by interpolating the tangents of these pointson the base surface. The tangent of each point is the exterior product of tangent of the point on the curve and normal of the point on the base surface.The B-spline curve is also a piecewise Bezier curve. The Blending surface patch is constructed with interpolating the two Bezier curve segment by Hermite method. The method guarantees G~1 continuity between the patches and G~1 continuity between base surface and blending surface only on the points.Similarly, we can construct a B-spline surface as the Blending surface.Bezier surface and B-spline surface' shapes can be adjusted by control its'tangent curve. The B-spline surface can add more control constraits to get the better shape .Next we change the algorithm to improve the precision.The second algorithm bases on accurate method.To avoid the imprecision in the mapping of trimming curve in parameter space to the base surface , we construct precise Space trimming curve.First trimming curve is replaced by B-spline curve.Here,quadric B-spline curve is used . The precise trimming B-spline curve is got when the quadric B-spline curve is mapped to the bicubic B-spline surface. It is a piecewise polygon with twelve rank .we also can get its' tangent curve that is piecewise polygon with 62 rank. The blending surface patch is constructed by interpolating the trimming B-spline curve and tangent curve using quartic Hermite method.The blending surface is made up of patches.The method guarantees G~1 continuity between the patches and G~1 continuity between base surface and blending surface. We can control the shape of blending surface by adjusting the middle control curve.Each method has its'trait.The first can construct and display blending surface faster.The second one has higher precision.Additionally ,some works are done about the display of the trimmed surface.The...