Approximate Merging Of Tensor Product Rational B(?)zier Surfaces

Rational Bezier surface is one of the most commonly used modeling tools in CAD/CAM systems. During the development of a system, the research of approximate merging algorithms for multiple rational Bezier surfaces is of great importance. The approximate merging algorithms is that finding a Bezier surface approachs multiple rational Bezier surfaces.In this paper, an approximate merging method for tensor product rational Bezier surfaces is presented by using the surface’s scatter formula and degree elevation formula, and using minimizing the distance function defined between the original Bezier surfaces and the merged Bezier surface. The explicit representation for control points of the merged surface is obtained.Chapter1simply introduces the background of approximate merging algorithms, tensor product type rational Bezier surfaces and contents of this article.Chapter2introduces the approximate merging algorithms of tensor product type Bezier surfaces.Chapter3is the focus of this article, is given the approximate merging algorithms for multiple rational Bezier surfaces. The algorithm uses rational Bezier surface discrete formula and the degree elevation formula to the discussion of the piecewise. According to the Moore-Penrose generalized inverse principle to solve the minimum of the function of the distance between the blending surface and merging surfaces. In this chapter, according to the merging algorithm, we give two issues about rational Bezier surfaces merge, one is solving the combined surface for a Rational Bezier Surface, another is Bezier surface. And ultimately, the algorithm based on numerical experiments is effective and feasible.