Rational B-splines Curves With Prescribed Poles And Their Properties

This paper studies the rational B-splines curves with prescribed poles and surfaces for the first time, and studies the properties of this new surface modeling. The result indicate that this modeling not only have the property of geometric modeling, but also have the agility and availability, and score the singular of curve. The main research contented and achieved are as follows:First, The paper define the rational space, then require the construction of the rational B-spline basis function, on this basic, paper define a kind of rational B-spline curve with prescribe pole. By the way, this paper research the properties of these basis and these curves, then find they have many good properties of polynomial B-spline. Especially,paper research that the K-order rational B-spline function change to polynomial B-spline when h limit to 0,+∞.Last the spline function can be used to express the hyperbolic curves.Then, when k = 3,4, paper research the infection of curve because qi is changed. After this work, the paper discusses the property of uniform curve. When the multiplies of end knots equal the order of the basis, the inner knots are also the simple knots ,the rational B-splines are translated to the rational Bézier-like basis. Studies show that these basis have the similar properties with the Bézier basis, and satisfied the new recurrence relation. Similarly, when control parameter hâ†'0~+,+∞, the k-order uniform B-spline is translate into rational Bézier. On this basic, paper find the connection of rational B-spline basis and rational Bézier basis,based on these relation ,find the control polygons'relation.Last, the tensor product surfaces are generated by the non-uniform B-spline and Bézier-like basis, then, paper research the property of this surface.