This Demonstration shows global Bspline surface interpolation. The implementation is fully described in the Details.
 Contributed by: Shutao Tang
 (Northwestern Polytechnical University, Xi'an City, China)
Given a set of data points , and , this Demonstration constructs a nonrational degree Bspline surface interpolating these points, namely: (1) Again, the first order of business is to compute reasonable values for the and the knot vectors and . We show how to compute the ; the are analogous. A common method is to use equations (2) or (3) to compute parameters , , ⋯, for each and then to obtain each by averaging across all for , that is, , , where for each fixed , was computed by equation (2) or (3). (a) Let , then (b) Let , then Once the are computed, the knot vectors and can be obtained by equation (4): Now to the computation of the control points. Clearly, equation (1) represents linear equations in the unknown . However, since is a tensor product surface, the can be obtained more simply and efficiently as a sequence of curve interpolations. For fixed , write equation (1) as , (5) where . (6) Notice that equation (5) is just curve interpolation through the points . The are the control points of the isoparametric curve on at fixed . Now fixing and letting vary, equation (6) is curve interpolation through the points , with as the computed control points. Thus, the algorithm to obtain all the is as follows: 1. Using and the , do curve interpolations through , which yields the . 2. Using and the , do curve interpolations through , which yields the . [1] L. Piegl and W. Tiller, The NURBS Book, 2nd ed., Berlin: SpringerVerlag, 1997 pp. 376–382.
