HP Workstation zx2000 OpenGL 1.1 Reference for HP-UX 11.x - Page 279

M glMap2 Equation 11-5 v1, v2 vstride vorder Specify a linear mapping of ˆv, as presented to glEvalCoord2, to one of the two variables that are evaluated by the equations specified by this command. Initially, v1 is 0 and v2 is 1. Specifies the number of floats or doubles between the beginning of control point Rij and the beginning of control point Ri(j+1), where i and j are the u and v control point indices, respectively. This allows control points to be embedded in arbitrary data structures. The only constraint is that the values for a particular control point must occupy contiguous memory locations. The initial value of vstride is 0. Specifies the dimension of the control point array in the v axis. Must be positive. The initial value is 1. points Specifies a pointer to the array of control points. Description Evaluators provide a way to use polynomial or rational polynomial mapping to produce vertices, normals, texture coordinates, and colors. The values produced by an evaluator are sent on to further stages of GL processing just as if they had been presented using glVertex, glNormal, glTexCoord, and glColor commands, except that the generated values do not update the current normal, texture coordinates, or color. All polynomial or rational polynomial splines of any degree (up to the maximum degree supported by the GL implementation) can be described using evaluators. These include almost all surfaces used in computer graphics, including B-spline surfaces, NURBS surfaces, Bezier surfaces, and so on. Evaluators define surfaces based on bivariate Bernstein polynomials. Define p(û, v) as nm ∑ ∑ p(uˆ, vˆ ) = Bin(uˆ )B jm(vˆ )Rij i = 0j = 0 where Rij is a control point, Bin(û) is the ith Bernstein polynomial of degree n (uorder = n + 1) Equation 11-6 Bin(uˆ ) =  n  i uˆ i ( 1 - uˆ )n - i and Bjm(v) is the jth Bernstein polynomial of degree m (vorder = m + 1) Equation 11-7 B m j ( vˆ ) =  m  j vˆ j(1 - vˆ )m - j Recall that Chapter 11 279