M
glMap2
Chapter 11
279
v1, v2 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.
vstride Specifies the number of floats or doubles between the beginning of
control point R
ij
and the beginning of control point R
i(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.
vorder 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
Equation 11-5
where R
ij
is a control point, B
i
n
(û) is the ith Bernstein polynomial of degree n (uorder = n
+ 1)
Equation 11-6
and B
j
m
(v) is the jth Bernstein polynomial of degree m (vorder = m + 1)
Equation 11-7
Recall that
pu
ˆ
v
ˆ
,() B
i
n
j 0=
m
∑
u
ˆ
()B
j
m
v
ˆ
()R
ij
i 0=
n
∑
=
B
i
n
u
ˆ
()
n
i
u
ˆ
i
1 u
ˆ
–()
ni–
=
B
j
m
v
ˆ
()
m
j
v
ˆ
j
1 v
ˆ
–()
mj–
=
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