The RenderMan Interface - Paul Bourke

NURBS may contain trim regions and holes that are specified by giving curves in parameter
space.
RiNuPatch ( RtInt nu, RtInt uorder, RtFloat uknot[], RtFloat umin, RtFloat umax,
RtInt nv, RtInt vorder, RtFloat vknot[], RtFloat vmin, RtFloat vmax,
...parameterlist...)
This procedure creates a tensor product rational or polynomial non-uniform B-spline
surface patch mesh. parameterlist is a list of token-array pairs where each token is
one of the standard geometric primitive variables or a variable that has been defined
with RiDeclare. The parameter list must include at least position (”P” or ”Pw”) information.
The surface specified is rational if the positions of the vertices are 4-vectors (x,y,z,w),
and polynomial if the positions are 3-vectors (x,y,z). The number of control points in
the u direction equals nu and the number in the v direction equals nv. The total number
of vertices is thus equal to (nu)*(nv). The order must be positive and is equal to
the degree of the polynomial basis plus 1. There may be different orders in each parametric
direction. The number of control points should be at least as large as the order
of the polynomial basis. If not, a spline of order equal to the number of control points
is computed. The knot vectors associated with each control point (uknot[], vknot[])
must also be specified. Each value in these arrays must be greater than or equal to
the previous value. The number of knots is equal to the number of control points plus
the order of the spline. The surface is defined in the range umin to umax and vmin to
vmax. This is different from other geometric primitives where the parameter values
are always assumed to lie between 0 and 1. Each min must be less than its max. min
must also be greater than or equal to the corresponding (order-1)th knot value. max
must be less than or equal to the nth knot value.
A NuPatch may be thought of as a nonperiodic uniform B-spline mesh with (1+nu−uorder)
segments in the u parametric direction, and (1+nv−vorder) segments in the v parametric
direction. RiNuPatch primitive variables are therefore defined to have one
uniform value per segment and one varying value per segment corner. The number
of uniform primitive variables is therefore nusegments × nvsegments, and the number
of varying variables is (nusegments+1) × (nvsegments+1). Note that this results in redundant
parameter values corresponding to repeated knot values, for instance when
the knot vector indicates the RiNuPatch is in Bezier form. Primitive variables of class
vertex contain nu × nv values of the appropriate type, and are interpolated using
the same methods as the surface position ”P”. Primitive variables that are of class
constant will have a single value for the entire mesh.
If texture coordinates primitive variables are not present, the current texture coordinates
are assigned to corners defined by the rectangle (umin,umax) and (vmin,vmax)
in parameter space.
RIB BINDING
NuPatch nu uorder uknot umin umax nv vorder vknot vmin vmax ...parameterlist...
EXAMPLE
NuPatch 9 3 [ 0 0 0 1 1 2 2 3 3 4 4 4 ] 0 4
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