3D Graphics Programming with QuickDraw 3D 1.5.4
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NURB Patches
Figure 15 shows a NURB patch.
Data Format
Uns32 uOrder
Uns32 vOrder
Uns32 numMPoints
Uns32 numNPoints
RationalPoint4D points[numMPoints * numNPoints]
Float32 uKnots[uOrder + numMPoints]
Float32 vKnots[vOrder + numNPoints]
- uOrder
- The order of a NURB patch in the u parametric direction. For NURB patches defined by ratios of B-spline polynomials that are cubic in u , the order is 4. In general, the order of a NURB patch defined by polynomial equations in which u is of degree n is n +1.
- vOrder
- The order of a NURB patch in the v parametric direction. For NURB patches defined by ratios of B-spline polynomials that are cubic in v , the order is 4. In general, the order of a NURB patch defined by polynomial equations in which v is of degree n is n +1.
- numMPoints
- The number of control points in the u parametric direction. The value of this field must be greater than 1.
- numNPoints
- The number of control points in the v parametric direction. The value of this field must be greater than 1.
- points[]
- An array of rational four-dimensional control points that define the NURB patch. The size of this array is as indicated in the data format.
- uKnots[]
- An array of knots in the u parametric direction that define the NURB patch. The values in this array must be nondecreasing, but successive values may be equal. The size of this array is as indicated in the data format.
- vKnots[]
- An array of knots in the v parametric direction that define the NURB patch. The values in this array must be nondecreasing, but successive values may be equal. The size of this array is as indicated in the data format.
Description
A NURB patch is a three-dimensional surface defined by ratios of B-spline surfaces, which are three-dimensional analogs of B-spline curves.
Default Surface Parameterization
The default surface parameterization of a NURB patch is as shown in Figure 15 .
Child Objects
Trim curves (optional). A trim curves object is a collection of two-dimensional NURB curves that are used to trim a NURB surface. See "Trim Loops" , and "2D NURB Curves" , for descriptions of these objects.
Example
NURBPatch (
4 #uOrder
4 #vOrder
4 #numMPoints
4 #numNPoints
-2 2 0 1 -1 2 0 1 1 2 0 1 2 2 0 1 #points
-2 2 0 1 -1 2 0 1 1 0 5 1 2 2 0 1
-2 -2 0 1 -1 -2 0 1 1 -2 0 1 2 -2 0 1
-2 -2 0 1 -1 -2 0 1 1 -2 0 1 2 -2 0 1
0 0 0 0 1 1 1 1 #uKnots
0 0 0 0 1 1 1 1 #vKnots
)
The control points of a NURB patch are listed in a rectangular order, first in order of increasing v , then in order of increasing u .
© 1997 Apple Computer, Inc.
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