3D Graphics Programming with QuickDraw 3D 1.5.4
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NURB Curves
Figure 14 shows a NURB curve.
Data Format
Uns32 order
Uns32 nPoints
RationalPoint4D points[nPoints]
Float32 knots[order + nPoints]
- order
- The order of the NURB curve. For NURB curves defined by ratios of cubic B-spline polynomials, the order is 4. In general, the order of a NURB curve defined by polynomial equations of degree n is n +1. The value of this field must be greater than 1.
- nPoints
- The number of control points that define the NURB curve. The value of this field must be greater than 1.
- points[]
- An array of rational four-dimensional control points that define the NURB curve. The w coordinate of each control point must be greater than 0.
- knots[]
- An array of knots that define the NURB curve. The number of knots in a NURB curve is the sum of the values in the order and nPoints fields. The values in this array must be nondecreasing. Successive values may be equal, up to a multiplicity equivalent to the order of the curve; that is, if the order of a NURB curve is n, then at most n successive values may be equal.
Description
A nonuniform rational B-spline (NURB) curve is a three-dimensional projection of a four-dimensional curve. A NURB curve is specified by its order, the number of control points used to define it, the control points themselves, and the knots used to define it. Attributes may be applied only to the entire NURB curve.
Example
NURBCurve (
4 # order
7 # nPoints
0 0 0 1 # points
1 1 0 1
2 0 0 1
3 1 0 1
4 0 0 1
5 1 0 1
6 0 0 1
0 0 0 0 0.25 0.5 0.75 1 1 1 1 # knots
)
© 1997 Apple Computer, Inc.
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