3D Graphics Programming with QuickDraw 3D 1.5.4

NURB Curves

Figure 14 shows a NURB curve.

Figure 14 A NURB curve

Labels

ASCII: NURBCurve
Binary: nrbc ( = 0x6E726263 )

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.

Data Size

8 + (nPoints * 16) + ((nPoints + order) * 4)

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.

Default Surface Parameterization

None.

Parent Hierarchy

Shared, shape, geometry.

Parent Objects

None.

Child Objects

Attribute set (optional).

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

)

Default Size

None.