3D Graphics Programming with QuickDraw 3D 1.5.4

NURB Patches

A NURB patch is a surface defined by ratios of B-spline surfaces, which are three-dimensional analogs of B-spline curves. A NURB patch is defined by the TQ3NURBPatchData data type. See "Creating and Editing NURB Patches" for a description of the routines you can use to create and edit NURB patches. Figure 30 shows a NURB patch.

Figure 30 A NURB patch



 
typedef struct TQ3NURBPatchData {

    unsigned long                       uOrder;

    unsigned long                       vOrder;

    unsigned long                       numRows;

    unsigned long                       numColumns;

    TQ3RationalPoint4D                  *controlPoints;

    float                               *uKnots;

    float                               *vKnots;

    unsigned long                       numTrimLoops;

    TQ3NURBPatchTrimLoopData            *trimLoops;

    TQ3AttributeSet                     patchAttributeSet;

} TQ3NURBPatchData;

uOrder: The order of the 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. The value in this field must be greater than 1.
vOrder: The order of the 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. The value in this field must be greater than 1.
numRows: The number of control points in the u parametric direction. The value of this field must be greater than 1.
numColumns: The number of control points in the v parametric direction. The value of this field must be greater than 1.
controlPoints: A pointer to an array of rational four-dimensional control points that define the NURB patch. The first control point in the array is the lower-left corner of the NURB patch. The control points are listed in a rectangular order, first in the direction of increasing u and then in the direction of increasing v . The number of elements in this array is the product of the values in the numRows and numColumns fields.
uKnots: A pointer to an array of knots in the u parametric direction that define the NURB patch. The number of u knots in a NURB patch is the sum of the values in the uOrder and numColumns fields. The values in this array must be nondecreasing (but successive values may be equal).
vKnots: A pointer to an array of knots in the v parametric direction that define the NURB patch. The number of v knots in a NURB patch is the sum of the values in the vOrder and numRows fields. The values in this array must be nondecreasing (but successive values may be equal).
numTrimLoops: The number of trim loops in the array pointed to by the trimLoops field. Currently this field should contain 0.
trimLoops: A pointer to an array of trim loop data structures that define the loops used to trim a NURB patch. See below for the structure of the trim loop data structure. Currently this field should contain the value NULL .
patchAttributeSet: A set of attributes for the NURB patch. The value in this field is NULL if no NURB patch attributes are defined.

A trim loop data structure is defined by the TQ3NURBPatchTrimLoopData data type.



 
typedef struct TQ3NURBPatchTrimLoopData {

    unsigned long                                   numTrimCurves;

    TQ3NURBPatchTrimCurveData                       *trimCurves;

} TQ3NURBPatchTrimLoopData;

numTrimCurves: The number of trim curves in the array pointed to by the trimCurves field.
trimCurves: A pointer to an array of trim curve data structures that define the curves used to trim a NURB patch. See below for the structure of the trim curve data structure.

A trim curve data structure is defined by the TQ3NURBPatchTrimCurveData data type.



 
typedef struct TQ3NURBPatchTrimCurveData {

    unsigned long                                   order;

    unsigned long                                   numPoints;

    TQ3RationalPoint3D                              *controlPoints;

    float                                           *knots;

} TQ3NURBPatchTrimCurveData;

order: The order of the NURB trim curve. In general, the order of a NURB trim curve defined by polynomial equations of degree n is n +1. The value in this field must be more than 1.
numPoints: The number of control points that define the NURB trim curve. The value in this field must be greater than 2.
controlPoints: A pointer to an array of three-dimensional rational control points that define the NURB trim curve.
knots: A pointer to an array of knots that define the NURB trim curve. The number of knots in a NURB trim curve is the sum of the values in the order and numPoints fields. The values in this array must be nondecreasing (but successive values may be equal).