Open GL Super Bible:Curves and Surfaces: What the #%@!&* Are NURBS?















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Open GL Super Bible


(Publisher: Macmillan Computer Publishing)

Author(s): Waite group Press

ISBN: 1571690735

Publication Date: 08/01/96

 




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gluNurbsSurface

Purpose
Defines the shape of a NURBS surface.
Include File
<glu.h>
Syntax
void gluNurbsSurface(GLUnurbsObj *nObj, GLint uknotCount, GLfloat *uknot, GLint vknotCount, GLfloat *vknot, GLint uStride, GLint vStride, GLfloat *ctlArray, GLint uorder, GLint vorder, GLenum type);
Description
This function defines the shape of a NURBS
surface. Must be delimited by gluBeginSurface and gluEndSurface. The
shape of the surface is defined before any trimming takes place. A NURBS
surface can be trimmed by using the gluBeginTrim/gluEndTrim and
gluNurbsCurve and/or gluPwlCurve to do the trimming.


Parameters

nObj

GLUnurbsObj*: Pointer to the NURBS object (created with gluNewNurbsRenderer).
uknotCount

GLint: The number of knots in the parametric u direction.
uknot

GLfloat*: An array of knot values that represent the knots in the u direction. These values must be nondescending. The length of the array is specified in uknotCount.
vknotCount

GLint: The number of knots in the parametric v direction.
vknot

GLfloat*: An array of knot values that represent the knots in the v direction. These values must be nondescending. The length of the array is specified in vknotCount.
uStride

GLint: Specifies the offset, as a number of single-precision, floating point values, between successive control points in the parametric u direction in ctlarray.
vStride

GLint: Specifies the offset, as a number of single-precision, floating point values, between successive control points in the parametric v direction in ctlarray.
ctlArray

GLfloat*: Pointer to an array containing the control points for the NURBS surface. The offsets between successive control points in the parametric u and v directions are given by uStride and vStride.
uorder

GLint: The order of the NURBS surface in the parametric u direction. The order is 1 more than the degree; hence a surface that is cubic in u has a u order of 4.
vorder

GLint: The order of the NURBS surface in the parametric v direction. The order is 1 more than the degree; hence a surface that is cubic in v has a v order of 4.
type

GLenum: The type of surface. This can be any of the 2D evaluator types: GL_MAP2_VERTEX_3, GL_MAP2_VERTEX_4, GL_MAP2_INDEX, GL_MAP2_COLOR_4, GL_MAP2_NORMAL, GL_MAP2_TEXTURE_COORD_1, GL_MAP2_TEXTURE_COORD_2, GL_MAP2_TEXTURE_COORD_3, and GL_MAP2_TEXTURE_COORD_4.
Returns
None.
Example
See the example for gluBeginSurface.
See Also
gluBeginSurface, gluBeginTrim,
gluNewNurbsRenderer, gluNurbsCurve, gluPwlCurve


gluPwlCurve

Purpose
Specifies a piecewise NURBS trimming curve.
Include File
<glu.h>
Syntax
void gluPwlCurve(GLUnurbsObj *nObj, GLint count, GLfloat *array, GLint stride, GLenum type);
Description
This function defines a piecewise linear
trimming curve for a NURBS surface. The array of points are in terms of
the parametric u and v coordinate space. This space is a unit square
exactly 1 unit in length along both axes. Clockwise-wound trimming
curves eliminate the enclosed area; counterclockwise trimming curves
discard the exterior area. Typically, a trimming region is first
established around the entire surface area that trims away all points
not on the surface. Then smaller trimming areas wound clockwise are
placed within it to cut away sections of the curve. Trimming curves can
be piecewise. This means one or more calls to gluPwlCurve or
gluNurbsCurve can be called to define a trimming region as long as they
share endpoints and define a close region in u/v space.


Parameters

nObj

GLUnurbsObj*: Specifies the NURBS object being trimmed.
count

GLint: Specifies the number of points on the curve listed in *array.
array

GLfloat*: Specifies the array of boundary points for this curve.
stride

GLint: Specifies the offset between points on the curve.
type

GLenum: Specifies the type of curve. May be GLU_MAP1_TRIM_2, used when the trimming curve is specified in terms of u and v coordinates; or GLU_MAP1_TRIM_3, used when a w (scaling) coordinate is also specified.
Returns
None.


Example
The following code from this chapterłs program NURBT shows a NURBS curve being trimmed with a triangular shaped region. A large trimming area encloses the surface that includes all the area within it. A secondary trimming area defines a triangle and discards any surface area within it.

// Outside trimming points to include entire surface
GLfloat outsidePts[5][2] = /* counter clockwise */
{{0.0f, 0.0f};, {1.0f, 0.0f}, {1.0f, 1.0f}, {0.0f, 1.0f}, {0.0f, 0.0f}};

// Inside trimming points to create triangle shaped hole in surface
GLfloat insidePts[4][2] = /* clockwise */
{{0.25f, 0.25f}, {0.5f, 0.5f}, {0.75f, 0.25f}, { 0.25f, 0.25f}};

...
...

// Render the NURB
// Begin the NURB definition
gluBeginSurface(pNurb);

// Evaluate the surface
gluNurbsSurface(pNurb,
8, Knots,
8, Knots,
4 * 3,
3,
&ctrlPoints[0][0][0],
4, 4,
GL_MAP2_VERTEX_3);

// Outer area, include entire curve
gluBeginTrim (pNurb);
gluPwlCurve (pNurb, 5, &outsidePts[0][0], 2, GLU_MAP1_TRIM_2);
gluEndTrim (pNurb);

// Inner triangluar area
gluBeginTrim (pNurb);
gluPwlCurve (pNurb, 4, &insidePts[0][0], 2, GLU_MAP1_TRIM_2);
gluEndTrim (pNurb);

// Done with surface
gluEndSurface(pNurb);


See Also
gluBeginTrim, gluEndTrim, gluNurbsCurve






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