OpenGL Programming Guide

Chapter 11Evaluators and NURBS

The GLU NURBS Interface

A Simple NURBS Example

If you understand NURBS, writing OpenGL code to manipulate NURBS curves and surfaces is relatively easy, even with lighting and texture mapping. Follow these steps to draw NURBS curves or untrimmed NURBS surfaces. (Trimmed surfaces are discussed in "Trimming." )

1. If you intend to use lighting with a NURBS surface, call glEnable() with GL_AUTO_NORMAL to automatically generate surface normals. (Or you can calculate your own.)
   
   

2. Use gluNewNurbsRenderer() to create a pointer to a NURBS object, which is referred to when creating your NURBS curve or surface.
   
   

3. If desired, call gluNurbsProperty() to choose rendering values, such as the maximum size of lines or polygons that are used to render your NURBS object.
   
   

4. Call gluNurbsCallback() if you want to be notified when an error is encountered. (Error checking may slightly degrade performance.)
   
   

5. Start your curve or surface by calling gluBeginCurve() or gluBeginSurface().
   
   

6. Generate and render your curve or surface. Call gluNurbsCurve() or gluNurbsSurface() at least once with the control points (rational or nonrational), knot sequence, and order of the polynomial basis function for your NURBS object. You might call these functions additional times to specify surface normals and/or texture coordinates.
   
   

7. Call gluEndCurve() or gluEndSurface() to complete the curve or surface.

Example 11-5 renders a NURBS surface in the shape of a symmetrical hill with control points ranging from -3.0 to 3.0. The basis function is a cubic B-spline, but the knot sequence is nonuniform, with a multiplicity of 4 at each endpoint, causing the basis function to behave like a Bézier curve in each direction. The surface is lighted, with a dark gray diffuse reflection and white specular highlights. Figure 11-4 shows the surface as a wireframe and lighted.

Figure 11-4 : A NURBS Surface

Example 11-5 : Drawing a NURBS Surface: surface.c

#include <GL/gl.h>
#include <GL/glu.h>
#include "aux.h"

GLfloat ctlpoints[4][4][3];
GLUnurbsObj *theNurb;

void init_surface(void)
{
    int u, v;
    for (u = 0; u < 4; u++) {
        for (v = 0; v < 4; v++) {
            ctlpoints[u][v][0] = 2.0*((GLfloat)u - 1.5);
            ctlpoints[u][v][1] = 2.0*((GLfloat)v - 1.5);

        if ( (u == 1 || u == 2) && (v == 1 || v == 2))
            ctlpoints[u][v][2] = 3.0;
        else
            ctlpoints[u][v][2] = -3.0;
        }
    } 
}

void myinit(void)
{
    GLfloat mat_diffuse[] = { 0.7, 0.7, 0.7, 1.0 };
    GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 };
    GLfloat mat_shininess[] = { 100.0 };

    glClearColor (0.0, 0.0, 0.0, 1.0);
    glMaterialfv(GL_FRONT, GL_DIFFUSE, mat_diffuse);
    glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular);
    glMaterialfv(GL_FRONT, GL_SHININESS, mat_shininess);

    glEnable(GL_LIGHTING);
    glEnable(GL_LIGHT0);
    glDepthFunc(GL_LEQUAL);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_AUTO_NORMAL);
    glEnable(GL_NORMALIZE);
    init_surface();

    theNurb = gluNewNurbsRenderer();
    gluNurbsProperty(theNurb, GLU_SAMPLING_TOLERANCE, 25.0);
    gluNurbsProperty(theNurb, GLU_DISPLAY_MODE, GLU_FILL);
}

void display(void)
{
    GLfloat knots[8] = {0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0};

    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glPushMatrix();
        glRotatef(330.0, 1.,0.,0.);
        glScalef (0.5, 0.5, 0.5);

        gluBeginSurface(theNurb);
        gluNurbsSurface(theNurb, 
            8, knots,
            8, knots,
            4 * 3,
            3,
            &ctlpoints[0][0][0], 
            4, 4,
            GL_MAP2_VERTEX_3);
        gluEndSurface(theNurb);

    glPopMatrix();
    glFlush();
}

void myReshape(GLsizei w, GLsizei h)
{
    glViewport(0, 0, w, h);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective (45.0, (GLdouble)w/(GLdouble)h, 3.0, 8.0);

    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glTranslatef (0.0, 0.0, -5.0);
}


int main(int argc, char** argv)
{
    auxInitDisplayMode (AUX_SINGLE | AUX_RGBA);
    auxInitPosition (0, 0, 500, 500);
    auxInitWindow (argv[0]);
    myinit();
    auxReshapeFunc (myReshape);
    auxMainLoop(display);
}

As shown in Example 11-5 , gluNewNurbsRenderer() returns a new NURBS object, whose type is a pointer to a GLUnurbsObj structure. The gluBeginSurface() and gluEndSurface() pair bracket the rendering routine, saving and restoring the evaluator state. These three routines are summarized in Appendix C . The more complex routines, gluNurbsProperty() and gluNurbsSurface(), are discussed in this section. void gluNurbsProperty(GLUnurbsObj *nobj, GLenum property, GLfloat value);

Controls attributes of a NURBS object, nobj. The property argument specifies the property and can be GLU_SAMPLING_TOLERANCE, GLU_DISPLAY_MODE, GLU_CULLING, or GLU_AUTO_LOAD_MATRIX. The value argument indicates what the property should be. Since a NURBS object is rendered as primitives, it's sampled at different values of its parameter(s) (u and v) and broken down into small line segments or polygons for rendering. GLU_SAMPLING_TOLERANCE controls how often the NURBS object is sampled. The default value of 50.0 makes the largest sampled line segment or polygon edge 50.0 pixels long.

The default value for GLU_DISPLAY_MODE is GLU_FILL, which causes the surface to be rendered as polygons. If GLU_OUTLINE_POLYGON is used for the display-mode property, the outlines of polygons are rendered. Finally, GLU_OUTLINE_PATCH renders the outlines of patches and trimming curves (see the next section on trimming).

GLU_CULLING can speed up performance by not performing tessellation if the NURBS object falls completely outside the viewing volume; set this property to GL_TRUE to enable culling (the default is GL_FALSE). The GLU_AUTO_LOAD_MATRIX property determines whether the projection matrix, modelview matrix, and viewport are downloaded from the OpenGL server (GL_TRUE, the default), or whether the application must supply these matrices with gluLoadSamplingMatrices() (GL_FALSE).

void gluNurbsSurface (GLUnurbsObj *nobj, GLint uknot_count, GLfloat *uknot, GLint vknot_count, GLfloat *vknot, GLint u_stride, GLint v_stride, GLfloat *ctlarray, GLint uorder, GLint vorder, GLenum type);

Describes the vertices (or surface normals or texture coordinates) of a NURBS surface, nobj. Several of the values must be specified for both u and v parametric directions, such as the knot sequences (uknot and vknot), knot counts (uknot_count and vknot_count), and order of the polynomial (uorder and vorder) for the NURBS surface. Note that the number of control points isn't specified. Instead, it's derived by determining the number of control points along each parameter as the number of knots minus the order. Then, the number of control points for the surface is equal to the number of control points in each parametric direction, multiplied by one another. The ctlarray argument points to an array of control points.

The last parameter, type, is one of the two-dimensional evaluator types. Commonly, you might use GL_MAP2_VERTEX_3 for nonrational or GL_MAP2_VERTEX_4 for rational control points, respectively. You might also use other types, such as GL_MAP2_TEXTURE_COORD_* or GL_MAP2_NORMAL to calculate and assign texture coordinates or surface normals.

The u_stride and v_stride arguments represent the number of floating-point values between control points in each parametric direction. The evaluator type, as well as its order, affects the u_stride and v_stride values. In Example 11-5 , u_stride is 12 (4 * 3) because there are three coordinates for each vertex (set by GL_MAP2_VERTEX_3) and four control points in the parametric v direction; v_stride is 3 because each vertex had three coordinates, and v control points are adjacent to one another.

Drawing a NURBS curve is similar to drawing a surface, except that all calculations are done with one parameter, u, rather than two. Also, for curves, gluBeginCurve() and gluEndCurve() are the bracketing routines. void gluNurbsCurve (GLUnurbsObj *nobj, GLint uknot_count, GLfloat *uknot, GLint u_stride, GLfloat *ctlarray, GLint uorder, GLenum type);

Defines a NURBS curve for the object nobj. The arguments have the same meaning as those for gluNurbsSurface(). Note that this routine requires only one knot sequence, and one declaration of the order of the NURBS object. If this curve is defined within a gluBeginCurve()/gluEndCurve() pair, then the type can be any of the valid one-dimensional evaluator types (such as GL_MAP1_VERTEX_3 or GL_MAP1_VERTEX_4).

OpenGL Programming Guide