2024年4月1日发(作者：)
上一节讲了一般的曲线与曲面的绘制，本节讲NURBS曲线和曲面的绘制。
例11：此例绘制两个相同形状的NURBS曲面，不同之处是一个为线框式，一个是由
实多边形组成。运行后可以看到其中的区别，如图十三所示。
#include
#include
GLUnurbsObj *theNurb1;
GLUnurbsObj *theNurb2;
GLfloat ctrlpoints[5][5][3] = {{{-3,0.5,0},{-1,1.5,0},{-2,2,0},{1,-1,0},{-5,0,0}},
{{-3,0.5,-1},{-1,1.5,-1},{-2,2,-1},{1,-1,-1},{-5,0,-1}},
{{-3,0.5,-2},{-1,1.5,-2},{-2,2,-2},{1,-1,-2},{-5,0,-2}},
{{-3,0.5,-3},{-1,1.5,-3},{-2,2,-3},{1,-1,-3},{-5,0,-3}},
{{-3,0.5,-4},{-1,1.5,-4},{-2,2,-4},{1,-1,-4},{-5,0,-4}}};//控制点
GLfloat mat_diffuse[] = {1.0,0.5,0.1,1.0};
GLfloat mat_specular[] = {1.0,1.0,1.0,1.0};
GLfloat mat_shininess[] = {100.0};
GLfloat light_position[] = {0.0,-10.0,0.0,1.0};
void myInit(void)
{
glClearColor(1.0,1.0,1.0,0.0);//设置背景色
/*为光照模型指定材质参数*/
glMaterialfv(GL_FRONT,GL_DIFFUSE,mat_diffuse);
glMaterialfv(GL_FRONT,GL_SPECULAR,mat_specular);
glMaterialfv(GL_FRONT,GL_SHININESS,mat_shininess);
glLightfv(GL_FRONT,GL_POSITION,light_position);//设置光源参数
glLightModeli(GL_LIGHT_MODEL_TWO_SIDE,GL_TRUE);//设置光照模型参数
/*激活光照*/
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glDepthFunc(GL_LEQUAL);
glEnable(GL_DEPTH_TEST);
glEnable(GL_LEQUAL);
glEnable(GL_AUTO_NORMAL);
glEnable(GL_NORMALIZE);
/*设置特殊效果*/
glBlendFunc(GL_SRC_ALPHA,GL_ONE_MINUS_SRC_ALPHA);
glHint(GL_LINE_SMOOTH_HINT,GL_DONT_CARE);
glEnable(GL_BLEND);
glFrontFace(GL_CW);
glShadeModel(GL_SMOOTH);
glEnable(GL_LINE_SMOOTH);
theNurb1 = gluNewNurbsRenderer();//创建NURBS对象theNurb1
gluNurbsProperty(theNurb1,GLU_SAMPLING_TOLERANCE,25.0);
gluNurbsProperty(theNurb1,GLU_DISPLAY_MODE,GLU_OUTLINE_POLYGON);
theNurb2 = gluNewNurbsRenderer();//创建NURBS对象theNurb2
gluNurbsProperty(theNurb2,GLU_SAMPLING_TOLERANCE,25.0);
gluNurbsProperty(theNurb2,GLU_DISPLAY_MODE,GLU_FILL);
}
int spin = 0;
/*接收键盘指令*/
static void myKey(unsigned char key,int x,int y)
{
switch(key)
{
case'd':
spin = spin + 1;
glRotatef(spin,1.0,1.0,0.0);
glutPostRedisplay();
break;
case 27:
exit(0);
default:
break;
}
}
/*绘制曲面*/
void myDisplay(void)
{
GLfloat knots[10] = {0.0,0.0,0.0,0.0,0.0,1.0,1.0,1.0,1.0,1.0};
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glRotatef(50.0,1.0,1.0,0.0);
/*第一个曲面*/
glPushMatrix();
glTranslatef(1.0,0.0,0.0);
gluBeginSurface(theNurb1);
/*定义曲面形状*/
gluNurbsSurface(theNurb1,10,knots,10,knots,5*3,3,&ctrlpoints[0][0][0],5,5,GL_MAP2_VERTEX_3);
gluEndSurface(theNurb1);
glPopMatrix();
/*第二个曲面*/
glPushMatrix();
glTranslatef(7.0,0.0,0.0);
gluBeginSurface(theNurb2);
/*定义曲面形状*/
gluNurbsSurface(theNurb2,10,knots,10,knots,5*3,3,&ctrlpoints[0][0][0],5,5,GL_MAP2_VERTEX_3);
gluEndSurface(theNurb2);
glPopMatrix();
glutSwapBuffers();
}
void myReshape(GLsizei w,GLsizei h)
{
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluPerspective(50.0,(GLfloat)w/(GLfloat)h,1.0,15.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.0,0.0,-9.0);
}
int main(int argc,char ** argv)
{
/*初始化*/
glutInit(&argc,argv);
glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB|GLUT_DEPTH);
glutInitWindowSize(600,400);
glutInitWindowPosition(200,200);
/*创建窗口*/
glutCreateWindow("NURBS surface");
/*绘制与显示*/
myInit();
glutKeyboardFunc(myKey);
glutReshapeFunc(myReshape);
glutDisplayFunc(myDisplay);
/*进入GLUT事件处理循环*/
glutMainLoop();
return(0);
}
·GLUnurbsObj* glNewNurbsRenderer（）创建一个NURBS对象，并返回一个指向该
对象的指针。如果没有足够的内存分配给该对象，则返回值为0。
·void gluNurbsProperty(GLUnurbsObj* nobj, GLenum property, GLfloat value)设置
NURBS属性。
nobj 指向NURBS对象的指针。
property需设置的属性。
value 设置指定属性的值。
·glBeginSurface及gluEndSurface两个函数一起限定一个NURBS面的定义。返回值
均为void，参数均为GLUnurbsObj* nobj，为指向NURBS对象的指针。
·void gluNurbsSurface(GLUnurbsObj *nobj, Glint knot_count, GLfloat tknot_count,
GLfloat *tknot, Glint s_stride, Glint t_stride, GLfloat *ctlarry, GLint sorder, GLint
torder,GLenum type) 定义NURBS曲面形状。
nobj 指向NURBS对象的指针。
sknot_count 参数化u方向上的节点数。
sknot 参数化u方向上的非递减节点值。
tknot_count 参数化v方向上的节点数。
tknot 参数化v方向上的非递减节点值。
s_stride在ctlarry中参数化u方向上相邻控制点的偏移量。
t_stride在ctlarry中参数化v方向上相邻控制点的偏移量。
ctlarryNURBS的控制点数组。
sorder参数化u方向上NURBS的阶数，阶数比维数大1。
torder参数化v方向上NURBS的阶数，阶数比维数大1。
type曲面类型。
图十三：NURBS曲面
例12：绘制一个彩色的曲线，曲线闭合成圆。在曲线的边缘绘制8个点，如图十四所
示。
#include
#include
GLUnurbsObj *theNurb;
GLfloat ctrlpoints[12][3] = {{4,0,0},{2.828,2.828,0},{0,4,0},{-2.828,2.828,0},
{-4,0,0},{-2.828,-2.828,0},{0,-4,0},{2.828,-2.828,0},
{4,0,0},{2.828,2.828,0},{0,4,0},{2.828,2.828,0}};//控制点
GLfloat color[12][3]={{1.0,0.0,0.0},{1.0,1.0,0.0},{0.0,1.0,0.0},{-1.0,1.0,0.0},
{-1.0,0.0,0.0},{-1.0,-1.0,0.0},{0.0,-1.0,0.0},{1.0,-1.0,0.0},
{1.0,0.0,0.0},{1.0,1.0,0.0},{0.0,1.0,0.0},{1.0,1.0,0.0}};
GLfloat knots[15] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};
void myInit(void)
{
glClearColor(1.0,1.0,1.0,0.0);//设置背景色
theNurb = gluNewNurbsRenderer();//创建NURBS对象theNurb
gluNurbsProperty(theNurb,GLU_SAMPLING_TOLERANCE,10);
}
/*绘制曲线*/
void myDisplay(void)
{
int i;
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glColor3f(0.0,0.0,0.0);
glLineWidth(3.0);
/*绘制曲线*/
gluBeginCurve(theNurb);
gluNurbsCurve(theNurb,15,knots,3,&ctrlpoints[0][0],3,GL_MAP1_VERTEX_3);
gluNurbsCurve(theNurb,15,knots,3,&ctrlpoints[0][0],3,GL_MAP1_COLOR_4);
gluEndCurve(theNurb);
/*绘制点*/
glColor3f(1.0,0.0,0.0);
glPointSize(5.0);
glBegin(GL_POINTS);
for(i = 0;i < 8;i++)
glVertex2fv(&ctrlpoints[i][0]);
glEnd();
glutSwapBuffers();
}
void myReshape(GLsizei w,GLsizei h)
{
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
if(w <=h)
glOrtho(-10.0,10.0,-10.0*(GLfloat)h/(GLfloat)w,10.0*(GLfloat)h/(GLfloat)w,-10.0,10.0);
else
glOrtho(-10.0*(GLfloat)w/(GLfloat)h,10.0*(GLfloat)w/(GLfloat)h,-10.0,10.0,-10.0,10.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glTranslatef(0.0,0.0,-9.0);
}
int main(int argc,char ** argv)
{
/*初始化*/
glutInit(&argc,argv);
glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGB|GLUT_DEPTH);
glutInitWindowSize(600,400);
glutInitWindowPosition(200,200);
/*创建窗口*/
glutCreateWindow("NURBS curve");
/*绘制与显示*/
myInit();
glutReshapeFunc(myReshape);
glutDisplayFunc(myDisplay);
glutMainLoop();
return(0);
}
·gluBeginCurve，gluEndCurve限定NURBS曲面。返回值均为void，参数均为
GLUnurbsObj* nobj，为指向NURBS对象的指针。
·void gluNurbsCurve（GLUnurbsObj *nobj， GLint nknots， GLfloat *knot， Glint stride，
GLfloat *ctlarray， GLint order，GLenum type）定义曲线形状。
nobj 指向NURBS对象的指针。
nknots 节点数，节点数等于控制点数加上阶数。
knot nknots数组非递减节点值。
stride相邻控制点的偏移量。
Ctlarry指向NURBS的控制点数组的指针。
order NURBS曲线的阶数，阶数比维数大1。
type曲面类型。
图十四：NURBS曲线
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