OpenGL编程轻松入门之NURBS曲线和曲面

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　　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 　　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 下载本文示例代码


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