OpenGL曲面
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曲面的构造可以是网格线和填充曲面形式，其实与曲线很类似只是变为二维而已。 1.曲面定义 void glMap2{fd}(GLenum target,TYPE u1,TYPE u2,GLint ustride,GLint uorder, TYPE v1,TYPE v2,GLint vstride,GLint vorder,TYPE points); target的定义同上次介绍的曲线中target的定义。 U V是二维曲面坐标 uorder,vorder;ustride,vstride的定义都类似曲线定义。 points是控制点坐标 2.曲面任意一点的计算 void glEvalCoord2{fd}[v](TYPE u,TYPE v); 以曲线坐标U V来计算曲面内任意一点的世界坐标的位置 3.曲面绘制的控制 void glMapGrid2{fd}(GLenum nu,TYPE u1,TYPE u2,GLenum nv,TYPE v1,TYPE v2); 定义曲面参数空间均匀网格，从u1到u2分为等间隔nu步，从v1到v2分为等间隔nv步。 下面给出一个以网格线描绘曲面的例子： //////////////////////////////////////////////////////////// #include <gl/gl.h>#include <gl/glu.h>#include <gl/glaux.h>#pragma comment(lib, "OpenGl32.lib")#pragma comment(lib, "glu32.lib")#pragma comment(lib, "glaux.lib")#pragma warning(disable : 4244)// MIPS#pragma warning(disable : 4136)// X86#pragma warning(disable : 4051)// ALPHAvoid myinit(void); void CALLBACK display(void); void CALLBACK reshape(GLsizei w,GLsizei h); //控制点坐标 GLfloat points[4][4][3]={ {{-1.5,-1.5,2.0},{-0.5,-1.5,2.0}, {0.5,-1.5,-1.0},{1.5,-1.5,2.0}}, {{-1.5,-0.5,1.0},{-0.5,1.5,2.0}, {0.5,0.5,1.0},{1.5,-0.5,-1.0}}, {{-1.5,0.5,2.0},{-0.5,0.5,1.0}, {0.5,0.5,3.0},{1.5,-1.5,1.5}}, {{-1.5,1.5,-2.0},{-0.5,1.5,-2.0}, {0.5,0.5,1.0},{1.5,1.5,-1.0}}}; //为了清楚显示控制点而设置的一组颜色 GLfloat color[4][3]={ {1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}}; void myinit(void) { auxInitDisplayMode(AUX_SINGLE|AUX_RGBA); auxInitPosition(0,0,500,500); auxInitWindow("sample1"); glClearColor(0.0,0.0,0.0,0.0); glClear(GL_COLOR_BUFFER_BIT); //利用glEnable()来启用曲面模式 glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]); glEnable(GL_MAP2_VERTEX_3); glMapGrid2f(20,0.0,1.0,20,0.0,1.0); glEnable(GL_DEPTH_TEST); } void CALLBACK reshape(GLsizei w,GLsizei h) { glViewport(0,0,w,h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if(w<=h) glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0); else glOrtho(-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); } void CALLBACK display(void) { glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glColor3f(0.0,0.0,1.0); glPushMatrix(); glRotatef(35.0,1.0,1.0,1.0); //用直线段的连接描绘曲面结构 glBegin(GL_LINE_STRIP); int i,j; //在U V方向各画出8条网格线，用以构造曲面结构 for(j=0;j<=8;j++) { //在U方向用30条直线段描绘一条曲线 glBegin(GL_LINE_STRIP); for(i=0;i<=30;i++) glEvalCoord2f((GLfloat)i/30.0,(GLfloat)j/8.0); glEnd(); //在V方向用30条直线段描绘一条曲线 glBegin(GL_LINE_STRIP); for(i=0;i<=30;i++) glEvalCoord2f((GLfloat)j/8.0,(GLfloat)i/30.0); glEnd(); } //用不同的颜色把控制点显示出来 glPointSize(4.0); glBegin(GL_POINTS); for(i=0;i<4;i++) for(j=0;j<4;j++) { glColor3fv(color[i]); glVertex3fv(&points[i][j][0]); } glEnd(); glPopMatrix(); glFlush(); } void main(void) { myinit(); auxReshapeFunc(reshape); auxMainLoop(display); } //end of sample /////////////////////////////////////////////////////// 应用中常常不满足曲面的框架结构。下面就介绍填充曲面的绘制方法： void glEvalMesh2(GLenum mode,GLint p1,GLint p2,GLint q1,GLint q2); 把用glMapGrid2{fd}()设置的网格应用到已经启用的曲面计算上。 mode可以是GL_POINT GL_LINE GL_FILL。顾名思义，GL_FILL就是生成填充曲面 这里给出一个有光照处理的BEZIER曲面的例子（这个曲面除了绘制方法不同，数学 形式和前面的是一样的）。 /////////////////////////////////////////////////////// //sample.cpp #include <gl/gl.h>#include <gl/glu.h>#include <gl/glaux.h>#pragma comment(lib, "OpenGl32.lib")#pragma comment(lib, "glu32.lib")#pragma comment(lib, "glaux.lib")#pragma warning(disable : 4244)// MIPS#pragma warning(disable : 4136)// X86#pragma warning(disable : 4051)// ALPHAvoid myinit(void); void CALLBACK display(void); void CALLBACK reshape(GLsizei w,GLsizei h); GLfloat points[4][4][3]={ {{-1.5,-1.5,2.0},{-0.5,-1.5,2.0}, {0.5,-1.5,-1.0},{1.5,-1.5,2.0}}, {{-1.5,-0.5,1.0},{-0.5,1.5,2.0}, {0.5,0.5,1.0},{1.5,-0.5,-1.0}}, {{-1.5,0.5,2.0},{-0.5,0.5,1.0}, {0.5,0.5,3.0},{1.5,-1.5,1.5}}, {{-1.5,1.5,-2.0},{-0.5,1.5,-2.0}, {0.5,0.5,1.0},{1.5,1.5,-1.0}}}; GLfloat color[4][3]={ {1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}}; //初始化光照、材质的过程 void initlights(void) { GLfloat ambient[]={0.4,0.6,0.2,1.0}; GLfloat position[]={0.0,1.0,3.0,1.0}; GLfloat mat_diffuse[]={0.2,0.4,0.8,1.0}; GLfloat mat_specular[]={1.0,1.0,1.0,1.0}; GLfloat mat_shininess[]={80.0}; glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glLightfv(GL_LIGHT0,GL_AMBIENT,ambient); glLightfv(GL_LIGHT0,GL_POSITION,position); glMaterialfv(GL_FRONT,GL_DIFFUSE,mat_diffuse); glMaterialfv(GL_FRONT,GL_SPECULAR,mat_specular); glMaterialfv(GL_FRONT,GL_SHININESS,mat_shininess); } void myinit(void) { auxInitDisplayMode(AUX_SINGLE|AUX_RGBA); auxInitPosition(0,0,500,500); auxInitWindow("sample1"); glClearColor(0.0,0.0,0.0,0.0); glClear(GL_COLOR_BUFFER_BIT); glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]); glEnable(GL_MAP2_VERTEX_3); glEnable(GL_AUTO_NORMAL); // glEnable(GL_NORMALIZE); glMapGrid2f(20,0.0,1.0,20,0.0,1.0); glEnable(GL_DEPTH_TEST); //初始化光照、材质 initlights(); // glShadeModel(GL_FLAT); } void CALLBACK reshape(GLsizei w,GLsizei h) { glViewport(0,0,w,h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if(w<=h) glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0); else glOrtho(-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); } void CALLBACK display(void) { glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT); glColor3f(0.0,0.0,1.0); glPushMatrix(); glRotatef(35.0,1.0,1.0,1.0); //将原来网格的绘制部分注释掉，代替以填充曲面的绘制方法 glEvalMesh2(GL_FILL,0,20,0,20); int i,j; /* for(j=0;j<=8;j++) { glBegin(GL_LINE_STRIP); for(i=0;i<=30;i++) glEvalCoord2f((GLfloat)i/30.0,(GLfloat)j/8.0); glEnd(); glBegin(GL_LINE_STRIP); for(i=0;i<=30;i++) glEvalCoord2f((GLfloat)j/8.0,(GLfloat)i/30.0); glEnd(); } */ glPointSize(4.0); glBegin(GL_POINTS); for(i=0;i<4;i++) for(j=0;j<4;j++) { glColor3fv(color[i]); glVertex3fv(&points[i][j][0]); } glEnd(); glPopMatrix(); glFlush(); } void main(void) { myinit(); auxReshapeFunc(reshape); auxMainLoop(display); } //end of sample //////////////////////////////////////////////////////////////// 一个真正具有实体的曲面就展现出来乐。控制点的不同，可以控制曲面的形状 可以看出OPENGL的强大功能，只用很少的原代码就产生真实的3D效果。 在以此篇结束复杂建模前，给出一个绘制NURBS曲面（非均匀B样条曲面）的例子， 这里用到乐一些OPENGL实用库提供的专门函数。所有的新东东都在程序中做乐注 释，注释给出过程的含义，具体函数的操作可以详细查阅联机手册。 /////////////////////////////////////////////////////////////// //sample.cpp #include <gl/gl.h>#include <gl/glu.h>#include <gl/glaux.h>#pragma comment(lib, "OpenGl32.lib")#pragma comment(lib, "glu32.lib")#pragma comment(lib, "glaux.lib")#pragma warning(disable : 4244)// MIPS#pragma warning(disable : 4136)// X86#pragma warning(disable : 4051)// ALPHA void myinit(void); void CALLBACK display(void); void CALLBACK reshape(GLsizei w,GLsizei h); //定义一组控制点的存储空间 GLfloat points[4][4][3]; //定义一个指向NURBS曲面对象的指针 GLUnurbsObj *theNurb; //用来生成控制点的过程，取代被注释掉的原来直接赋值方式生成控制点 void init_surface(void) { int u,v; for(u=0;u<4;u++) { for(v=0;v<4;v++) { points[u][v][0]=2.0*((GLfloat)u-1.5); points[u][v][1]=2.0*((GLfloat)v-1.5); if((u==1||u==2)&&(v==1||v==2)) points[u][v][2]=3.0; else points[u][v][2]=-3.0; } } } /* GLfloat points[4][4][3]={ {{-1.5,-1.5,2.0},{-0.5,-1.5,4.0}, {0.5,-1.5,3.0},{1.5,-1.5,2.0}}, {{-1.5,-0.5,3.0},{-0.5,1.5,4.0}, {0.5,0.5,2.0},{1.5,-0.5,-1.0}}, {{-1.5,0.5,2.0},{-0.5,0.5,4.0}, {0.5,0.5,5.0},{1.5,-1.5,1.5}}, {{-1.5,1.5,-2.0},{-0.5,1.5,3.0}, {0.5,0.5,1.0},{1.5,1.5,-1.0}}}; */ GLfloat color[4][3]={ {1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0},{1.0,1.0,1.0}}; void initlights(void) { GLfloat ambient[]={0.4,0.6,0.2,1.0}; GLfloat position[]={0.0,1.0,3.0,1.0}; GLfloat mat_diffuse[]={0.2,0.4,0.8,1.0}; GLfloat mat_specular[]={1.0,1.0,1.0,1.0}; GLfloat mat_shininess[]={80.0}; glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glLightfv(GL_LIGHT0,GL_AMBIENT,ambient); glLightfv(GL_LIGHT0,GL_POSITION,position); glMaterialfv(GL_FRONT,GL_DIFFUSE,mat_diffuse); glMaterialfv(GL_FRONT,GL_SPECULAR,mat_specular); glMaterialfv(GL_FRONT,GL_SHININESS,mat_shininess); //首先初始化控制点 init_surface(); //创建一个NURBS曲面的对象 theNurb=gluNewNurbsRenderer(); //修改此曲面对象的属性 gluNurbsProperty(theNurb,GLU_SAMPLING_TOLERANCE,25.0); gluNurbsProperty(theNurb,GLU_DISPLAY_MODE,GLU_FILL); } void myinit(void) { auxInitDisplayMode(AUX_SINGLE|AUX_RGBA); auxInitPosition(0,0,500,500); auxInitWindow("sample1"); glClearColor(0.0,0.0,0.0,0.0); glClear(GL_COLOR_BUFFER_BIT); glMap2f(GL_MAP2_VERTEX_3,0,1,3,4,0,1,12,4,&points[0][0][0]); glEnable(GL_MAP2_VERTEX_3); glEnable(GL_AUTO_NORMAL); glEnable(GL_NORMALIZE); glMapGrid2f(20,0.0,1.0,20,0.0,1.0); glEnable(GL_DEPTH_TEST); initlights(); // glShadeModel(GL_FLAT); } void CALLBACK reshape(GLsizei w,GLsizei h) { glViewport(0,0,w,h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); if(w<=h) glOrtho(-5.0,5.0,-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0); else glOrtho(-5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w,-5.0,5.0,-5.0,5.0); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); } void CALLBACK display(void) { //B样条曲面（NURBS）的控制向量，可以参阅图形学的相关书籍 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); glColor3f(0.0,0.0,1.0); glPushMatrix(); glRotatef(35.0,1.0,1.0,1.0); glRotatef(-60.0,1.0,0.0,0.0); glScalef(0.5,0.5,0.5); //注释掉原来的曲面绘制函数，代之以新的NURBS曲面绘制函数 // glEvalMesh2(GL_FILL,0,20,0,20); //定义曲面的数学模型，确定其形状 gluNurbsSurface(theNurb, 8,knots, 8,knots, 4*3, 3, &points[0][0][0], 4,4, GL_MAP2_VERTEX_3); //结束曲面的绘制，此结构很类似于标准的glBegin()...glEnd() gluEndSurface(theNurb); int i,j; glPointSize(4.0); glBegin(GL_POINTS); for(i=0;i<4;i++) for(j=0;j<4;j++) { glColor3fv(color[i]); glVertex3fv(&points[i][j][0]); } glEnd(); glPopMatrix(); glFlush(); } void main(void) { myinit(); auxReshapeFunc(reshape); auxMainLoop(display); } //end of sample ////////////////////////////////////////////////////////////////// 至此，复杂建模告于段落。下次介绍特殊光照
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