OpenGL的学习之路 -5

1.视景体 正交投影 

人眼看世界，有一个可见范围。范围内可见，范围外不可见。视景体就是这么一个概念。

（上图仅学习记录用）

在OGL中，有两种投影方式，对应两种视景体。第一种，正交投影；第二种，透视投影（更符合人眼）。

正交投影 

 

透视投影（可见，从视觉效果上，透视投影更符合人眼）

正交投影（代码）

 #include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>// Rotation amounts
static GLfloat xRot = 0.0f;
static GLfloat yRot = 0.0f;void ChangeSize(GLsizei w, GLsizei h) {GLfloat nRange = 100.0f;if (h == 0)  h = 1;glViewport(0, 0, w, h);  //视口是一个矩形区域，它定义了OpenGL窗口中可以显示图形的区域glMatrixMode(GL_PROJECTION);  //下面对堆栈的操作是对 投影堆栈glLoadIdentity();//保持视景体的 纵横比 为w/hif (w <= h)glOrtho (-nRange, nRange, -nRange*h/w, nRange*h/w, -nRange*2.0f, nRange*2.0f);elseglOrtho (-nRange*w/h, nRange*w/h, -nRange, nRange, -nRange*2.0f, nRange*2.0f);glMatrixMode(GL_MODELVIEW);  //再把堆栈由 投影栈 转换为 变换栈glLoadIdentity();
}//先不看这个（灯光什么的，初始化）
void SetupRC() {// Light values and coordinatesGLfloat  whiteLight[]  = { 0.45f, 0.45f, 0.45f, 1.0f };GLfloat  sourceLight[] = { 0.25f, 0.25f, 0.25f, 1.0f };GLfloat  lightPos[]    = { -50.f, 25.0f, 250.0f, 0.0f };glEnable(GL_DEPTH_TEST);	// Hidden surface removal <<============glFrontFace(GL_CCW);		// Counter clock-wise polygons face outglEnable(GL_CULL_FACE);		// Do not calculate inside of jet// Enable lightingglEnable(GL_LIGHTING);// Setup and enable light 0glLightModelfv(GL_LIGHT_MODEL_AMBIENT,whiteLight);glLightfv(GL_LIGHT0,GL_AMBIENT,sourceLight);glLightfv(GL_LIGHT0,GL_DIFFUSE,sourceLight);glLightfv(GL_LIGHT0,GL_POSITION,lightPos);glEnable(GL_LIGHT0);// Enable color trackingglEnable(GL_COLOR_MATERIAL);// Set Material properties to follow glColor valuesglColorMaterial(GL_FRONT, GL_AMBIENT_AND_DIFFUSE);// Black blue backgroundglClearColor(0.0f, 0.0f, 0.0f, 1.0f );
}void SpecialKeys(int key, int x, int y) {if (key == GLUT_KEY_UP)    xRot -= 5.0f;if (key == GLUT_KEY_DOWN)  xRot += 5.0f;if (key == GLUT_KEY_LEFT)  yRot -= 5.0f;if (key == GLUT_KEY_RIGHT) yRot += 5.0f;xRot = (GLfloat)((const int)xRot % 360);yRot = (GLfloat)((const int)yRot % 360);// Refresh the WindowglutPostRedisplay();
}void RenderScene(void) {float fZ,bZ;// Clear the window with current clearing colorglClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);fZ = 100.0f;bZ = -100.0f;// Save the matrix state and do the rotationsglPushMatrix();glRotatef(xRot, 1.0f, 0.0f, 0.0f);glRotatef(yRot, 0.0f, 1.0f, 0.0f);// Set material color, RedglColor3f(1.0f, 0.0f, 0.0f);// Front FaceglBegin(GL_QUADS);// Pointing straight out ZglNormal3f(0.0f, 0.0f, 1.0f);// Left PanelglVertex3f(-50.0f, 50.0f, fZ);glVertex3f(-50.0f, -50.0f, fZ);glVertex3f(-35.0f, -50.0f, fZ);glVertex3f(-35.0f,50.0f,fZ);// Right PanelglVertex3f(50.0f, 50.0f, fZ);glVertex3f(35.0f, 50.0f, fZ);glVertex3f(35.0f, -50.0f, fZ);glVertex3f(50.0f,-50.0f,fZ);// Top PanelglVertex3f(-35.0f, 50.0f, fZ);glVertex3f(-35.0f, 35.0f, fZ);glVertex3f(35.0f, 35.0f, fZ);glVertex3f(35.0f, 50.0f,fZ);// Bottom PanelglVertex3f(-35.0f, -35.0f, fZ);glVertex3f(-35.0f, -50.0f, fZ);glVertex3f(35.0f, -50.0f, fZ);glVertex3f(35.0f, -35.0f,fZ);// Top length section// Normal points up Y axisglNormal3f(0.0f, 1.0f, 0.0f);glVertex3f(-50.0f, 50.0f, fZ);glVertex3f(50.0f, 50.0f, fZ);glVertex3f(50.0f, 50.0f, bZ);glVertex3f(-50.0f,50.0f,bZ);// Bottom sectionglNormal3f(0.0f, -1.0f, 0.0f);glVertex3f(-50.0f, -50.0f, fZ);glVertex3f(-50.0f, -50.0f, bZ);glVertex3f(50.0f, -50.0f, bZ);glVertex3f(50.0f, -50.0f, fZ);// Left sectionglNormal3f(1.0f, 0.0f, 0.0f);glVertex3f(50.0f, 50.0f, fZ);glVertex3f(50.0f, -50.0f, fZ);glVertex3f(50.0f, -50.0f, bZ);glVertex3f(50.0f, 50.0f, bZ);// Right SectionglNormal3f(-1.0f, 0.0f, 0.0f);glVertex3f(-50.0f, 50.0f, fZ);glVertex3f(-50.0f, 50.0f, bZ);glVertex3f(-50.0f, -50.0f, bZ);glVertex3f(-50.0f, -50.0f, fZ);glEnd();glFrontFace(GL_CW);		// clock-wise polygons face outglBegin(GL_QUADS);// Back section// Pointing straight out ZglNormal3f(0.0f, 0.0f, -1.0f);// Left PanelglVertex3f(-50.0f, 50.0f, bZ);glVertex3f(-50.0f, -50.0f, bZ);glVertex3f(-35.0f, -50.0f, bZ);glVertex3f(-35.0f,50.0f,bZ);// Right PanelglVertex3f(50.0f, 50.0f, bZ);glVertex3f(35.0f, 50.0f, bZ);glVertex3f(35.0f, -50.0f, bZ);glVertex3f(50.0f,-50.0f,bZ);// Top PanelglVertex3f(-35.0f, 50.0f, bZ);glVertex3f(-35.0f, 35.0f, bZ);glVertex3f(35.0f, 35.0f, bZ);glVertex3f(35.0f, 50.0f,bZ);// Bottom PanelglVertex3f(-35.0f, -35.0f, bZ);glVertex3f(-35.0f, -50.0f, bZ);glVertex3f(35.0f, -50.0f, bZ);glVertex3f(35.0f, -35.0f,bZ);// Insides /glColor3f(0.75f, 0.75f, 0.75f);// Normal points up Y axisglNormal3f(0.0f, 1.0f, 0.0f);glVertex3f(-35.0f, 35.0f, fZ);glVertex3f(35.0f, 35.0f, fZ);glVertex3f(35.0f, 35.0f, bZ);glVertex3f(-35.0f,35.0f,bZ);// Bottom sectionglNormal3f(0.0f, 1.0f, 0.0f);glVertex3f(-35.0f, -35.0f, fZ);glVertex3f(-35.0f, -35.0f, bZ);glVertex3f(35.0f, -35.0f, bZ);glVertex3f(35.0f, -35.0f, fZ);// Left sectionglNormal3f(1.0f, 0.0f, 0.0f);glVertex3f(-35.0f, 35.0f, fZ);glVertex3f(-35.0f, 35.0f, bZ);glVertex3f(-35.0f, -35.0f, bZ);glVertex3f(-35.0f, -35.0f, fZ);// Right SectionglNormal3f(-1.0f, 0.0f, 0.0f);glVertex3f(35.0f, 35.0f, fZ);glVertex3f(35.0f, -35.0f, fZ);glVertex3f(35.0f, -35.0f, bZ);glVertex3f(35.0f, 35.0f, bZ);glEnd();glFrontFace(GL_CCW);		// Counter clock-wise polygons face out// Restore the matrix stateglPopMatrix();// Buffer swapglutSwapBuffers();
}int main(int argc, char *argv[]) {glutInit(&argc, argv);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);   //需要动画，使用的是双缓冲glutInitWindowSize(800, 600);glutCreateWindow("Orthographic Projection");//回调函数glutReshapeFunc(ChangeSize);    //改变窗口大小glutSpecialFunc(SpecialKeys);   //敲击特殊键glutDisplayFunc(RenderScene);   //显示//初始化函数SetupRC();glutMainLoop();return 0;
}

透视投影（替换代码）

2.几个代码示例（主要目的：弄明白 变换栈）

（1）三个球绕红球转

效果：

#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>// Rotation amounts
static float xRot = 0.0f;void RenderScene(void) {// Angle of revolution around the nucleusstatic float fElect1 = 0.0f;// Clear the window with current clearing colorglClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);// Reset the modelview matrixglMatrixMode(GL_MODELVIEW);glLoadIdentity();glTranslatef(0.0f, 0.0f, -100.0f); //AglColor3ub(255, 0, 0);glutSolidSphere(10.0f, 15, 15);  // 红色实心球（A）glColor3ub(255,255,0);glPushMatrix();glRotatef(fElect1, 0.0f, 1.0f, 0.0f);  //BglTranslatef(90.0f, 0.0f, 0.0f);       //CglutSolidSphere(6.0f, 15, 15);         //黄色实心球1（ABC）glPopMatrix();//xRot由特殊键控制glPushMatrix();glRotatef(45.0f, 0.0f, 0.0f, 1.0f);  //DglRotatef(xRot, 0.0f, 1.0f, 0.0f);   //EglTranslatef(-70.0f, 0.0f, 0.0f);    //FglutSolidSphere(6.0f, 15, 15);       //黄色实心球2（ADEF）glPopMatrix();glPushMatrix();glRotatef(300.0f,0.0f, 0.0f, 1.0f);    //GglRotatef(fElect1, 0.0f, 1.0f, 0.0f);  //HglTranslatef(0.0f, 0.0f, 60.0f);       //IglutSolidSphere(6.0f, 15, 15);         //黄色实心球3（AGHI)glPopMatrix();// Increment the angle of revolutionfElect1 += 1.0f;if (fElect1 > 360.0f)fElect1 = 0.0f;// Show the imageglutSwapBuffers();
}void SetupRC() //初始化函数
{glEnable(GL_DEPTH_TEST);	// Hidden surface removalglFrontFace(GL_CCW);		// Counter clock-wise polygons face outglEnable(GL_CULL_FACE);		// Do not calculate inside of jetglClearColor(0.0f, 0.0f, 0.0f, 1.0f );
}void SpecialKeys(int key, int x, int y) {if (key == GLUT_KEY_UP)    xRot -= 5.0f;if (key == GLUT_KEY_DOWN)  xRot += 5.0f;//if (key == GLUT_KEY_LEFT)  yRot -= 5.0f;//if (key == GLUT_KEY_RIGHT) yRot += 5.0f;if (key > 356.0f) xRot = 0.0f;if (key < -1.0f)  xRot = 355.0f;//if (key > 356.0f) yRot = 0.0f;//if (key < -1.0f)  yRot = 355.0f;glutPostRedisplay();    // Refresh the Window
}void TimerFunc(int value) {glutPostRedisplay();     // Refresh the Window/*millis：指定的时间间隔，以毫秒为单位。callback：指向回调函数的指针，该回调函数在指定时间间隔过后被调用。data：传递给回调函数的整型数值参数*/glutTimerFunc(10, TimerFunc, 1); //seconds, func, para(注册了一个定时器）
}void ChangeSize(int w, int h) {float nRange = 100.0f;if (h == 0) h = 1;glViewport(0, 0, w, h);glMatrixMode(GL_PROJECTION);glLoadIdentity();//正交投影(left, right, bottom, top, near, far)if (w <= h)glOrtho (-nRange, nRange, nRange*h/w, -nRange*h/w, -nRange*2.0f, nRange*2.0f);elseglOrtho (-nRange*w/h, nRange*w/h, nRange, -nRange, -nRange*2.0f, nRange*2.0f);
}int main(int argc, char* argv[]) {glutInit(&argc, argv);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);glutInitWindowSize(800, 600);glutCreateWindow("OpenGL Atom");glutReshapeFunc(ChangeSize);    //改变窗口大小时的回调函数glutSpecialFunc(SpecialKeys);   //敲击特殊键的回调函数glutDisplayFunc(RenderScene);   //显示的回调函数glutTimerFunc(500, TimerFunc, 1);   ///new!!(保持连续变化）SetupRC();glutMainLoop();return 0;
}

（2）键盘控制的自转和公转

效果：

///
#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>
#include <stdlib.h>
#include <iostream>///
static int year = 0, day = 0;///
void init(void) {glClearColor(0.0, 0.0, 0.0, 0.0);glShadeModel(GL_FLAT);
}///
void display(void) {glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0, 1.0, 1.0);glPushMatrix();glRotatef((GLfloat)year, 0.0, 1.0, 0.0);   //A（实现自传效果）glutWireSphere(1.0, 20, 16);               //画线框太阳（A）///思考：加上这两句的效果会怎样？//glPopMatrix();//glPushMatrix();glTranslatef(2.0, 0.0, 0.0);                //BglRotatef((GLfloat) day, 0.0, 1.0, 0.0);    //CglutWireSphere(0.2, 10, 8);                 //画线框地球（ABC）glPopMatrix();glutSwapBuffers();
}///
void reshape(int w, int h) {glViewport(0, 0,(GLsizei) w,(GLsizei) h);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluPerspective(60.0,(float) w/(float) h, 1.0, 20.0);glMatrixMode(GL_MODELVIEW);glLoadIdentity();gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
}///
void keyboard(unsigned char key, int x, int y) {switch(key) {case 'd':  day =(day + 10) % 360;   break;case 'D':  day =(day - 10) % 360;   break;case 'y':  year =(year + 5) % 360;  break;case 'Y':  year =(year - 5) % 360;  break;case 27:   exit(0);default:   break;}glutPostRedisplay();
}///
int main(int argc, char** argv) {std::cout<<"D/d: 行星转动\nY/y: 太阳转动\n";glutInit(&argc, argv);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);glutInitWindowSize(500, 500);glutInitWindowPosition(500, 100);glutCreateWindow("earthmoon");init();   //初始化函数glutDisplayFunc(display);    //显示的回调函数glutReshapeFunc(reshape);    //改变窗口大小的回调函数glutKeyboardFunc(keyboard);  //点击键盘的回调函数glutMainLoop();return 0;
}

如果点击‘D’或者‘d’，矩阵C变化，地球实现自转的效果；如果点击‘Y’或者‘y’，矩阵A变化，太阳自转，地球跟着太阳转；如果同时按下‘D’或者‘d’以及‘Y’或者‘y’，地球自转的同时绕着太阳公转，同时，太阳也在自转。

（3）星系

效果：

#include <math.h>
#include <gl/gl.h>
#include <gl/glu.h>
#include <gl/glut.h>
#define N  6///
// Lighting values
float whiteLight[]  = { 0.2f, 0.2f, 0.2f, 1.0f };
float sourceLight[] = { 1.0f, 1.0f, 1.0f, 1.0f };
float	lightPos[]  = { 0.0f, 0.0f, 0.0f, 1.0f };float para[N][3] = { {2.0f,  30.0f, 99.f},{3.0f,  50.0f, 44.f},{6.0f,  70.0f, 20.f},{5.0f,  90.0f, 80.f},{9.0f, 110.0f, 10.f},{2.0f, 120.0f, 15.f}};
float fEarthRot = 0;///
void RenderScene(void) {glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);glMatrixMode(GL_MODELVIEW);glPushMatrix();glLoadIdentity();glTranslatef(0.0f, 0.0f, -300.0f);  //AglRotatef(15, 1.0f, 0.0f, 0.0f);    //BglDisable(GL_LIGHTING);glColor3ub(255, 255, 0);glutSolidSphere(10.0f, 18, 17);  // 太阳(AB)glEnable(GL_LIGHTING);glLightfv(GL_LIGHT0, GL_POSITION, lightPos); // Move the light after we draw the sun!for (int i=0; i<N; ++i)   //画几大行星{glPushMatrix();  //AB再复制一份放到栈顶glRotatef(fEarthRot*para[i][2], 0.0f, 1.0f, 0.0f);   //CglColor3ub(0,0,255);glTranslatef(para[i][1],0.0f,0.0f);                  //DglutSolidSphere(para[i][0], 30, 17);                 //画行星（ABCD）glPushMatrix();      //ABCD再复制一份放到栈顶glLoadIdentity();    //转化为单位阵（I）glTranslatef(0.0f, 0.0f, -300.0f);   //EglRotatef(15, 1.0f, 0.0f, 0.0f);     //FglDisable(GL_LIGHTING);glColor3f(1,0,0);glBegin(GL_LINE_LOOP);  //画轨迹for (float j=0; j<2*3.14149265; j+=0.1f) {glVertex3f(para[i][1]*sin(j), 0.0f, para[i][1]*cos(j));  //轨迹（EF）}glEnd();glPopMatrix(); //将当前栈顶矩阵 EF 弹出glPopMatrix(); //将当前栈顶矩阵 ABCD 弹出，弹出后，栈顶元素变为ABglEnable(GL_LIGHTING);}glPopMatrix();	//将当前栈顶矩阵 AB 弹出fEarthRot += 0.1f;if (fEarthRot > 360.0f)	fEarthRot = 0.0f; //转起来glutSwapBuffers();
}//初始化函数，关于灯光的一些操作
///
void SetupRC() {glEnable(GL_DEPTH_TEST);glFrontFace(GL_CCW);glEnable(GL_CULL_FACE);glEnable(GL_LIGHTING);glLightModelfv(GL_LIGHT_MODEL_AMBIENT,whiteLight);glLightfv(GL_LIGHT0,GL_DIFFUSE,sourceLight);glLightfv(GL_LIGHT0,GL_POSITION,lightPos);glEnable(GL_LIGHT0);glEnable(GL_COLOR_MATERIAL);glColorMaterial(GL_FRONT, GL_AMBIENT_AND_DIFFUSE);glClearColor(0.3f, 0.3f, 0.3f, 1.0f );
}///
void TimerFunc(int value) {glutPostRedisplay();               //重新绘制glutTimerFunc(100, TimerFunc, 1);  //设置定时器
}///
void ChangeSize(int w, int h) {float fAspect;if (h == 0)  h = 1;glViewport(0, 0, w, h);fAspect = (float)w/(float)h;glMatrixMode(GL_PROJECTION);glLoadIdentity();gluPerspective(40.0f, fAspect, 1.0, 600.0);  //透视投影glMatrixMode(GL_MODELVIEW);glLoadIdentity();
}///
int main(int argc, char* argv[]) {glutInit(&argc, argv);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);glutInitWindowSize(800, 600);glutCreateWindow("Earth/Moon/Sun System");glutReshapeFunc(ChangeSize);        //改变窗口大小的回调函数glutDisplayFunc(RenderScene);       //显示的回调函数glutTimerFunc(250, TimerFunc, 1);   ///new!!SetupRC();  //初始化glutMainLoop();return 0;
}

程序分析：

（4）月亮绕着地球转、地球绕着太阳转

效果：

#include <math.h>
#include <gl/gl.h>
#include <gl/glu.h>
#include <gl/glut.h>///
// Lighting values
float  whiteLight[]  = { 0.2f, 0.2f, 0.2f, 1.0f };
float  sourceLight[] = { 1.0f, 1.0f, 1.0f, 1.0f };
float	lightPos[]    = { 0.0f, 0.0f, 0.0f, 1.0f };///
void RenderScene(void) {static float fMoonRot  = 0.0f;static float fEarthRot = 0.0f;glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);// Save the matrix state and do the rotationsglMatrixMode(GL_MODELVIEW);glPushMatrix();glLoadIdentity();glTranslatef(0.0f, 0.0f, -300.0f);  //AglDisable(GL_LIGHTING);glColor3ub(255, 255, 0);glutSolidSphere(18.0f, 18, 17);  /// 太阳(A)glEnable(GL_LIGHTING);// Move the light after we draw the sun!glLightfv(GL_LIGHT0, GL_POSITION, lightPos);glRotatef(fEarthRot, 0.0f, 1.0f, 0.0f); //BglColor3ub(0,0,255);glTranslatef(105.0f,0.0f,0.0f);   //CglutSolidSphere(6.0f, 30, 17);    ///地球（ABC）glColor3ub(200,200,200);glRotatef(fMoonRot,0.0f, 0.0f, 1.0f); //DglTranslatef(15.0f, 0.0f, 0.0f);      //EglutSolidSphere(3.0f, 30, 17);        ///月亮（ABCDE）// Restore the matrix stateglPopMatrix();	// Modelview matrixfMoonRot += 10.0f;if (fMoonRot > 360.0f)fMoonRot = 0.0f;fEarthRot += 2.0f;if (fEarthRot > 360.0f)fEarthRot = 0.0f;// Show the imageglutSwapBuffers();
}///
// This function does any needed initialization on the rendering context.
void SetupRC() {glEnable(GL_DEPTH_TEST);	// Hidden surface removalglFrontFace(GL_CCW);	   	// Counter clock-wise polygons face outglEnable(GL_CULL_FACE);		// Do not calculate inside of jetglEnable(GL_LIGHTING);glLightModelfv(GL_LIGHT_MODEL_AMBIENT,whiteLight);glLightfv(GL_LIGHT0,GL_DIFFUSE,sourceLight);glLightfv(GL_LIGHT0,GL_POSITION,lightPos);glEnable(GL_LIGHT0);glEnable(GL_COLOR_MATERIAL);glColorMaterial(GL_FRONT, GL_AMBIENT_AND_DIFFUSE);glClearColor(0.3f, 0.3f, 0.3f, 1.0f );
}///
void TimerFunc(int value) {glutPostRedisplay();glutTimerFunc(100, TimerFunc, 1);
}///
void ChangeSize(int w, int h) {float fAspect;if (h == 0)  h = 1;glViewport(0, 0, w, h);fAspect = (float)w/(float)h;glMatrixMode(GL_PROJECTION);glLoadIdentity();gluPerspective(45.0f, fAspect, 1.0, 425.0); //透视投影// Modelview matrix resetglMatrixMode(GL_MODELVIEW);glLoadIdentity();}///
int main(int argc, char* argv[]) {glutInit(&argc, argv);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);glutInitWindowSize(800, 600);glutCreateWindow("Earth/Moon/Sun System");glutReshapeFunc(ChangeSize);    //改变窗口大小的回调函数glutDisplayFunc(RenderScene);   //显示的回调函数glutTimerFunc(250, TimerFunc, 1);   ///new!!SetupRC();  //初始化函数glutMainLoop();return 0;
}

 推广：

（5）机器人的手臂

效果：

///
#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>
#include <stdlib.h>
#include <stdio.h>///
static int shoulder = 0, elbow = 0;///
void init(void) {glClearColor (0.0, 0.0, 0.0, 0.0);glShadeModel (GL_FLAT);
}///
void display(void) {glClear (GL_COLOR_BUFFER_BIT);glPushMatrix();         //将当前栈顶矩阵A复制一份，放在栈顶glTranslatef (-1.0f, 0.0, 0.0);   //BglRotatef ((GLfloat) shoulder, 0.0, 0.0, 1.0f);   //CglTranslatef (1.0, 0.0, 0.0);     //DglPushMatrix();         //将当前栈顶矩阵ABCD复制一份，放在栈顶glScalef (2.0f, 0.4f, 1.0f);       //EglutWireCube (1.0);     ///机器人 上手臂(ABCDE)glPopMatrix();          //将当前栈顶矩阵ABCDE弹出glTranslatef (1.0f, 0.0, 0.0);     //FglRotatef ((GLfloat) elbow, 0.0, 0.0, 1.0f);   //GglTranslatef (1.0f, 0.0, 0.0);     //HglScalef (2.0f, 0.4f, 1.0f);  //IglutWireCube (1.0f);    ///机器人 下手臂（ABCDFGHI）glPopMatrix();          //将当前栈顶矩阵ABCDFGHI弹出glPopMatrix();          //将当前栈顶矩阵ABCD弹出glPopMatrix();          //将当前栈顶矩阵A弹出glutSwapBuffers();
}///
void reshape (int w, int h) {glViewport (0, 0, (GLsizei) w, (GLsizei) h);glMatrixMode (GL_PROJECTION);glLoadIdentity ();gluPerspective(65.0, (GLfloat) w/(GLfloat) h, 1.0, 20.0);  //透视投影glMatrixMode(GL_MODELVIEW);glLoadIdentity();glTranslatef (0.0, 0.0, -5.0);   // A
}///
void keyboard (unsigned char key, int x, int y) {switch (key) {case 's':  shoulder = (shoulder + 5) % 360;  break;case 'S':  shoulder = (shoulder - 5) % 360;  break;case 'e':  elbow = (elbow + 5) % 360;  break;case 'E':  elbow = (elbow - 5) % 360;  break;case 27:   exit(0);default:   break;}glutPostRedisplay();
}///
int main(int argc, char** argv) {printf("S, Or E\n");glutInit(&argc, argv);glutInitDisplayMode (GLUT_DOUBLE | GLUT_RGB);glutInitWindowSize (500, 500);glutInitWindowPosition (100, 100);glutCreateWindow ("robot");init ();     //初始化函数glutDisplayFunc(display);    //显示的回调函数glutReshapeFunc(reshape);    //改变窗口大小时的回调函数glutKeyboardFunc(keyboard);  //敲击键盘的回调函数glutMainLoop();return 0;
}

简单分析：

显示函数中，旋转之前都有一个平移。也就是物体进行缩放后（长度变为2），先向右平移一个单位，之后再进行旋转，这样物体的最左侧位于原点位置，相当于物体以其最右侧为旋转固定中心进行旋转。完成这一效果之后，再进行平移也不影响这一效果（物体以其最右侧为旋转固定中心进行旋转）。