OpenGL视图和模型变换中各变换发生顺序的思考

http://blog.csdn.net/xiajun07061225/article/details/7037020

 

在视图模型变换中，顶点v的变换是按照相反的顺序发生的，而不是按照它的代码中先后顺序出现的。下面举例说明。

考虑下面的代码：

glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glMultMatrixf(N);
    glMultMatrixf(M);
    glMultMatrixf(L);
    glBegin(GL_POINTS);
    glVertex3dv(v);
    glEnd();

glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
	glMultMatrixf(N);
	glMultMatrixf(M);
	glMultMatrixf(L);
	glBegin(GL_POINTS);
	glVertex3dv(v);
	glEnd();

在这段代码中，模型视图矩阵按顺序分别包含I、N、NM，最后是NML，其中I表示单位矩阵。经过变化的顶点是NMLv。因此顶点变换就是N(M(Lv))。

下面看绘制机器人手臂的display()函数的代码：

void display()
{
    glClear(GL_COLOR_BUFFER_BIT);
    glPushMatrix();

    glTranslatef(-1.0,0.0,0.0);
    glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
    glTranslatef(1.0,0.0,0.0);

    //绘制第一段手臂
    glPushMatrix();
    glScalef(2.0,0.4,1.0);
    glutWireCube(1.0);
    glPopMatrix();

    glTranslatef(1.0,0.0,0.0);
    glRotatef((GLfloat)elbow,0.0,0.0,1.0);
    glTranslatef(1.0,0.0,0.0);

    //绘制第二段手臂
    glPushMatrix();
    glScalef(2.0,0.4,1.0);
    glutWireCube(1.0);
    glPopMatrix();

    glPopMatrix();
    glutSwapBuffers();
}

void display()
{
	glClear(GL_COLOR_BUFFER_BIT);
	glPushMatrix();

	glTranslatef(-1.0,0.0,0.0);
	glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
	glTranslatef(1.0,0.0,0.0);

	//绘制第一段手臂
	glPushMatrix(); 
	glScalef(2.0,0.4,1.0);
	glutWireCube(1.0);
	glPopMatrix();

	glTranslatef(1.0,0.0,0.0);
	glRotatef((GLfloat)elbow,0.0,0.0,1.0);
	glTranslatef(1.0,0.0,0.0);

	//绘制第二段手臂
	glPushMatrix(); 
	glScalef(2.0,0.4,1.0);
	glutWireCube(1.0);
	glPopMatrix();

	glPopMatrix();
	glutSwapBuffers();	
}

我们通过逐步调试运行来查看效果。

现在注释掉代码：

glTranslatef(-1.0,0.0,0.0);
    glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
    glTranslatef(1.0,0.0,0.0);

glTranslatef(-1.0,0.0,0.0);
	glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
	glTranslatef(1.0,0.0,0.0);

以及绘制第二段手臂的代码：

//绘制第二段手臂
    glPushMatrix();
    glScalef(2.0,0.4,1.0);
    glutWireCube(1.0);
    glPopMatrix();

//绘制第二段手臂
	glPushMatrix(); 
	glScalef(2.0,0.4,1.0);
	glutWireCube(1.0);
	glPopMatrix();

只保留绘制第一段的代码，便于查看效果。

运行结果：

显示的是经过缩放了的立方体。

然后解除下面这行代码的注释：glTranslatef(1.0,0.0,0.0);(位于旋转之下的代码)

运行结果：

显示的是经过缩放、平移的结果。

在解除这行代码的注释：glRotatef((GLfloat)shoulder,0.0,0.0,1.0);

运行结果：

显示的是经过缩放、平移、再旋转地结果。

再解除这行代码的注释：glTranslatef(-1.0,0.0,0.0);(位于旋转之上的代码)

运行结果：

可以看出是上一步的结果又平移之后的效果。

从上面的单步效果可以看出，乘法的出现顺序和他们的代码中得出现顺序相反。

最后给出绘制两端机器人手臂整个代码：

//绘制机器人手臂
#include <GL/glut.h>

static int shoulder = 0,elbow = 0;//两段手臂旋转的角度

void init ()
{
    glClearColor(0.0,0.0,0.0,0.0);
    glShadeModel(GL_FLAT);
}

void display()
{
    glClear(GL_COLOR_BUFFER_BIT);
    glPushMatrix();

    glTranslatef(-1.0,0.0,0.0);
    glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
    glTranslatef(1.0,0.0,0.0);

    //绘制第一段手臂
    glPushMatrix();
    glScalef(2.0,0.4,1.0);
    glutWireCube(1.0);
    glPopMatrix();

    glTranslatef(1.0,0.0,0.0);
    glRotatef((GLfloat)elbow,0.0,0.0,1.0);
    glTranslatef(1.0,0.0,0.0);

    //绘制第二段手臂
    glPushMatrix();
    glScalef(2.0,0.4,1.0);
    glutWireCube(1.0);
    glPopMatrix();

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

void keyboard(unsigned char key,int x,int y)
{
    switch(key)//s和e键控制两端手臂的旋转角度
    {
    case 's':
        shoulder = (shoulder + 5)% 360;
        glutPostRedisplay();
        break;
    case 'S':
        shoulder = (shoulder - 5)% 360;
        glutPostRedisplay();
        break;
    case 'e':
        elbow = (elbow + 5) % 360;
        glutPostRedisplay();
        break;
    case 'E':
        elbow = (elbow - 5) % 360;
        glutPostRedisplay();
        break;
    default:
        break;
    }
}

int main(int argc,char** argv)
{
    glutInit(&argc,argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
    glutInitWindowSize(400,400);
    glutInitWindowPosition(100,100);
    glutCreateWindow(argv[0]);
    init();
    glutDisplayFunc(display);
    glutReshapeFunc(reshape);
    glutKeyboardFunc(keyboard);
    glutMainLoop();
    return 0;
}

//绘制机器人手臂
#include <GL/glut.h>

static int shoulder = 0,elbow = 0;//两段手臂旋转的角度

void init ()
{
	glClearColor(0.0,0.0,0.0,0.0);
	glShadeModel(GL_FLAT);
}

void display()
{
	glClear(GL_COLOR_BUFFER_BIT);
	glPushMatrix();

	glTranslatef(-1.0,0.0,0.0);
	glRotatef((GLfloat)shoulder,0.0,0.0,1.0);
	glTranslatef(1.0,0.0,0.0);

	//绘制第一段手臂
	glPushMatrix(); 
	glScalef(2.0,0.4,1.0);
	glutWireCube(1.0);
	glPopMatrix();

	glTranslatef(1.0,0.0,0.0);
	glRotatef((GLfloat)elbow,0.0,0.0,1.0);
	glTranslatef(1.0,0.0,0.0);

	//绘制第二段手臂
	glPushMatrix(); 
	glScalef(2.0,0.4,1.0);
	glutWireCube(1.0);
	glPopMatrix();

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

void keyboard(unsigned char key,int x,int y)
{
	switch(key)//s和e键控制两端手臂的旋转角度
	{
	case 's':
		shoulder = (shoulder + 5)% 360;
		glutPostRedisplay();
		break;
	case 'S':
		shoulder = (shoulder - 5)% 360;
		glutPostRedisplay();
		break;
	case 'e':
		elbow = (elbow + 5) % 360;
		glutPostRedisplay();
		break;
	case 'E':
		elbow = (elbow - 5) % 360;
		glutPostRedisplay();
		break;
	default:
		break;
	}
}

int main(int argc,char** argv)
{
	glutInit(&argc,argv);
	glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
	glutInitWindowSize(400,400);
	glutInitWindowPosition(100,100);
	glutCreateWindow(argv[0]);
	init();
	glutDisplayFunc(display);
	glutReshapeFunc(reshape);
	glutKeyboardFunc(keyboard);
	glutMainLoop();
	return 0;
}

运行效果(通过s和e键可以控制两端手臂的旋转角度)：