OpenGL进阶（二）自定义矩阵加载

opengl里面的平移，旋转，缩放都是基于矩阵的运算，我们可以很方便地通过设定参数的方式调用一些接口函数来实现，同时我们也可以通过自定义的矩阵来实现上述的基本变换。

首先来看一个渲染程序。

[cpp]  view plain copy

1. GLfloat rtri;                          
2. GLfloat posX;  
3. GLfloat posY;  
4. GLfloat scale=0.5f;  

[cpp]  view plain copy

1. void renderGL()  
2. {  
3.     // Clear the color and depth buffers.   
4.     glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );  
5.     // We don't want to modify the projection matrix. */  
6.     glMatrixMode( GL_MODELVIEW );  
7.     glLoadIdentity( );  
8.     glTranslatef(posX,0.0f,-6.0f);    
9.     glRotatef(rtri,0.0f,1.0f,0.0f);                 
10.     glScalef(scale,scale,scale);  
11.     glBegin(GL_TRIANGLES);                    
12.         glColor3f(1.0f,0.0f,0.0f);              
13.         glVertex3f( 0.0f, 1.0f, 0.0f);            
14.         glColor3f(0.0f,1.0f,0.0f);              
15.         glVertex3f(-1.0f,-1.0f, 0.0f);            
16.         glColor3f(0.0f,0.0f,1.0f);              
17.         glVertex3f( 1.0f,-1.0f, 0.0f);            
18.     glEnd();                          
19.     if(posX<3.0f) posX+=0.001f;  
20.     else posX=-3.0f;  
21.     if(scale<2.0f) scale+=0.0005f;  
22.     else scale=0.5f;  
23.     rtri+=0.2f;                                                                                                                     
24.     SDL_GL_SwapBuffers( );  
25. }  

程序很简单，运行的结果就是一个不断旋转+缩放+平移的三角形。

所谓的变换就是于矩阵相乘，下面来看看不同的变换所对应的是什么样的矩阵。

平移变换：

P=[

1,0,0,0,

0,1,0,0,

0,0,1,0,

posX,posY,posZ,1

]

旋转变换（以Y轴为例,a为旋转角度）

Y=[

cos(a),0,-sin(a),0,

0,1,0,0,

sin(a),0,cos(a),0,

0,0,0,1

]

比例变换

S=[

qx,0,0,0,

0,qy,0,0,

0,0,qz,0,

0,0,0,1

]

对于矩阵运算不了解的可以参考《计算机图形》或者DirectX的龙书。

在OpenGL中关于使用自定义矩阵的函数有两个glLoadMatrixf(m)和glMultMatrixf(m).

前者是加载一个矩阵，后者则是将m与当前矩阵相乘。

下面是使用自定义矩阵的程序。

[cpp]  view plain copy

1. void renderGL()  
2. {  
3.     GLfloat moveMatrix[]=  
4.     {1.0f, 0.0f, 0.0f,0.0f,             
5.     0.0f,1.0f, 0.0f, 0.0f,            
6.     0.0f, 0.0f, 1.0f, 0.0f,           
7.     posX, 0.0f, -6.0f, 1.0f};  
8.   
9.     GLfloat scaleMatrix[]=  
10.     {  
11.     scale, 0.0f, 0.0f,0.0f,             
12.     0.0f,scale, 0.0f, 0.0f,            
13.     0.0f, 0.0f, scale, 0.0f,           
14.     0.0, 0.0f, 0.0f, 1.0f   
15.     };  
16.   
17.     GLfloat rotateYMatrix[]=  
18.     {  
19.     cos(rtri),0.0f,-sin(rtri),0.0f,  
20.     0.0f,1.0f,0.0f,0.0f,  
21.     sin(rtri),0.0f,cos(rtri),0.0f,  
22.     0.0f,0.0f,0.0f,1.0f  
23.     };  
24.   
25.     // Clear the color and depth buffers.   
26.     glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );  
27.     // We don't want to modify the projection matrix. */  
28.     glMatrixMode( GL_MODELVIEW );  
29.     glLoadIdentity();  
30.     glMultMatrixf(moveMatrix);   
31.     glMultMatrixf(scaleMatrix);   
32.     glMultMatrixf(rotateYMatrix);   
33.     glBegin(GL_TRIANGLES);                    
34.         glColor3f(1.0f,0.0f,0.0f);              
35.         glVertex3f( 0.0f, 1.0f, 0.0f);            
36.         glColor3f(0.0f,1.0f,0.0f);              
37.         glVertex3f(-1.0f,-1.0f, 0.0f);            
38.         glColor3f(0.0f,0.0f,1.0f);              
39.         glVertex3f( 1.0f,-1.0f, 0.0f);            
40.     glEnd();                          
41.     if(posX<3.0f) posX+=0.001f;  
42.     else posX=-3.0f;  
43.     if(scale<2.0f) scale+=0.0005f;  
44.     else scale=0.5f;  
45.     rtri+=0.002f;                                                                                                 
46.     SDL_GL_SwapBuffers( );  
47. }  

得到的效果和前面的程序完全相同。