OpenGL進階(二) – 自訂矩陣載入

opengl裡面的平移，旋轉，縮放都是基於矩陣的運算，我們可以很方便地通過設定參數的方式調用一些介面函數來實現，同時我們也可以通過自訂的矩陣來實現上述的基本變換。

首先來看一個渲染程式。

GLfloat rtri;                        GLfloat posX;GLfloat posY;GLfloat scale=0.5f;

void renderGL(){    // Clear the color and depth buffers.     glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );    // We don't want to modify the projection matrix. */    glMatrixMode( GL_MODELVIEW );    glLoadIdentity( );    glTranslatef(posX,0.0f,-6.0f);      glRotatef(rtri,0.0f,1.0f,0.0f);                   glScalef(scale,scale,scale);    glBegin(GL_TRIANGLES);                          glColor3f(1.0f,0.0f,0.0f);                    glVertex3f( 0.0f, 1.0f, 0.0f);                  glColor3f(0.0f,1.0f,0.0f);                    glVertex3f(-1.0f,-1.0f, 0.0f);                  glColor3f(0.0f,0.0f,1.0f);                    glVertex3f( 1.0f,-1.0f, 0.0f);              glEnd();                            if(posX<3.0f) posX+=0.001f;    else posX=-3.0f;    if(scale<2.0f) scale+=0.0005f;    else scale=0.5f;    rtri+=0.2f;                                                                                                                       SDL_GL_SwapBuffers( );}

程式很簡單，啟動並執行結果就是一個不斷旋轉+縮放+平移的三角形。

所謂的變換就是於矩陣相乘，下面來看看不同的變換所對應的是什麼樣的矩陣。

平移變換：

P=[

1,0,0,0,

0,1,0,0,

0,0,1,0,

posX,posY,posZ,1

]

旋轉變換（以Y軸為例,a為旋轉角度）

Y=[

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

0,1,0,0,

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

0,0,0,1

]

比例變換

S=[

qx,0,0,0,

0,qy,0,0,

0,0,qz,0,

0,0,0,1

]

對於矩陣運算不瞭解的可以參考《電腦圖形》或者DirectX的龍書。

在OpenGL中關於使用自訂矩陣的函數有兩個glLoadMatrixf(m)和glMultMatrixf(m).

前者是載入一個矩陣，後者則是將m與當前矩陣相乘。

下面是使用自訂矩陣的程式。

void renderGL(){    GLfloat moveMatrix[]=    {1.0f, 0.0f, 0.0f,0.0f,               0.0f,1.0f, 0.0f, 0.0f,              0.0f, 0.0f, 1.0f, 0.0f,             posX, 0.0f, -6.0f, 1.0f};    GLfloat scaleMatrix[]=    {    scale, 0.0f, 0.0f,0.0f,               0.0f,scale, 0.0f, 0.0f,              0.0f, 0.0f, scale, 0.0f,             0.0, 0.0f, 0.0f, 1.0f     };    GLfloat rotateYMatrix[]=    {    cos(rtri),0.0f,-sin(rtri),0.0f,    0.0f,1.0f,0.0f,0.0f,    sin(rtri),0.0f,cos(rtri),0.0f,    0.0f,0.0f,0.0f,1.0f    };    // Clear the color and depth buffers.     glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );    // We don't want to modify the projection matrix. */    glMatrixMode( GL_MODELVIEW );    glLoadIdentity();    glMultMatrixf(moveMatrix);     glMultMatrixf(scaleMatrix);     glMultMatrixf(rotateYMatrix);     glBegin(GL_TRIANGLES);                          glColor3f(1.0f,0.0f,0.0f);                    glVertex3f( 0.0f, 1.0f, 0.0f);                  glColor3f(0.0f,1.0f,0.0f);                    glVertex3f(-1.0f,-1.0f, 0.0f);                  glColor3f(0.0f,0.0f,1.0f);                    glVertex3f( 1.0f,-1.0f, 0.0f);              glEnd();                            if(posX<3.0f) posX+=0.001f;    else posX=-3.0f;    if(scale<2.0f) scale+=0.0005f;    else scale=0.5f;    rtri+=0.002f;                                                                                                   SDL_GL_SwapBuffers( );}

得到的效果和前面的程式完全相同。