[openGL] glLoadIdentity() 實作時的問題

因為之前自己在實作 "不用gluLookAt(), glOrtho(), glFrustum(), gluPerspective()"這些 function 只透過自

己算 transformation matrix 來畫出3D圖，除了這些，translate、rotate和scale也承接著自己來動手做看看

，當時遇到一個問題就是單獨只做 translate 或 rotate 等等這些動作，執行正確，但是當要在rotate之後做

translate時，就會出現問題，座標的方向好像變了，x, y, z不再是原本的方向，查了一下，網路上說做之前

要先 loadIdentity()，那這就又出現了另一個問題，loadIdentity() 是做什麼用的，要怎麼實作它，才能讓我

自己寫的translate和rotate正常執行，查了很久，每個地方都只說 set the current matrix to identity

matrix，卡關卡了好久，後來看到:

http://stackoverflow.com/questions/628796/what-does-glloadidentity-do-in-opengl

裡面寫的:

The identity matrix, in terms of the projection and modelview matrices, essentially resets the matrix back to its default state.

As you hopefully know, glTranslate and glRotate are always relative to the matrix's current state. So for instance, if you call glTranslate, you are translating from the matrix's current 'position', not from the origin. But if you want to start over at the origin, that's when you call glLoadIdentity(), and then you can glTranslate from the matrix which is now located at the origin, or glRotate from the matrix which is now oriented in the default direction.

I think Boon's answer, that it is the equivalent of 1, is not exactly correct. The matrix actually looks like this:

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

That is the identity matrix. Boon is correct, mathematically, that any matrix multiplied with that matrix (or a matrix that looks like that; diagonal ones, all else 0s) will result in the original matrix, but I don't believe he explained why this is important.

The reason why this is important is because OpenGL multiplies all positions and rotations through each matrix; so when for instance you draw a polygon (glBegin(GL_FACE), some points, glEnd()), it translates it to "world space" by multiplying it with the MODELVIEW, and then translates it from 3D to 2D by multiplying it with the PROJECT matrix, and that gives it the 2D points on screen, along with the depth (from the screen 'camera'), which it uses to draw pixels. But when one of these matrices are the identity matrix, the points are multiplied with the identity matrix and therefore are not changed, so the matrix has no effect; it does not translate the points, it does not rotate them, it leaves them as-is.

簡單說，

在做 translate 或 rotate 時，是以相對於儲存在 current matrix 裡面資訊的位置來做動作，以之前遇到的例

子來說，在rotate之後，單位座標向量跑掉了，所以 x, y, z 軸的方向都跟原本不同，因此在 translate 時，

移動的方向也會跟著改變，此時就須要透過 loadIdentity() 把 current matrix 變回去 default 的樣子，這樣

就可以對正確的相對位置做動作，而前面提到的 current matrix 也就真的是 current matrix 的意思XD

但是 translate 和 rotate 都是屬於 modelview 的 matrix，所以這裡的 current matrix 是 model_view matrix