Question

我刚开始进行opengl学习，我将发布一段代码，并解释我的理解，你能按照我的解释并指出任何问题吗？

glMatrixMode(GL_MODELVIEW); 
glLoadIdentity();   //start with an identity matrix

glPushMatrix();  
//push the current identity matrix onto the stack, and start with a new identity matrix as 
  the transformation matrix

    glPushMatrix();  
    //copy the current matrix which is the identity as the new transformation matrix and then push the current transformation matrix onto stack

        glScalef(10, 10, 1.0);
        **Question 1**
        //I feels like the order which the image is built is kinda reversed
        //It's like drawSquare happens first, then color, then scale
        //can anyone clarify?
        //Second, the drawsquare defines the 4 vertices around the origin(+/-0.5,+/-0.5)
        //is the origin located at the center of the window by default?
        //what happen when it is scaled? does point (0.5,0.5) scaled to (5,5)?
        glColor3f(0.0, 1.0, 0.0);
        drawSquare(1.0);
    glPopMatrix(); 
    //forget the current transformation matrix, pop out the one on top of the stack
    //which is the identity matrix

    //In the code below:
    //my understanding is 4 vertices is defined around origin, but is this the same origin?
    //then the unit square is moved just below the X-axis
    //and the 4 vertices are scaled one by one?
    //ex: (0.5,0) -> (1,0)  (0.5,-1) -> (1,-2)
    glScalef(2, 2, 1.0);
    glTranslatef(0.0, -0.5, 0.0);
    glColor3f(1.0, 0.0, 0.0);
    drawSquare(1.0);
    //last question, if I want to make the second square rotate at a point along z-axis
    //do I have to specify it here? 
    //for example: add glRotatef(rotate_degree, 0.0, 0.0, 1.0); above the glScalef(2, 2, 1.0);
    //such that later i can change the value in the rotate_degree?

glPopMatrix(); //forget about the current transformation matrix, pop out the top matrix on the stack.

Answer 1

操作的顺序似乎是反转的，因为矩阵是非交换的，当与列向量相乘时是右关联的。假设您在模型空间中有一个位置列向量↑p 。为了将它带入世界空间，你将它乘以矩阵 M ，即

↑p _world = M ·↑p

请注意，您无法更改操作顺序！列向量像键一样匹配到矩阵中，键从右侧进入矩阵锁。

在下一步中，您想要转换为视图空间，使用矩阵 V ，以便您编写

↑p _view = V ·↑p _world

但你可以用

代替

↑p _view = V · M ·↑p

但是当然如果你有很多↑p -s你想要保存计算，那么你收缩这两个矩阵 M 和 V 到一个矩阵中，你称之为modelview。当您使用OpenGL构建modelview时，您可以像这样构建它：

MV = 1
MV = MV · V
MV = MV · M

由于列顺序矩阵乘法的正确关联性，应用于向量的第一个变换是最后一个乘以堆栈的变换。

请注意，通过使用行顺序矩阵数学，事物变为左关联，即事情按照您编写它们的顺序发生。但是，列顺序正确的关联性是非常有用的，因为它使得构建分支转换层次变得更加容易。

有人可以检查我的逻辑是否正确吗？

1 个答案: