# 随笔档案

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### 最新评论 First, think what you want these matrices do.
Let we have transformation matrices A and B . We want to transform vector V by both and get vector V'.
But above is not enough to specify what we want to do, as
first transform by A then transform by B
and
first transform by B then transform by A
are different. You can just try to play with rotations in real world.(get a cube, paint x,y,z on sides, etc.)

Now, more on how it's done:

first transform by A then transform by B
It is easy to see that this is accomplished by:
In openGL's convention:
V'=B*(A*V)
Note that it is same as
V'=(B*A)*V
so you can do it as
C=B*A;
V'=C*V;
In DX's convention:
V'=(V*A)*B
C=A*B;
V'=V*C;
(note: real operations done on memory is the same. It's just matter how we map matrix indices to memory)
As you see, V*A*B and B*A*V is kind of symmetrical. Same for consequently applied transforms like V*A*B*C*D*E*F or F*E*D*C*B*A*V

Now, write it down for "transform by B then transform by A" yourself to remember it better.

When you render something , you want points to be transformed by
matrix of object
matrix of parent object
matrix of grandparent object ...
matrix of camera
(and done by API, projection matrix)
From there you can find what order of multiplications you want. In OGL, you need to
m=matrix_of_camera*matrix_of_grandparent_objectmatrix_of_parent object*matrix_of_object;
...
then if you'll glLoadMatrix, OpenGL will do
vertice=m*vertice;

Some more notes: Let you have spacecraft with spacecraft-to-world matrix M
And you use OpenGL convention.
For example, to turn spacecraft around spacecraft's local X direction, you need to
M=M*axis_angle_to_matrix(Vector(1,0,0),angle);
(note: you need to reorthonormalize matrix if you do that incrementally)
To turn spacecraft around global X direction, you need to
M=axis_angle_to_matrix(Vector(1,0,0),angle)*M;

On openGL:

This sequence

glMatrixMode(GL_MODELVIEW);
glMultMatrix(A);
glMultMatrix(B);
glMultMatrix(C);
works as if your mesh would be transformed by C,then B, then A
It makes lot of sense, if you for example want to render a robot with matrices giving positions of child nodes (fingers) relativelty to parent (arm), and arm are responsible for positioning fingers, you can do
RenderArm(){
glPushMatrix();
glMultMatrix(matrix_of_first_finger);
RenderFinger();
glPopMatrix();
glPushMatrix();
glMultMatrix(matrix_of_second_finger);
RenderFinger();
glPopMatrix();
}
and so-on(simplified example)
Then, you can have
glPushMatrix();
glMultMatrix(matrix_of_arm);
RenderArm();
glPopMatrix();

and it will work properly.

If you have more questions, ask.
posted on 2008-04-30 22:05 w2001 阅读(1247) 评论(2)  编辑 收藏 引用 FeedBack:
# re: OpenGL中的矩阵计算[未登录] 2009-09-04 19:22 joe