Matrix Multiplication opengl rotating around an object

Question

I have created 2 circles, where one rotates around the other, like the moon rotating around the sun.

I translated down the z axis then applied a rotation around the y axis for the object to orbit. I need to work out the matrix multiplications of yRotation * ZTranslation * (0,0,0,1)

i.e.

(cos(angle)   0  sin(angle)  0  ) ( 1  0  0   0   ) ( 0 )
(    0        1      0       0  ) ( 0  1  0   0   ) ( 0 )
(-sin(angle)  0  cos(angle)  0  ) ( 0  0  1 zTran ) ( 0 ) 
(    0        0      0       1  ) ( 0  0  0   1   ) ( 1 )

How can I do this?

Shahbaz Shahbaz · Accepted Answer · 2012-12-07T15:08:33

Since you are talking about circles, I am assuming you are making a 2D application.

In OpenGL, you have the following coordinates:

   Y
   |
   |
   |
   O---- X
  /
 /
Z

This means that your 2D application is in X-Y space, with Z being perpendecular to the monitor (and towards the outside).

So, if you have a circle going around the other, you probably meant to first translate the circle in the X-Y plane (for example on the Y axis), and then apply a rotation on the Z axis.

So your matrix multiplication should be:

(cos(angle)   sin(angle)  0  0 ) ( 1  0  0   0   ) ( circle_center_x )
(-sin(angle)  cos(angle)  0  0 ) ( 0  1  0 yTran ) ( circle_center_y ) 
(    0            0       1  0 ) ( 0  0  1   0   ) (        0        )
(    0            0       0  1 ) ( 0  0  0   1   ) (        1        )

Or just in 2D:

(cos(angle)   sin(angle) 0 ) ( 1  0   0   ) ( circle_center_x )
(-sin(angle)  cos(angle) 0 ) ( 0  1 yTran ) ( circle_center_y ) 
(    0            0      1 ) ( 0  0   1   ) (        1        )

Using OpenGL functions:

glRotatef(angle, 0, 0, 1);
glTranslatef(0, yTran, 0);
glBegin(GL_LINE_LOOP);
for (...)
    /* points of circle around circle_center_x/y */
glEnd();

Note that in OpenGL, the matrices are multiplied on the right. So if you write glRotatef before glTranslatef, the rotation will be applied after the translation.

Matrix Multiplication opengl rotating around an object

1 Answers