# Coordinates after rotation?

I have a polygon that is displayed after a rotation. How do I find the new world-view coordinates of that polygon’s points after it has been pushed through the rotation matrix?

Thanks a bunch,
Dan

Hi
I saw your question on the OpenML message board!here’s your responce:

for more information about the rotation, i suggest you to read the book Interactive Computer Graphics by EDWARD ANGEL.but in summery, i explain you that how this action is performmed.
if you rotate about the z axis by theta degrees, you can compute the new points with the following equations:

Newx = x * cos(theta) - y * sin(theta)
Newy = x * sin(theta) + y * cos(that)
Newz = z

or in matrix form
Pnew = Rz * P
where Rz is
|cos(theta) -sin(theta) 0 0|
|sin(theta) cos(theta) 0 0|
| 0 0 1 0|
| 0 0 0 1|
For rotation about the x axis, we have the following equations:
Newx = x
Newy = y * cos(theta) - z * sin( theta)
Newz = y * sin( theta) + z * cos(theta)

And for y rotation:

Newx = x * cos(theta) + z * sin(theta)
Newy = y
Newz = - x* sin(theta) + z * cos(theta)

Note that with these operations, the coordinate system also is rotated. it means that you actually are rotating both of these objects–polygon and coordinate system.if you use from another rotation before your rotation-because the OpenGL transformations are from down to top-you are changing the new changed coordinat system.
Ehsan Kamrani
OpenML visitor

[ November 06, 2004: Message edited by: ehsan_kamrani ]

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