Dan

11-05-2004, 03:23 AM

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

Thanks a bunch,

Dan

View Full Version : Coordinates after rotation ?

Dan

11-05-2004, 03:23 AM

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

Thanks a bunch,

Dan

ehsan2004

11-06-2004, 05:44 AM

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 ]

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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