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OpenGL Free Rotation of a 3D Object

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I'm writing a program in opengl that involves the rotation of an object in 3d space. I've been able to get rotation down, but I have the same problem as many seem to have. The first rotation I perform is as expected, but every rotation after that is affected by the first one. Say I rotate around my x axis 90 degrees. If I do this, rotations around the y-axis are no longer shown as rotations along the y-axis, because the y-axis has moved. They now appear as rotations around the z-axis. I have read many a forum post on this subject, and on every single one the response is "gimbal lock". I've read a lot about gimbal lock in the past few days, and I'm pretty sure all those people are wrong. They say use matrices, use quaternions. Your gimbal woes will disappear. I am using quaternions, and I assure you, the problem persists. How can I rotate the object and not its axes?

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Original post by eOgas
How can I rotate the object and not its axes?

You can't. If you rotate the object you rotate its local coordinate system ... its axes. But gimbal lock ist mostly a problem for camera classes not when rotating objects. Just keep the rotated axes of your object and use them for rotation like so:

void Object::rotateX (float angle)
Mat4x4 mat = Mat4x4::getRotationMatrixForAxis(angle, m_x_axis);
m_y_axis = mat * m_y_axis;
m_z_axis = mat * m_z_axis;

Note that the rotateX,Y,Z() methods do rotate the Y and Z, X and Z, and X and Y axis respectively. So after each call to rotate the object's corresponding axes have been rotated. Thus the following rotation does not take the standard x, y, and z axis for rotation.

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You can't, this issue is always going to exist. No storage type can get around it. It's how you use the stored value and how you increment it.

You'll basically store the final transform as a quaternion, if you choose. And increment it with another. The way you compute the incremental transform will be arbitrarily chosen based on how you want the rotation to work. You could build one with 3 euler angles that are all concatenated in a particular order, as you found out. Or you can create the quaternion based off a combination of rotations about specific axis. The concatenation order will be significant here.

There is no general rule, it's all dependent on how you want it to perform. If you could describe more clearly how it should behave, I might be of some help.

For instance, if you wanted to rotate with the mouse, every time the mouse moves you get a deltaXY. You'd create two delta quaternions, each rotating deltaX, or deltaY around the current view vectors in those directions. Then you'd multiply them together, and then multiply this into your finalOrientation quaternion.

But each time you increment it, you lose the incremental value. Trying to keep it around, like using euler angles to always recompute the finalOrientation, is asking for trouble. Just store the final arbitrary orientation.

This has to be the most confusing and pointless post ever. :)

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All I want is to be able to rotate the object around a stationary set of axes. It seems like I should be able to do this with a bit of trig, but I'm not quite sure how.

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Quaternion modelOrientation;

void IncrementAroundStationaryAxes(float axis1delta, float axis2delta)
Quaternion delta1(AxisAngle(axis1, axis1delta);
Quaternion delta2(AxisAngle(axis2, axis2delta);
Quaternion totalDelta = delta1 * delta2;

modelOrientation *= totalDelta;

Axis1 and Axis2 are your fixed world axes. Such as +x and +y or something..

Or you can use the camera's current world axes as your rotation axes. Or anything you choose, it's very arbitrary.

The order of delta1 and delta 2 will make a difference. The larger axis[1,2]delta's are the more you'll notice. If the deltas are small enough you wont notice at all. But if you try to do 90degrees on both deltas, the multiplication order will be very apparent.

There's nothing wrong with that, it's doing exactly what you asked it to. You just need to understand what it is EXACTLY you want it to do. In other words, the rotations must be combined in some order, that order must be chosen by you, each order will have different outcomes. There is NO way to get around this.

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Thank you so much bzroom. This is a very good explanation on how this is supposed to work. I actually understand it now, and I have my rotation working flawlessly.

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