Does anyone know a way to combine two rotation matrices that are based upon different control axis? To control the orientation of a flying object, such as an airplane, I use a rotation matrix for the control surfaces such as elevator and rudder, and another rotation matrix for gravity. Because, no matter what attitude the plane is in, I want gravity to pull the nose straight toward the ground. Concatenating these two matrices doesn't seem to work. Can someone tell me how this is done? Does anyone know what I'm talking about? Thanks.

What do you mean by "doesn't seem to work" ?

One thing you can try is to convert your two matrices to two quaternions, do a slerp between these, and convert back to a matrix. It might behave better.

Y.

Thanks for the help.

By "doesn't seem to work", I mean that it definitely doesn't work, but maybe I'm just doing it wrong.

Here's an example of what should happen. The airplane is flying level, but banked (rolled) at a 45* angle. Gravity will pitch the nose downward toward the ground, but not at a 45* angle.

Gravity is causing rotation on an axis different than any of the plane's 3 defined axis, and different than the x,y,z axis defined in the plane's rotation matrix. How can I apply these off-axis rotations to the matrix?

Is this what quaternions can do? I have read about, but not used them. How are they different? Where should I start?

Thanks.

Quote:Gravity is causing rotation on an axis different than any of the plane's 3 defined axis, and different than the x,y,z axis defined in the plane's rotation matrix. How can I apply these off-axis rotations to the matrix?

Is this what quaternions can do? I have read about, but not used them. How are they different? Where should I start?

Short answer on quaternions: forget about them for now. You can do just about anything with a matrix that you can do with a quaternion. Quaternions do have some advantages, but if you introduce quaternions without fully understanding what those advantages are (and, more importantly, are not), you'll just be confusing the issue. All IMHO, but my advice is to just stick with matrices for now.

As for your specific question, I don't know how your airplane orientation matrix is set up, but I think the problem you describe will be easiest to solve if you avoid Euler angles (more specifically, avoid constructing your matrix from scratch each frame from an Euler angle triple).

Let's say your airplane matrix is maintained from frame to frame using relative rotations about the local axes. Then, to pull the nose toward the ground plane, you need to apply one more axis-angle rotation. I'm just guessing at this point (because I really don't know anything about how airplanes actually behave), but I believe the axis for this rotation should have the properties that a) it lies in the ground plane, and b) it is perpendicular to the airplane's forward vector. You should be able to find such a vector as the normalized cross-product of the plane's forward vector and the world up vector. The angle to rotate is then the angle between the forward vector and the ground plane. Presumably, you will only apply some fraction of this angle so as to drop the nose gradually.

That was a little vague - let me know if you'd like a more concrete example.

thanks jyk,

Quote:Let's say your airplane matrix is maintained from frame to frame using relative rotations about the local axes.

Yes, that's what I'm doing.

Quote:Then, to pull the nose toward the ground plane, you need to apply one more axis-angle rotation. I'm just guessing at this point (because I really don't know anything about how airplanes actually behave), but I believe the axis for this rotation should have the properties that a) it lies in the ground plane, and b) it is perpendicular to the airplane's forward vector. You should be able to find such a vector as the normalized cross-product of the plane's forward vector and the world up vector. The angle to rotate is then the angle between the forward vector and the ground plane. Presumably, you will only apply some fraction of this angle so as to drop the nose gradually.

I can picture exactly what you're saying, and I will try it. Yes, the nose will drop gradually and I will do that by subtracting a constant (gravity) from the 'y' value of this 4th vector, then normalize.

But, because this 4th vector will require its own matrix, I have just used 2 distinct rotation matrices to get the plane into its orientation. How do I then combine these into just one matrix that can be carried to the next frame? --This is the part I don't know how to do.--

Any ideas?

Thanks.

I must say, i still do not understand what's this "gravity matrix". Gravity is a force that is applied to the center of mass of a rigid body - it does not induce rotations. Can you explain what's your logic behind this ?

Y.