Update Quaternion Slowly

Math and Physics Programming

Started by Medo Mex November 30, 2012 01:57 PM

10 comments, last by Medo Mex 11 years, 4 months ago

891

Author

November 30, 2012 01:57 PM

Okay, guys I know I'm asking alot of questions, but I have alot alot of work to do to finish the 3D Game Engine I'm working on.

I have a RigidBody, I can rotate it by supplying a new Quaternion value, but here is the problem:

I want to rotate it SLOWLY, something like the following:



// We might need to call this method 500 times from rendering to make the RigidBody rotation is equal to FinalQuaternion



void RotateSlowly(btQuaternion FinalQuaternion)

{

	  btMatrix3x3 orn = body->getWorldTransform().getBasis();

	  // Code here to change 'orn' according to FinalQuaternion to keep rotating with certain speed until orn rotation is EQUAL to FinalQuaternion

	  body->getWorldTransform().setBasis(orn);

}

How can I do that?

alvaro

21,604

November 30, 2012 02:13 PM

You can compute the quaternion that would turn orn into FinalQuaternion, with a division. If you want to limit the angle, you force the real part of the quaternion to be at least cos(max_angle/2) and rescale the imaginary part of the quaternion to make it unit-length. I posted some code to do that here.

Medo Mex

891

Author

November 30, 2012 03:17 PM

@Álvaro: I'm not sure exactly how to implement that to use it with Bullet, I thought about converting the quaternion to euler and supplying the updated value to setYPR but I don't know how should I do it with frame independent, same like the following example:
x += speed * elapsedTime; // Frame independent

alvaro

21,604

November 30, 2012 03:44 PM

What part of what I describe don't you understand? The code I provided uses Boost quaternions, but if you understand what it does, you should be able to write the code to work with any quaternion implementation.

Medo Mex

891

Author

November 30, 2012 03:58 PM

Some parts I don't understand like:
q.real();
q.unreal();

I'm dealing with btQuaternion which doesn't have those methods, I would prefer using Euler but having a little problem with as I mentioned above.

alvaro

21,604

November 30, 2012 07:03 PM

q.real() returns the real part of q (duh ;) ). So if q = w + xi + yj + zk, q.real() returns w.
q.unreal() returns a quaternion where the real part has been zeroed out. So if q = w + xi + yj + zk, q.unreal() returns 0 + xi + yj + zk.

In any case, the procedure is this:

Start with q = w + xi + yj + zk
If w is negative, flip the sign of all four components
if w is less than cos(alpha/2), set w to cos(alpha/2) and rescale the vector (x,y,z) so that w^2 + x^2 + y^2 + z^2 = 1.

The last part is the trickiest. You have to multiply x, y and z by a constant factor that is computed as sqrt((1-w^2)/(x^2+y^2+z^2)).

Is that clear?

Medo Mex

891

Author

December 02, 2012 06:56 AM

@Álvaro: I found out that I can do that easily by using quaternion slerp to animate the rotation, how can I know that the rotation is completed when using btQuaternion::slerp?

alvaro

21,604

December 02, 2012 07:04 AM

@Álvaro: I found out that I can do that easily by using quaternion slerp to animate the rotation, how can I know that the rotation is completed when using btQuaternion::slerp?

Well, the rotation is completed when you pass a 1 to slerp. How exactly are you calling it?

Medo Mex

891

Author

December 02, 2012 08:58 AM

I want to know when the rotation animation is completed, here is what I'm doing:



// This method should return true when the rotation is completed, otherwise, return false

bool lookAt(float x, float y, float z, float elapsedTime)

{

	 btQuaternion FinalQuat = GetLookAtRotation(x, y, z);

	 btQuaternion currentQuat;

	 orn.getRotation(currentQuat);

	 float speed = 0.001f;



         // Instead of just setting FinalQuat to the rigidbody, I want to animate it

	 btQuaternion newQuat = currentQuat.slerp(FinalQuat, elapsedTime * speed);

	 if (???) // If slerp() have done animating the rotation

	 {

		 return true; // Animation completed

	 } else {

		 return false;

	 }

}

alvaro

21,604

December 02, 2012 10:13 AM

You are using slerp in a funny way. The second argument is supposed to be a number between 0 and 1 indicating at what point between currentQuat and FinalQuat you want to be. But once you have gone through the code once, the value of currentQuat has changed, so you are moving from one to the other in a non-linear fashion. Anyway, whenever you pass a 1 as the second argument, the result will be FinalQuat.

Why did you give up on the other solution I proposed?

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