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Martin Winged

Custom rotateTowards function and a problem with the rotation axis (probably)

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I'm building a framework for my WebGL project and at the moment I have a problem with a function which will rotate an object towards a target vector with a given angular speed. 
 
In Unity engine it's called rotateTowards(), and since I'm coding my framework from a scratch, I'm basing on my observations about how this function works. 
 
Lately I have abandoned an idea about interpolating two quaternions in this function using nLERP method, because an angular speed seems to be far more suitable factor. 
 
The function seems to be almost working - it works well only when there is no roll or pitch angle in the camera rotation involved, otherwise it makes strange curves and sets the final position after ridiculously long time. After some time I've figured out that the problem must be lying in a conversion of an axis-angle info to quaternion, but the function is not coded wrong by itself, because a 6DOF camera mode works flawlesly using this function (`this.rotation.multiply(this.tempQuat.axisToQuaternion(radY, rightVec()));`), so I guess that the problem may be in the rotation axis. Is this the right way to code this function?
 
How does it look like?
 
PS For camera, I store pitch and yaw in separate variables because I don't want any roll to appear.
 
The code of this function below:
rotateTowards: function(target, angularSpeed) { // TODO
	// If is on the same position
	if (this.position.isEqual(target)) {
		return;
	}

	var vecStart = this.rotation.getForwardVector();
	var vecTarget = this.position.sub(target).normalize();
	var angleLeft = Math.acos(vecStart.dot(vecTarget));
	var fullAngle = angularSpeed * deltaT;

	// If already rotated towards the target
	if (Math.areScalarsSimilar(angleLeft, 0)) {
		return;
	}
	// If vectors are opposite
	else if (Math.areScalarsSimilar(angleLeft, Math.PI)) {
		// Turn around up-axis
		this.rotation.multiply(new Quaternion().axisToQuaternion(fullAngle, upVec()));
	}
	// If vectors casually differs
	else {
		var rotAxis = vecStart.cross(vecTarget);

		// If able to make another full rotation step
		if (angleLeft > fullAngle) {
			this.tempQuat.axisToQuaternion(fullAngle, rotAxis);
			this.pitch += this.tempQuat.getPitch();
			this.yaw += this.tempQuat.getYaw();
			this.adjustAngles();
			this.rotation.pitchYawRollToQuaternion(this.pitch, this.yaw, 0);
			log(vecStart.toString());
		}
		// If the angle left is smaller than the angular speed
		else {
			// Set the final rotation
			this.tempQuat.axisToQuaternion(angleLeft, rotAxis);
			this.pitch += this.tempQuat.getPitch();
			this.yaw += this.tempQuat.getYaw();
			this.adjustAngles();
			this.rotation.pitchYawRollToQuaternion(this.pitch, this.yaw, 0);
		}
	}

	MVMatrix.setRotation(this.rotation.quaternionToMatrix());
},

And a math library that I use: https://www.dropbox.com/s/9ejj64v59xzqn6y/myMath.js

Edited by Winged
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I have kinda solved the problem - instead of using quaternions by themselves I have calculated a new vector between the forward vector and the vector pointing to the model using a modified spherical interpolation method (instead of passing a fraction I pass an angular speed) and then calculated a lookAt matrix like in this article http://stackoverflow.com/questions/349050/calculating-a-lookat-matrix . Now I'm just still wondering what is wrong with the quaternion method. I hope that my actual solution doesn't introduce Gimbal Lock problem.

 

Code of my current rotateTowards function:

	rotateTowards: function(target, angularSpeed) {
		if (this.position.isEqual(target)) { // If is on the same position
			return;
		}

		var vecStart = this.rotation.getForwardVector();
		var vecTarget = this.position.sub(target).normalize();
		var angleLeft = Math.acos(vecStart.dot(vecTarget));
		var fullAngle = angularSpeed * deltaT;

		if (Math.areScalarsSimilar(angleLeft, 0)) { // If already rotated towards the target
			return;
		}
		else if (Math.areScalarsSimilar(angleLeft, Math.PI)) { // If vectors are opposite
			// Turn around up-axis a bit
			this.rotation.multiply(new Quaternion().axisToQuaternion(fullAngle, upVec()));
			MVMatrix.setRotation(this.rotation.quaternionToMatrix());
		}
		else { // If vectors casually differs
			if (angleLeft > fullAngle) { // If able to make another full rotation step
				var zAxis = new vec3().angularSlerp(vecStart, vecTarget, fullAngle);
				var xAxis = upVec().cross(zAxis).normalize();
				var yAxis = zAxis.cross(xAxis);
				MVMatrix.make(
					xAxis.x,			xAxis.y,			xAxis.z,
					yAxis.x,			yAxis.y,			yAxis.z,
					zAxis.x,			zAxis.y,			zAxis.z,
					this.position.x,	this.position.y,	this.position.z);

				this.rotation.matrixToQuaternion(MVMatrix);
				this.pitch = this.rotation.getPitch();
				this.yaw = this.rotation.getYaw();
				this.adjustAngles();
			}
			else { // If the angle left is smaller than the angular speed
				// Set the final rotation
				this.lookAt(target);
			}
		}
	},

And the simple angularSlerp function:

	angularSlerp: function(v0, v1, angularSpeed) {
		var angleBetween = Math.acos(v0.dot(v1));

		v0.multiplyByScalar(Math.sin(angleBetween - angularSpeed)/Math.sin(angleBetween));
		v1.multiplyByScalar(Math.sin(angularSpeed)/Math.sin(angleBetween));
		return v0.add(v1);
	},
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