Quaternions

[roman_suvorov]

Damn, forgot about that acos. Then to get no rotation I need to use w=-1: 2*acos(-1) = 360 degrees. Thanks again farshizzo!

EDIT: The following code makes MainView look down X.

import viz
viz.go(viz.FULLSCREEN)

ROTATION_INC = 2
TRANSLATE_INC = 0.1

i = 0
while (i < 10):
	redBall = viz.add("white_ball.wrl")
	redBall.setPosition([i, 0, 0])
	redBall.color([1 - 0.1*i, 0, 0])
	
	greenBall = viz.add("white_ball.wrl")
	greenBall.setPosition([0, i, 0])
	greenBall.color([0, 1 - 0.1*i, 0])
	
	blueBall = viz.add("white_ball.wrl")
	blueBall.setPosition([0, 0, i])
	blueBall.color([0, 0, 1 - 0.1*i])
	
	i += 0.1
	
viz.MainView.setQuat([0,1,0,-1])
viz.MainView.setPosition(5, 0, 0.5)
	
vizact.whilekeydown(viz.KEY_UP, viz.move, 0, 0, TRANSLATE_INC)
vizact.whilekeydown(viz.KEY_DOWN, viz.move, 0, 0, -TRANSLATE_INC)
vizact.whilekeydown(viz.KEY_LEFT, viz.rotate, viz.BODY_ORI, -ROTATION_INC, 0, 0)
vizact.whilekeydown(viz.KEY_RIGHT, viz.rotate, viz.BODY_ORI, ROTATION_INC, 0, 0)
vizact.whilekeydown(viz.KEY_PAGE_UP, viz.rotate, viz.HEAD_ORI, 0, -ROTATION_INC, 0)
vizact.whilekeydown(viz.KEY_PAGE_DOWN, viz.rotate, viz.HEAD_ORI, 0, ROTATION_INC, 0)

and also produces much prettier axes. Hold on though, why [0,1,0]? We're speciifying no rotation around Y, not X as it seems?

[farshizzo]

Now you're dealing with non-normalized quaternions, so all bets are off. In general, you don't need to deal with quaternions at such a low level. You can use Vizards matrix routines to deal with rotation transformations.

[roman_suvorov]

Originally Posted by farshizzo

Now you're dealing with non-normalized quaternions, so all bets are off.

Do you then know by any chance what course of action does Vizard take if you try to set an object's quaternion to [x,y,z,w] such that x^2+y^2+z^2+w^2 > 1?
For example, add this function definition to my previous code:

# Normalizes the passed quaternion (which is assumed to have the form
# [x,y,z,w]) so that the vector [x,y,z,w] has unit length.
# Note: normalization is done in place (i.e., the correct way
# of calling this function is 'normalizeQuat(q1)' rather than 'q1 = normalizeQuat(q2)'.
def normalizeQuat (quat):
	i = 0
	normFactor = 0
	while (i < len(quat)):
		normFactor += quat[i]**2
		i += 1
	normFactor = normFactor**0.5

	i = 0
	while (i < len(quat)):
		quat[i] /= normFactor
		i += 1

Now if you normalize quat [0,1,0,-1] we get the same MainView orientation as with the unnormalized quaternion. Is this behavior expected? Does a function similar to my 'normalizeQuat' get called in Vizard behind the scenes if you try to set an object's quaternion to an unnormalized one?

Originally Posted by farshizzo

In general, you don't need to deal with quaternions at such a low level. You can use Vizards matrix routines to deal with rotation transformations.

Unfortunately, seems like I do. This little script is just a way to fill in the gaps I have in my understanding of quaternions.

[farshizzo]

Yes, Vizard will internally normalize all quaternions that are passed to the setQuat function of nodes, views, and bones.