I represent general 3d rotations by using Unit-Quaternions. Unit-Quaternions are one of the best available representation for rotations in computer graphics because they provide an easy way of doing arithmetic with them and also because they allow us to use spherical linear interpolation (so-called "slerps") of rotations.

Indexed Variables:
a <Float> the real part of the quaternion
b <Float> the first imaginary part of the quaternion
c <Float> the second imaginary part of the quaternion
d <Float> the third imaginary part of the quaternion

	arithmetic
	* negated normalize

	converting
	asMatrix4x4 normalized

	initialize
	a:b:c:d: angle:axis: from:to: radiansAngle:axis: setIdentity x:y:z:a:

	interpolating
	interpolateTo:at: slerpTo:at: slerpTo:at:extraSpins:

	printing
	printOn:

	private
	bcd matrixClass

	instance creation
	a:b:c:d: angle:axis: axis:angle: from:to: identity numElements radiansAngle:axis: x:y:z:a:

	accessing	top
	a
	a:
	angle
	angle:
	axis
	axis:
	b
	b:
	c
	c:
	d
	d:

	arithmetic	top
	* Multiplying two rotations is the same as concatenating the two rotations.
	negated Negating a quaternion is the same as reversing the angle of rotation
	normalize Normalize the receiver. Note that the actual angle (a) determining the amount of rotation is fixed, since we do not want to modify angles. This leads to: a^2 + b^2 + c^2 + d^2 = 1. b^2 + c^2 + d^2 = 1 - a^2. Note also that the angle (a) can not exceed 1.0 (due its creation by cosine) and if it is 1.0 we have exactly the unit quaternion ( 1, [ 0, 0, 0]).

	converting	top
	asMatrix4x4 Given a quaternion q = (a, [ b, c , d]) the rotation matrix can be calculated as | 1 - 2(cc+dd), 2(bc-da), 2(db+ca) | m = | 2(bc+da), 1 - 2(bb+dd), 2(cd-ba) | | 2(db-ca), 2(cd+ba), 1 - 2(bb+cc) |
	normalized

	initialize	top
	a:b:c:d:
	angle:axis:
	from:to: Create a rotation from startVector to endVector
	radiansAngle:axis:
	setIdentity
	x:y:z:a:

	interpolating	top
	interpolateTo:at: Spherical linear interpolation (slerp) from the receiver to aQuaternion
	slerpTo:at: Spherical linear interpolation (slerp) from the receiver to aQuaternion
	slerpTo:at:extraSpins: Sperical Linear Interpolation (slerp). Calculate the new quaternion when applying slerp from the receiver (t = 0.0) to aRotation (t = 1.0). spin indicates the number of extra rotations to be added. The code shown below is from Graphics Gems III

	printing	top
	printOn: Append a sequence of characters that identify the receiver to aStream.

	private	top
	bcd
	matrixClass

	class initialization	top
	initialize B3DRotation initialize

	instance creation	top
	a:b:c:d:
	angle:axis:
	axis:angle:
	from:to:
	identity
	numElements
	radiansAngle:axis:
	x:y:z:a: