# Maths - Quaternion Notations - As a quantity similar to axis-angle

It is quite difficult to give a physical meaning to a quaternion, it is just a quantity which represents a rotation. If you need a physical meaning then this is probably the best way to think of it:

q = cos(a/2) + i ( x * sin(a/2)) + j (y * sin(a/2)) + k ( z * sin(a/2))

where:

• a=angle of rotation.
• x,y,z = vector representing axis of rotation.

So it is closely related to the axis angle representation of rotations.

In the following diagram:

• Rotation Axis: is a line we are rotating around, that is, during the rotation points maintain the same distance from the rotation axis.
• Rotation Plane: During the rotation points in the plain remain in the plane and other points remain the same distance from the plane.

Note: we are talking about rotations about the origin so both the rotation axis and the rotation plane go through the origin.

Imagine a point P1 which is a unit distance from the origin, we will be rotating it through an angle (a) to P3 through midpoint P2.

So the point P1 is transformed to P3, if it travels in a straight line it passes through a point cos(a/2) from the rotation axis and sin(a/2) from both P1 and P3.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

Quaternions and Rotation Sequences.

Commercial Software Shop

Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.

 Dark Basic Professional Edition - It is better to get this professional edition This is a version of basic designed for building games, for example to rotate a cube you might do the following: make object cube 1,100 for x=1 to 360 rotate object 1,x,x,0 next x Game Programming with Darkbasic - book for above software