NavList:

   

Reply

On Thursday, February 13, 2003, at 05:20 PM, Robert Eno wrote:

> What is a quaternion?

In the world of mathematics there are a variety of numbers:

* scalars
     - single numbers (3.14, 58)
* complex numbers
     - pairs of numbers like x,y points (1,2)
     - also written as real + imaginary (1+2i)
     - a set of arithmetic operations are defined such that
       the square root of -1 is an imaginary number called i
* vectors
     - several numbers (often 2-4) grouped together (1,2,3)
     - often used to represent dimensions of space and time
     - special operations like dot and cross product defined
     - used in navigation, i.e., a 2D vector is distance & course
* tensors
     - a matrix of numbers used in advanced physics & relativity
[(1,2,3)(4,5,6)]
     - a generalization of vectors
* quaternions
     - 4 numbers grouped together (q1,q2,q3,q4)
     - used in rigid body rotations and computer graphics
     - invented by Sir William Rowan Hamilton, circa 1866.
     - allows multiple rotations be to computed with fewer operations
     - think of them as a cross between a 3D vector and a complex number
     - shares some properties of both vectors and complex numbers

http://www.cs.berkeley.edu/~laura/cs184/quat/quaternion.html for more.

Dan

   

Reply