LYCOS RETRIEVER 
Quaternion
built 214 days ago
Quaternion is an old release of the OHRRPGCE. It was named for a non-commutative extension of the complex numbers discovered by Sir William Rowan Hamilton. When the formula occured to him, he thought it was so awesome that he stopped right where he was and scratched it into a rock.
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Quaternions have 4 dimensions (each quaternion consists of 4 scalar numbers), one real dimension and 3 imaginary dimensions. Each of these imaginary dimensions has a unit value of the square root of -1, but they are different square roots of -1 all mutually perpendicular to each other, known as i,j and k. So a quaternion can be represented as follows:
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Quaternion operations have extended applications in electrodynamics, general relativity, and 3D graphics programming. The use of quaternions can replace tensors in representation. It is sometimes easier to use quaternions with complex elements, leading to a form that is not a division algebra. However, the same operations can be performed using a combination of conjugate operations. Only quaternions with real elements will be discussed here.
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Quaternion is effectively, a 4 element vector with special functionality. This class is most often used for storing rotation data. This class is built from a Vector instance and a float for the additional w coordinate. The Vector holds data describing the axis of rotation and the w component holds the magnitude of the rotation.
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Quaternions can be added, subtracted, and scaled just like complex numbers or vectors -- they can ... be multiplied, but quaternion multiplication DOES NOT COMMUTE. That is to say, if you have quaternions $q1 and $q2, then in general $q1*$q2 != $q2*$q1. This is related to their use in representing rotations, which also do not commute.
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A Quaternion object represents the orientation of a three dimensional object, assumed to be a crystal, in three dimensional space in terms of four parameters which obey an interesting algebra. This representation of orientations is not common, but has its roots in the rigid-body mechanics community.
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Quaternion