CODEWITHSUNDEEP
graphicsvectorrotational-matricesquaternions
user2259784
user2259784

Reputation: 349

Why quaternion is defined by [vector,w] why not by [point,w]?

A quaternion rotation defines a point in 3d-space and rotation around the axis of that point. I am trying to understand why quaternion rotation requires a vector and rotation, why not just a 3d point in space and rotation ?

eg : In the following picture a hand points to a point in 3d-space which can be rotated around its axis. http://s29.postimg.org/ih79tirnr/quarternion.jpg

Thanks

Upvotes: 1

Views: 1968

Answers (1)

David Buck
David Buck

Reputation: 2847

Actually, the x, y and z components of a quaternion define a vector pointing in the direction of the axis of rotation. The w component defines the amount of the rotation along that axis. So, the x, y and z don't actually signify a point at all. As the amount of rotation changes, the length of the x, y, z vector will change but the vector always points in the same direction. It doesn't make sense, therefore, to consider this to be a point in space. It's merely a direction and a rotation around that axis.

I once defined a new class that included a quaternion to define the transformation of an object along with a vector to describe the translation of the object. The object could then represent a complete transformation in 3D space similar to a 3x4 transformation matrix.

Upvotes: 1

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