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# Quaterions?

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ämm ... yes, i know what quaterions are, i have seen a lot of Calculation Codes for them, the forumular they work is x² + Y² + z² + w² = 1 a friend said that i can use them as a Vector, but what happens if X = 0 , Y = 0 , Z = 0 , and W = 1 ??? ... could somebody explain this ( and please dont give me always links ! ) And how could i usw them, if i want to rotate about an axis .. ? Can i use them to Vector Calculations ... an how ?

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> the forumular they work is x² + Y² + z² + w² = 1

This is the condition for a quaternion to be a unit quaternion. It''s usual to impose this condition on quaternions you want to use for rotations - you can do rotations with non-unit quaternions but it''s more work.

> a friend said that i can use them as a Vector,

Vectors and quaternions are different things, although they look similar. Quaternions and rotation matrices are related, as they do the same thing [rotate] and it''s possible to convert betwwen them.

> but what happens if X = 0 , Y = 0 , Z = 0 , and W = 1 ??? ...
> could somebody explain this ( and please dont give me always

This is an identity quaternion. Like an identity matrix it is equivalent to a rotation that does not change anything.

> And how could i usw them, if i want to rotate about an
> axis .. ?

Look for code to convert from angle-axis to quaternion. E.g. there''s lots of info on this in gamedev''s articles. Often there''s a library call that does this, e.g. there''s one in D3D.

> Can i use them to Vector Calculations ... an how ?

You can use quaternions to rotate vectors. Again look for sample code to do this or use library functions.

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