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quaternion and matrix

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We know transform a point by point * matrix. but it come to quaternion ,it work too? can I use point * quaternion to transform a point? I must convert quaternion to matrix???

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You can rotate a point directly by converting it to a quaternion and multiplying it by the rotation and the inverse of the rotation:
    q   = rotation
q-1 = inverse (also conjugate) of q
p = point to rotate
p' = rotated point

[p', 0] = q * [p, 0] * q-1

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Quote:
Original post by JohnBolton
You can rotate a point directly by converting it to a quaternion and multiplying it by the rotation and the inverse of the rotation:
    q   = rotation
q-1 = inverse (also conjugate) of q
p = point to rotate
p' = rotated point

[p', 0] = q * [p, 0] * q-1


What is [P,0] ? do you mean:

[D3DXVECTOR3(x',y',z') ,0] = q * [[D3DXVECTOR3(x,y,z) ,0]] q-1

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Hi!

I'm not experienced with this stuff but i think what John wanted to say is:

A quaternion q is made up of the x, y, z and w compontent.

So [p', 0] means there is ie. a quaternion u' with

u'.x = p'.x;
u'.y = p'.y;
u'.z = p'.z;
u'.w = 0;

and [p,0] means there is a quaternion u with

u.x = p.x;
u.y = p.y;
u.z = p.z;
u.w = 0;


where p' is the rotated point and p the point you wanted to rotate.

so what you should do is creating two Quaternions. One(u') for the rotated point(p') and one(u) for the point you want to rotate(p).

should be something like:

D3DXVECTOR3 p = new D3DXVECTOR3(x,y,z);
D3DXQUATERNION q = ...;
D3DXQUATERNION u = D3DXQUATERNION(p.x, p.y, p.z, 0);
D3DXQUATERNION qInv = D3DXQUATERNIONInverse(null, q);
D3DXQUATERNION u' = q * u * qInv;

So p' = D3DXVECTOR3(u'.x, u'.y, u'.z);

John wrote:

q = rotation Quaternion
q-1 = inverse (also conjugate) of q
p = point to rotate
p' = rotated point

[p', 0] = q * [p, 0] * q-1

I hope, this will help you!
(and that i got it right ;) )

Martin

[Edited by - gammaGT on November 30, 2005 10:16:52 AM]

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