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Vector Math

Lets say you have 2 vectors which are normals, A and B.

how would you go about findind the rotations, so that you can rotate Vector A to equal Vector B.

thx in advanced

pimaster

The two vectors establish a plane.
First, find the angle Φ between the vectors A and B:
Φ = cosˉ¹ (Ax * Bx + Ay * By + Az * Bz) /
( sqrt(Ax²+Ay²+Az²) * sqrt(Bx²+By²+Bz²) )

Whew!

Next, find the vector normal to the plane:

Nx = Ay * Bz - Az * By
Ny = Ax * Bz - Az * Bx
Nz = Ax * By - Ay * Bx

The axis of rotation will be the normal vector N.

Rotate the point (Ax,Ay,Az) Φ radians about N.

The DirectX SDK contains a very useful routine which produces a rotation matrix from an arbritrary vector
& angle of rotation.

There are also routines to calculate normals, dot products, etc.

I don't know if this is the easiest way to do this, but it was the first method that came to mind. You'll have to modify the normal calculations for a right handed system. I haven't had time to test this, but the basic reasoning should be sound.

pimaster

Ok, let's try it WITHOUT the useless Unicode characters:

The two vectors establish a plane.
First, find the angle between the vectors A and B:
Theta = cos-1 (Ax * Bx + Ay * By + Az * Bz) /
( sqrt(Ax2+Ay2+Az2) * sqrt(Bx2+By2+Bz2) )

Whew!

Next, find the vector normal to the plane:

Nx = Ay * Bz - Az * By
Ny = Ax * Bz - Az * Bx
Nz = Ax * By - Ay * Bx

The axis of rotation will be the normal vector N.

Rotate the point (Ax,Ay,Az) Theta radians about N.

Ugh...

GoldStone32767

ASKER

I understand how to calculate the cross product between the 2 vectors... but the problem im having is, how do you rotate around that vector?

ASKER CERTIFIED SOLUTION

pimaster

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