aligning two vectors
Started by davidko, Sep 29 2001 12:55 PM
7 replies to this topic
#1 Members  Reputation: 122
Posted 29 September 2001  12:55 PM
Does anyone know of source code that generates a rotation matrix to align two vectors? I have written the code, but for some reason, the vectors do not match up exactly. It might be floating point errors, but the error can''t be THAT bad. Thank you.
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#2 Senior Moderators  Reputation: 1781
Posted 29 September 2001  07:15 PM
to generate this matrix, simply calculate the crossproduct of the two vectors, calculate the angle between them, and make a standard rotation matrix with the crossproduct as the axis, and the angle as... the angle.
A rotation matrix around an arbitrary axis may be found at http://www.gamedev.net/reference/articles/article1199.asp ... this one is, in turn, taken from "Graphics Gems".
If the vectors do not line up afterwards, this may be because you are rotating in the wrong direction.
Edited by  sneftel on September 30, 2001 2:17:11 AM
A rotation matrix around an arbitrary axis may be found at http://www.gamedev.net/reference/articles/article1199.asp ... this one is, in turn, taken from "Graphics Gems".
If the vectors do not line up afterwards, this may be because you are rotating in the wrong direction.
Edited by  sneftel on September 30, 2001 2:17:11 AM
#3 Members  Reputation: 122
Posted 29 September 2001  07:43 PM
Okay, I will try that. I was just trying to align the vector with the zaxis. The way I was doing it before, I was projecting the vector to two planes (XZ and XY) and calculating the angle with which to rotate about the x and y axis. I used those angles to get two rotation matricies and concatenated them. Unfortunately, the vectors weren''t matching up exactly. It was close, but definitely not close enough....
Thanks...I''ll try the link
Thanks...I''ll try the link
#4 Members  Reputation: 169
Posted 03 October 2001  11:19 AM
Yes, I''ve worked on things like this.
As Sneftel said, find the cross product of the two vectors and then their dot product.
The result of the cross product is the axis on which to rotate the vector, and the dot product is the cosine of the angle.
pseudocode would be:
You can optimize the crosses and dots because you always know that the z axis is (0,0,1):
To generate a Rotation matrix from an angle/axis:
Hope that helps!
As Sneftel said, find the cross product of the two vectors and then their dot product.
The result of the cross product is the axis on which to rotate the vector, and the dot product is the cosine of the angle.
pseudocode would be:

You can optimize the crosses and dots because you always know that the z axis is (0,0,1):

To generate a Rotation matrix from an angle/axis:

Hope that helps!
#6 Members  Reputation: 164
Posted 04 October 2001  06:40 AM
One thing that may affect this is that when the two vectors are roughly 180 degrees apart the axis of rotation that you generate from the cross product probably won''t be terribly accurate because of numerical error. Just something to think about.
#8 Members  Reputation: 122
Posted 04 October 2001  07:53 PM
I think the greatest accuracy comes when two normals are perpendicular.
Probably a robust formulation of this algorithm would be to rotate the normal to an intermediary vector, and then to the final destination. The two matricies can then be concatenated. I suppose you could do this when the vectors are very close to parallel, although I suspect you'd lose some precision this way...
Edited by  davidko on October 5, 2001 2:54:35 AM
Probably a robust formulation of this algorithm would be to rotate the normal to an intermediary vector, and then to the final destination. The two matricies can then be concatenated. I suppose you could do this when the vectors are very close to parallel, although I suspect you'd lose some precision this way...
Edited by  davidko on October 5, 2001 2:54:35 AM