How do I generate 2 vectors that are paralell to 1?

[Cuallito]

Okay, I need to generate 2 vectors that are perpendicular to each other and one that is already given ie. a normal. I've given it some thought and this is what I came up with: Let's say you have 3 vectors that are perpendicular to each other, a=<1,0,0>, b=<0,1,0>, c=<0,0,1>. Now all you have to do is rotate a to were it equals the normal in question, and rotate b and c to keep them perpendicular. So it all basicaly boils down to this: Find x, y, and z angles and rotate a by that angle so that it faces the same direction as the normal. Also, will someone care to explain 3D rotation using matices to me ?

[HarryW]

I think you mean perpendicular, not parallel.

Matrices aren't my strong point, so I'll leave it to someone else.

[kedaman]

A vector is perpendicular to a plane, in which all vectors are parallell. You can use the cross product for any direction. 3d rotation is quite simple if you have a 4x4 or 3x3 matrix. You have an amount of transformation matrices which you multiply with an absolute matrix to give a rotated transformation. i have some links for you:

http://www.geocities.com/siliconvall.../matrices.html
http://www.eng.iastate.edu/me516/not...ec20/index.htm
http://www.manning.com/Lussier/Chapter3.html
http://www.geocities.com/siliconvall...6/cam_matr.txt

[Cuallito]

All I need to do is find the 2 vectors that are perpendicular to vector n.

[kedaman]

you have to be more specific than that, or pick a random vector as a partner for the crossproduct.

[Cuallito]

I mean ALL 3 VECTORS have to be perpendicular to each other.

[kedaman]

the vectorproduct of them should give you the third vector, all perpendicular to each other.

[Illuminator]

current vector: u

For your second vector choose any vector that is not parallel to u.
This vector will constist of two parts. One parallel to u and one perpendicular to u.

second vector: v = v1 + v2
where v1 is the parallel component and v2 is the perpendicular component.

The parallel component can be found using the following equation (note a period "." will indicate the use of the dot product)

v1 = [(v.u)/(u.u)] * u

You can then find the perpendiculat vector

v2 = v - v1

The third vector can be found using the cross product between u and v2.

w = u x v2

you now have three perpendicual vectors u, v2 and w. For a useful basis simply unitize the vectors (set the length to 1).

Unit u = u / sqrt(u.u)

[kedaman]

that's another solution, and yeah i forgot to mention the picked vector should not be parallell to the original