need help with vector math

04-02-2007, 10:13 PM

i have 2 vectors, 1 normal n vector and 1 other vector v.
Both are in 3d space.
Wat would you guys suggest to do if i want to mirror vector v over vector n:
\|
will be
|/

And with only vector math please, no cos or sin. Possible matrix is fine, but i dont know matrix so i need an exact formula like the vector product thingy.

I ask this because i wanna find projection vector without using slow functions like sin and cos

04-02-2007, 11:03 PM

grim001

JASS:


   method project takes vector P returns vector
    local real l = this.x*P.x+this.y*P.y+this.z*P.z
    local vector R
       if (l==0.) then
           return 0
       endif
       set l = SquareRoot(P.x*P.x+P.y*P.y+P.z*P.z / l)
       set R = vector.create()
       set R.x = P.x * l
       set R.y = P.y * l
       set R.z = P.z * l
    return R
   endmethod

04-02-2007, 11:34 PM	#3
MaD[Lion]	i need a math forumla not code, i dont read this new code syntax tat well :P and wat is l, and where is normal vector

04-03-2007, 02:52 AM

PipeDream

we can see graphically or trigometrically that you are expressing the following relations:
1) n x v = v' x n
2) n . v = v' . n
crossing both sides of 1) with n, we find
3) n x (n x v) = n x (v' x n)
4) (n . v) n - (n . n) v = (n . n) v' - (n . v') n
plugging in 2) for the last term in 4) we find
5) (n . v) n - (n . n) v = (n . n) v' - (n . v) n
combining terms and solving for v':
6) v' = (2(n.v)/(n.n)) n - v aka 2 (v proj n) - v

grim showed you how to do (v proj n), assuming that graphically the extension to v' was obvious. which really it should be, this is only a difficult problem if you try to do it algebraically instead of just staring at the picture.

04-04-2007, 01:31 AM	#5
MaD[Lion]	hm thnx, but Infranse showed me a way already, since i ahve problems with wc3c so couldnt access