matrix to mirror a point

  • Thread starter Thread starter Guest
  • Start date Start date
G

Guest

Does anyone know of a generic matrix to mirror a point (x,y) about a line? I
can do this about the normal Cartesian axis but I would like to do it about a
user defined line (defined by 2 points).
 
Hi Paul,
I have done this in a very naive way:
1) translate the line so one point is at origin; use same translation on P
2) rotate the line by theta so it aligns with y-axis; use same rotation on P
3) generate the mirror of P (x of m = -x of p, y of m = y of p)
4) rotate everything by minus theta
5) translate by reverse amount of step 1
Hey presto, I have the old line and point plus the mirror of P
Send me private message and I will forward the file
Then you can do it in a more sophisticated way!
best wishes
 
... mirror a point (x,y) about a line? I
...I would like to do it about a user defined line (defined by 2 points).
Click to expand...

Hi. If I understand your "mirror" point, is there anything here that can
help?
http://mathworld.wolfram.com/Point-LineDistance2-Dimensional.html

What I'm thinking is that you know your perpendicular vector v (9), and you
can just double the distance given in (11).
The equation (11) appears to be correct, but I can only do it if I project r
onto v, and not v onto r as I believe it's written.
Note that the Determinate version in (13) is missing an implied {1,1,1} as
the third argument.
 
Back
Top