Let's say I have a cloud of points, and I know the equation of the symmetry plane. I'd like to mirror every single point with respect to this plane. It might be much simpler than I think, but I have some difficulties on finding a way to do that in Java.
I have the $x,y,z$ position of each point, its distance from the symmetry plane, the equation of the plane. How can I find the $x,y,z$ of the mirrored point ? I was trying to find the point of intersection between the symmetry plane and the line that passes through the point I have to mirror and with its normal being the symmetry plane.
I think it's more an Algebra problem than a Java one. But I still don't know how to do it without Java. I was trying to calculate a linear system :
Plane $a'x+b'y+c'z+d' =0$
But it looks like some informations are missing and I can't solve it (only two equations). I hope I explained myself properly.