I need to find the transformation matrix (homogeneous coordinates) that flips an object about a plane whose normal is directed towards (-2 2 0), and intersects the y-axis at y=2.
I know how to do that when I have 3 points on the plane (A,B,C): translate to origin, find the orthonormal basis of the plane (u,v,w axes) and then rotate the plane to match XYZ coordinate system (with the axes I found), perform the reflection, rotate back and translate back.
However in this case I have a normal and another data which I don't know how to use.
Any ideas?