Scaling 3D-Points in Plane

Question

I have some points (3D) all on the same (known) plane. Now I want to scale these points within the plane as opposed to the whole 3D space (as in scalar-multiplication of points in 2D space)

Is there a closed form solution for this e.g. a modified scaling matrix? Can someone help me?

Thanks.

Answer 1

Transform your plane to the $(x,y)$ plane by applying a suitable rotation matrix $R$, then apply your scaling matrix $S$ in the plane (you'll only need to add a third row and column $(0,0,1)$ to your 2d matrix) and then rotate everything back with $R^{-1}$.