I have a table in 3D space, represented by a plane.
I want to project arbitary points representing an object (cup, toy, etc) onto that table, run 2D principal components analysis to get an oriented bounding box (https://www.sciencedirect.com/topics/computer-science/oriented-bounding-box)
This gives me 2D oriented bounding boxes (defined by 8 corner points) that lie along the table plane. Now, I want to project these points back to 3D somehow so I can get 3D bounding boxes that are aligned with the plane.
The projection from 3D to 2D plane is not invertible.. so how do I do this?