Recently I was assigned to implement a procedure involving "3D projections" to "2D space". Supposing that 3D data is stored in a n x 3 matrix X, the final step involves Y=XP, where P is a 3x2 matrix. However, I would need to be sure about the actual meaning of the word "projection" to 2D. In my understanding (I deliberately tend to be descriptive), there are some points in 3D, I'm looking at it from above, and there is a piece of paper below the data (paper is fixed). So, each time I multiply XP to obtain Y in 2D, it actually means I'm changing the viewpoint, and Y actually corresponds to what I see when looking at the data (as on the fixed paper), right? In other words, with every P, I'm changing the viewpoint and taking the picture (or drawing on a paper, thus 2D) of what I see? If so, that would mean that for any P there is a viewpoint. Please correct me if I'm wrong.