Suppose a 3D configuration of points is given, $X\in\mathbb{R}^{n\times 3}$, and a non-zero matrix $Q\in\mathbb{3\times 2}$, with orthonormal columns. Now, suppose a mapping to 2D is obtained as $Y=XQ.$ I'm interested in the intuitive interpretation of the result $Y\in\mathbb{R}^{n\times 2}$. Suppose a plane $P$ is given; does the above mapping imply the result of overlaying the configuration with plane $P$ ? I introduced the plane since I'm not sure about the notion of the viewpoint in this mapping. Does the viewpoint enter the above? I'm also interested in the orthonormality condition of the direction vectors. What would happen if they are not orthogonal?
For instance, choosing $Q$ to contain the first two columns of a $3\times 3$ identity matrix would yield a solution where each point is mapped to a point that is obtained at the intersection of a line passing through that point and $xy$ plane, such that the the line is orhogonal to the $xy$ plane. Given such an interpretation, how could I cast the above?