I working on program for displaying 3-dimensional objects on the computer screen using Ray Tracing method. And now I came across a problem with throwing rays from the orthogonal camera. So, as you know the orthogonal camera can be defined as a rectangle on some supporting plane and rays are going straight forward from it in the direction of it's normal vector. I made two cycles one inside another for $X$ and $Y$ to scan through that rectangle and throw the rays. And the problem is how to convert coordinates on the plane to coordinates in the global world $X, Y, Z$ space. I need just to compute the origins of rays.
Sorry for my poor English and incompetence in linear algebra...