Computing Camera Rays

We are in a transition period, where ray tracing and rasterization coexist. Typical real-time rendering pipelines still use rasterization (often with deferred shading) for primary visibility and then trace rays for shadows, reflections or global illumination. Though, we are getting to the point where one can seriously consider to ditch rasterization and to use ray tracing for primary visibility as well, at least on some platforms. Then you need to compute camera rays, characterized by ray origin, ray direction and ray length, in a way that is consistent with what you would otherwise do for rasterization. In rasterization, you commonly use a world to clip space transformation matrix, also known as view-projection matrix to specify the camera. In this blog post, I will derive how to compute camera rays based on such a matrix.