I am looking for an advanced 3d mathematics geometry software where I can create equations of geometry,trace rays as in Optics,create equations of rays(Ray tracing),create different types of 3D and 2D geometry(shapes) and their equations, etc.
To be more specific, for example as I am sitting in a room, I want to create my room(simple 3d objects) not too Complex, and then I want to draw lines(light rays) coming from light source and where they will go, and then create equations about light rays.