I want to be able to render each pixel in a Povray coordinates individually.
For example, I want the pixel at coordinate <20,20,20> to be red, the
coordinates at <20,20,21> to be blue. From what I understood, if someone
wants to render something, for example a landscape, he must use the objects
that povray provides. However, I don't want to use any objects. I just want
to set each pixel color.

It's the same like reading an image into povray. The image pixels have to be
read one by one and rendered in the raytracer. Which function or functions
actually determine the pixel color and render it?

Can anyone suggest to me how I may proceed and what functions are available
in Povray that can allow me to do this.

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