HowTo:Extract 2D screen coordinates from 3D scenes

Introduction

At some point in your POV-Ray career you may need to retrieve high precision 2D screen coordinates of a point in a 3D POV-Ray render. Simply measuring the number of pixels in MS Paint is rarely a good solution because the precision is too low, even for very large renders. Instead, you need to use POV-Ray's own mechanisms to calculate and output finer measurements.

I faced this problem when designing two images for Wikipedia. For the first image, I needed to overlay 2D vector elements on top of a 3D POV-Ray render in order to show a series of measurements I made of important angles in the 3D bitmap. For the second image, I used the points outputted from a POV-Ray render to create a brand new 2D vector image from scratch. In both cases I used GeoGebra to create the 2D vector elements, but you could use InkScape as well.

(The first image is named "Graphical projection comparison.png". The second image is named "Various projections of cube above plane.svg". I can't link to them from here because the captcha widget on this website is broken, and I am prevented as a result from adding external links.)