> the math for perspective was developed long before computers with z-buffers existed
I would say long before computers existed. Perspective projection was the key algorithm of renaissance art!
I would say long before computers existed. Perspective projection was the key algorithm of renaissance art!
Funny story though, speaking of renaissance art- I was doing research for my Master's thesis on computer graphics, and got direct access to several books from the 1700s that outlined the geometry of perspective projection as well as the geometry of shadows. (My thesis was about rendering shadows.) They were hand-written tomes, with very ornate covers and bindings and hand-drawn diagrams. The books weren't allowed to leave, but they had a special reading room for them, with archive-safe lead weights to hold the pages down so I wouldn't spread my damaging finger oils everywhere. I was taking some digital photos, and at one point I forgot about the lead weights and turned the page. It tore a little bit, and I was completely mortified!
Sorry, history!
This is old now, and modern techniques have mostly surpassed it, but the basic idea was to combine single-sample ray casting for finding occluders probabilistically with an image-plane flood-fill using analytic methods to render the shadows. It's a way to only pay for accurate shadow calculations where shadows actually exist, and skip the shadow calculations in all the un-occluded areas.