Hacker News Reader

Comment by dahart | Hacker News Reader

Agreed, but I'd have to first put in a vote for not claiming one part is the mostest.

I like this post, among other things, it's a nice demonstration of the crazy amount of work your graphics card is doing to display a frame of your game. And it took some work and was put together with love.

But if you're going to call one single thing "the core algorithm of 3d", then yeah I'd have to second this one, perspective projection might be it - perspective is what makes 3d look 3d, you can do it without solid surfaces, and the math for perspective was developed long before computers with z-buffers existed.

I will totally grant that depth testing is the core algorithm of z-buffering, and iterating over triangles is the core algorithm of rendering triangle meshes. ;)

View on HN

Maybe I'm biased here by spending an awful lot of time in AutoCAD, but I'd tend toward the wireframe parts as being all you need for 3D. All this "shading," "hidden surface removal," and "triangles" shenanigans is just sugar on top.

Though I'm having second thoughts about calling perspective projection the most basic part, since most of my work happens from an orthographic camera. Let's call that a perspective projection from a camera at infinity and it all works out.

At any rate, mapping points in world space to points in screen space and then drawing lines between them is a pretty clever system, and the new software and hardware we've added since then is so incredible that it's hard to comprehend sometimes.

> 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!

You're absolutely right, I'd hoped that was my implication. ;)

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!

Are you by any chance comfortable with sharing your thesis here (if you still have it around)? It sounds interesting. I would have asked via email if I had known where to send it!

Sure! I'm not sure the complete thesis with the renaissance geometry images is online anywhere, but it's mostly an expanded version of this paper: http://www.graphics.cornell.edu/pubs/1999/HDG99.html

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.

Reply on news.ycombinator.com