Viewing profile — elengyel

> All modern vector renderers I know of avoid triangle rasterization entirely. Well, now you know of a modern renderer that does use triangle rasterization. The reason is simple --…

You don't seem to have grokked the main feature that makes Slug interesting. The algorithm handles every single possible case uniformly through the use of a very fast classificatio…

Thanks -- nice to hear from you!

The Slug Library can convert each cubic curve into a small set of quadratic curves that approximate extremely well.

Vello is intended more for general vector graphics and would probably perform better with pictures containing lots of large paths. Slug is designed specifically for rendering glyph…

Glyph complexity has no effect on the calculations done in the pixel shader and does not change how glyphs are preprocessed. There are no edge cases. If you'd like to see some ridi…

The plaque was a personal order from one of the many companies that make them. What you actually get from the USPTO looks like this: https://x.com/EricLengyel/status/11599170923316…

I took care of the whole thing myself without lawyers, so I ended up paying something like $950 in various filing fees.

I don't think you're missing anything. One of the goals of this article is to demonstrate how geometric algebra is really just another part of exterior algebra anyway. However, per…

My position is that the geometric product and antiproduct are good for one thing, performing transformations with sandwich products q ⟑ p ⟑ q̃ or q ⟇ p ⟇ q̰ and composing those tra…

Hi Alex -- In PGA, every operation comes in pairs. There are two exterior products, two inner products, and two geometric products (and the list goes on). If points are represented…

I think Macdonald's book is very concise and clean compared to others, but it does have some of the same issues that I wrote about in my post. In particular, Definition 6.15 gives …

Unfortunately, the Lundholm and Svensson text you've cited suffers from the same problems I wrote about in my post. Definition 2.7 connects the interior products to the scalar prod…

I don't remember the exact details, but I did try the G command, and it didn't work out. The problem was something like the program had nowhere to return to, so just ending with RT…

I'd very much like to revive my old code (which I still have) at some point and see how well it runs on modern computers. My guess is that a typical 64-bit ~3 GHz quad-core machine…

I'd like to clarify that my code was running only on machines that were otherwise idle. Not many people were in the lab late in the evenings. MPQS processing nodes could be added a…

Right, the post was not intended to be any kind of introduction or tutorial, but rather more of an announcement to those already familiar with the subject that there exists another…

Doing rotations about arbitrary points in geometric algebra requires the use of dual quaternions, but I agree that virtually every presentation of that material is awful. I'm tryin…

I think you might like Foundations of Game Engine Development, Volume 1. ( http://foundationsofgameenginedev.com/ ) It focuses on practical uses of Grassmann algebra and doesn't av…