elengyel

7 ms·

1.
by elengyel 7mo ago
> 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 -- Slug was designed to render text and vector graphics in
2.
by elengyel 7mo ago
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 classification and root eligibility determination technique. On some
3.
by elengyel 7mo ago
Thanks -- nice to hear from you!
4.
by elengyel 7mo ago
The Slug Library can convert each cubic curve into a small set of quadratic curves that approximate extremely well.
5.
by elengyel 7mo ago
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-like objects and would perform better with lots of text and
6.
by elengyel 7mo ago
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 ridiculously complex fonts get rendered with Slug, check ou
7.
by elengyel 7mo ago
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/1159917092331642880/photo/1
8.
by elengyel 7mo ago
I took care of the whole thing myself without lawyers, so I ended up paying something like $950 in various filing fees.
9.
by elengyel 1y ago
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, performing transformations in spacetime with the geom
10.
by elengyel 2y ago
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 transformations. Literally everything else (join, meet, contrac
11.
by elengyel 2y ago
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 by vectors, then the quaternion-like sandwich qpq* with the
12.
by elengyel 2y ago
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 one of the problematic definitions of the inner product
13.
by elengyel 2y ago
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 product, not the inner product. Definition 2.8 gives the sa
14.
by elengyel 5y ago
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 RTS would crash, and ending with a call to ExitToShe
15.
by elengyel 5y ago
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 could accomplish the same task in a few minutes today.
16.
by elengyel 5y ago
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 and removed dynamically, so if somebody needed a compute
17.
by elengyel 7y ago
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 way of doing the math that doesn't require inverting t
18.
by elengyel 7y ago
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 trying to change that.
19.
by elengyel 7y ago
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 avoid doing real-world calculations with a