[mjfisher]

And in case it helps further in the context of the article: traditional rendering pipelines for games don't render fuzzy Gaussian points, but triangles instead.

Having the model trained on how to construct triangles (rather than blobbly points) means that we're closer to a "take photos of a scene, process them automatically, and walk around them in a game engine" style pipeline.

[yazaddaruvala]

Any insights into why game engines prefer triangles rather than guassians for fast rendering?

Are triangles cheaper for the rasterizer, antialiasing, or something similar?

[mjfisher]

Cheaper for everything, ultimately.

A triangle by definition is guaranteed to be co-planer; three vertices must describe a single flat plane. This means every triangle has a single normal vector across it, which is useful for calculating angles to lighting or the camera.

It's also very easy to interpolate points on the surface of a triangle, which is good for texture mapping (and many other things).

It's also easy to work out if a line or volume intersects a triangle or not.

Because they're the simplest possible representation of a surface in 3D, the individual calculations per triangle are small (and more parallelisable as a result).

[jiggawatts]

Triangles are the simplest polygons, and simple is good for speed and correctness.

Older GPUs natively supported quadrilaterals (four sided polygons), but these have fundamental problems because they're typically specified using the vertices at the four corners... but these may not be co-planar! Similarly, interpolating texture coordinates smoothly across a quad is more complicated than with triangles.

Similarly, older GPUs had good support for "double-sided" polygons where both sides were rendered. It turned out that 99% of the time you only want one side, because you can only see the outside of a solid object. Rendering the inside back-face is a pointless waste of computer power. This actually simplified rendering algorithms by removing some conditionals in the mathematics.

Eventually, support for anything but single-sided triangles was in practice emulated with a bunch of triangles anyway, so these days we just stopped pretending and use only triangles.

[strangecasts]

As an aside, a few early 90s games did experiment with spheroid sprites to approximate 3D rendering, including the DOS game Ecstatica [1] and the (unfortunately named) SNES/Genesis game Ballz 3D [2]

[1] https://www.youtube.com/watch?v=nVNxnlgYOyk

[2] https://www.youtube.com/watch?v=JfhiGHM0AoE

[jplusequalt]

>triangles cheaper for the rasterizer

Yes, using triangles simplifies a lot of math, and GPUs were created to be really good at doing the math related to triangles rasterization (affine transformations).

[Daub]

Yes cheaper. Quads are subject to becoming non-planar leading to shading artifacts.

In fact, I belive that under the hood all 3d models are triangulated.

[adastra22]

Yes. Triangles are cheap. Ridiculously cheap. For everything.