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A wide linear algebra crate for games and graphics.
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README.md Replace 'clearn' with 'clear' in README.MD and lib.rs Dec 28, 2019

README.md

crates.io docs.rs

ultraviolet

This is a crate to computer-graphics and games-related linear algebra, but fast, both in terms of productivity and in terms of runtime performance.

In terms of productivity, ultraviolet uses no generics and is designed to be as straightforward of an interface as possible, resulting in fast compilation times and clear code. In addition, the lack of generics and Rust type-system "hacks" result in clear and concise errors that are easy to parse and fix for the user.

In terms of runtime performance, ultraviolet was designed from the start with performance in mind. To do so, we provide two separate kinds of each type, each with nearly identical functionality, one with usual scalar f32 values, and the other a 'wide' type which uses SIMD f32x4 vectors for each value. This design is clear and explicit in intent, and it also allows code to take full advantage of SIMD.

The 'wide' types use an "SoA" (Structure of Arrays) architecture such that each Wec (wide-Vec) actually contains the data for 4 Vecs and will do any operation on all 4 of the vector 'lanes' at the same time (the same concept applies to a Wat, or 'wide-Mat'). Doing this is potentially much (factor of 10) faster than an "AoS" (Array of Structs) layout, as all current Rust linear algebra libraries do, though it does depend on your workload. Algorithms must be carefully architected to take full advantage of this, and doing so can be easier said than done, especially if your algorithm involves significant branching.

Benchmarks

Benchmarks done using my own fork of mathbench-rs with support for ultraviolet added to some benchmarks.

For the euler 2d and 3d benchmarks, the work being done is exactly equivalent. For the rest of the benchmarks, the work being done is made equivalent by performing 4 of the benchmarked operation per iteration instead of just one for all of the other libraries, since ultraviolet is computing that operation on four Vec/Mats at a time.

benchmark glam cgmath nalgebra euclid ultraviolet
euler 2d 9.911 us 9.583 us 21.99 us 15.22 us 6.675 us
euler 3d 15.11 us 32.88 us 237.2 us 32.62 us 9.928 us
mat3 transform vector3 6.1533 ns 15.2933 ns 15.6202 ns N/A 4.4778 ns
vec3 cross 7.6824 ns 16.9919 ns 12.3683 ns 12.4657 ns 3.3286 ns
vec3 dot 5.6354 ns 10.4704 ns 8.7803 ns 7.4304 ns 2.4937 ns
vec3 length 5.8759 ns 4.2015 ns 4.5598 ns 4.2083 ns 1.9067 ns
vec3 normalize 8.7861 ns 8.1677 ns 33.2839 ns 7.6300 ns 4.4362 ns

Features

This crate is currently being dogfooded in my ray tracer rayn, and is being used by some Amethyst developers in experimental projects while it is considered for adoption into Amethyst. It does what those users have currently needed it to do.

There are a couple relatively unique/novel features in this lib, the most important being the use of the Geometric Algebra concepts of Bivectors and Rotors to represent 2d and 3d rotations, rather than implementing complex number algebra and Quaternion algebra.

What this means for the programmer is that you will be using the Rotor3 type in place of a Quaternion, though you can expect it to do basically all the same things that a Quaternion does. In fact, Quaternions are essentially just a special case of Rotors. The reason this decision was made was twofold: first, the derivation of the math is actually quite simple to understand. All the derivations for the code implemented in the Rotor structs in this library are written out in the docs folder of the GitHub repo; I derived them manually as part of the implementation. On the other hand, Quaternions are often basically just seen as black boxes that we programmers use to do rotations because they have some nice properties, but that we don't really understand. You can use Rotors this same way, but you can also easily understand them. Second is that in some sense they can be seen as 'more correct' than Quaternions, and especially they facilitate a more proper understanding of rotation as being something that occurs within a plane rather than something that occurs around an axis, as it is generally thought. Finally, Rotors also generalize do 4 and even higher dimensions, and if someone wants to they could implement a Rotor4 which retains all the properties of a Rotor3/Quaternion but does rotation in 4 dimensions instead, something which simply is not possible to do with Quaternions.

If it's missing something you need it to do, bug me on the GitHub issue tracker and/or Rust community discord server (I'm Fusha there) and I'll try to add it for you, if I believe it fits with the vision of the lib :)

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