GameMath provides common types, related functions, and operators commonly used for interactive realtime simulations (games).

GameMath Windows macOS Linux WebAssembly

GameMath provides common types, related functions, and operators commonly used for interactive realtime simulations (games). You can use this library to create simple games, or use it as a cornerstone for a more complex engine.

Swift 100%

GameMath uses protocols and generics to promote clear type intention. Vector types as an example have many variations including Position3, Direction3, and Size3 that all conform toVector3, a protocol that provides common functionality to these types.

Operators such as multiplication, division, addition, and subtraction, can be used across types so long as they use the same generic constraint. The type returned will be the logical result of the operation, usually the left side.

let pos: Position3<Float> = Position3(0, 1, 0) * Size3(1, 1, 1)

//Error: Size3 cannot be converted to Position3
let pos: Position3<Float> = Size3(1, 1, 1) * Position3(0, 1, 0) 

Most types work with Swift Generics. Some types have restrictions on generics. Using Size3<Int> instead of Size3<Float> makes sense and could be used for any number of reasons.

However a Direction3<Int> does not make sense because a normalized direction vector should have a length of 1, so Int cannot represent very many angles. While Direction3<Int>(0, 1, 0) is valid, it's usefulness is questionable so FloatingPoint is a requirement for Direction3<T: FloatingPoint>.

Easy To Understand

GameMath is intended to make doing gamming math easier for everyone. An example is interpolation.

The functions lerp() and slerp() are commonly seen in game libraries for linear interpolation. Without advanced knowledge of these functions it's difficult to reason about them and know what they do. GameMath attempts to improve on this issue by introducing a common syntax for interpolation for all types across the package.

let halfway = source.interpolated(to: destination, .linear(0.5))

This syntax will be expanded with new interpolation methods like easeIn and easeOut in the future.

Coordinate Space

GameMath uses a Y Up, -Z forward, coordinate system for 3D and Y Up, X Right for 2D.

Matrix types are assumed to always be "left handed". Use the transposedArray and transposedSIMD properties when sending data to Metal, Vulkan, OpenGL, and the array and simd properties when sending data to DirectX.

Cross Platform

GameMath is tested to work on Windows 10, macOS, Ubuntu, iOS, and tvOS; all of which work with Swift's minimum deployment target for each platform.

Other platforms should also work. Issues that may appear are likely to be loacted in math.swift where the availability of Float80 and Float16 could result in build errors on a platform not listed above.

Actively In Use

Check out my YouTube channel for video devlogs about the games I make using this package.

Strega's Gate: Espionage Strega's Gate: Shifter


  • Unit Tests
    A test suite is currently being implemented to ensure correctness of the API's before effort is put into making them faster.

  • Performance Testing
    GameMath is currently un-optimized. Once unit tests have full code coverage a performance test suite will be set up that runs tests for common real world use cases, such as matrix multiplication.

    At this stage perfromance can be played with, and compiler hints like @inlinable will also be added to enhance optimized builds.

  • 2D
    GameMath has not been used to create a 2D game and may be missing some necessary functionality.

  • Remove Foundation
    Foundation is currently imported in a few places because of math functions like sin, cos, and tan which will be part of the standard library at some point. It is a goal for GameMath to not require any dependencies, so I'd like to remove Foundation as soon as the math proposal gets merged into Swift.

Usage Notes

GameMath is under development and the API surface is not locked-in.

As such please use an explicit commit when adding GameMath to your packages. You may do so like this, while replacing the revision hash with the latests commit's.

.package(url: "", .revision("82d2817f2cf1eca44890d8173145d934bda55517"))

Doing this will prevent changes made to GameMath from halting development of your own package. When you are ready to update, use a newer hash and fix any API changes.

API changes are mostly final so changes should not be too much of a hassle, however please be aware they can and will happen.

A tag will be created at some point to mark version 1.0, at which point the main branch will become the stable release branch. This will happen once unit tests and a first pass of optimization is done. ETA unknown.

Game Package Family

This package works great by itself, but it's also included as part of higher level packages that I'm working on. You can check the availability of these packages on my GitHub profile @STREGAsGate.


  • Swift Tools 5.3.0
View More Packages from this Author


  • None
Last updated: Mon Jan 23 2023 21:14:43 GMT-0500 (GMT-05:00)