## Expand description

## glam

`glam`

is a simple and fast linear algebra library for games and graphics.

### Features

### SIMD

`glam`

is built with SIMD in mind. Many `f32`

types use 128-bit SIMD vector types for storage
and/or implementation. The use of SIMD generally enables better performance than using primitive
numeric types such as `f32`

.

Some `glam`

types use SIMD for storage meaning they are 16 byte aligned, these types include
`Mat2`

, `Mat3A`

, `Mat4`

, `Quat`

, `Vec3A`

, `Vec4`

, `Affine2`

an `Affine3A`

. Types
with an `A`

suffix are a SIMD alternative to a scalar type, e.g. `Vec3`

uses `f32`

storage and
`Vec3A`

uses SIMD storage.

When SIMD is not available on the target the types will maintain 16 byte alignment and internal padding so that object sizes and layouts will not change between architectures. There are scalar math fallback implementations exist when SIMD is not available. It is intended to add support for other SIMD architectures once they appear in stable Rust.

Currently only SSE2 on x86/x86_64 is supported as this is what stable Rust supports.

### Vec3A and Mat3A

`Vec3A`

is a SIMD optimized version of the `Vec3`

type, which due to 16 byte alignment results
in `Vec3A`

containing 4 bytes of padding making it 16 bytes in size in total. `Mat3A`

is composed
of three `Vec3A`

columns.

Despite this wasted space the SIMD implementations tend to outperform `f32`

implementations in
**mathbench** benchmarks.

`glam`

treats `Vec3`

as the default 3D vector type and `Vec3A`

a special case for optimization.
When methods need to return a 3D vector they will generally return `Vec3`

.

There are `From`

trait implementations for converting from `Vec4`

to a `Vec3A`

and between
`Vec3`

and `Vec3A`

(and vice versa).

```
use glam::{Vec3, Vec3A, Vec4};
let v4 = Vec4::new(1.0, 2.0, 3.0, 4.0);
// Convert from `Vec4` to `Vec3A`, this is a no-op if SIMD is supported.
let v3a = Vec3A::from(v4);
assert_eq!(Vec3A::new(1.0, 2.0, 3.0), v3a);
// Convert from `Vec3A` to `Vec3`.
let v3 = Vec3::from(v3a);
assert_eq!(Vec3::new(1.0, 2.0, 3.0), v3);
// Convert from `Vec3` to `Vec3A`.
let v3a = Vec3A::from(v3);
assert_eq!(Vec3A::new(1.0, 2.0, 3.0), v3a);
```

### Affine2 and Affine3A

`Affine2`

and `Affine3A`

are composed of a linear transform matrix and a vector translation. The
represent 2D and 3D affine transformations which are commonly used in games.

The table below shows the performance advantage of `Affine2`

over `Mat3A`

and `Mat3A`

over `Mat3`

.

operation | `Mat3` | `Mat3A` | `Affine2` |
---|---|---|---|

inverse | 11.4±0.09ns | 7.1±0.09ns | 5.4±0.06ns |

mul self | 10.5±0.04ns | 5.2±0.05ns | 4.0±0.05ns |

transform point2 | 2.7±0.02ns | 2.7±0.03ns | 2.8±0.04ns |

transform vector2 | 2.6±0.01ns | 2.6±0.03ns | 2.3±0.02ns |

Performance is much closer between `Mat4`

and `Affine3A`

with the affine type being faster to
invert.

operation | `Mat4` | `Affine3A` |
---|---|---|

inverse | 15.9±0.11ns | 10.8±0.06ns |

mul self | 7.3±0.05ns | 7.0±0.06ns |

transform point3 | 3.6±0.02ns | 4.3±0.04ns |

transform point3a | 3.0±0.02ns | 3.0±0.04ns |

transform vector3 | 4.1±0.02ns | 3.9±0.04ns |

transform vector3a | 2.8±0.02ns | 2.8±0.02ns |

Benchmarks were taken on an Intel Core i7-4710HQ.

### Linear algebra conventions

`glam`

interprets vectors as column matrices (also known as column vectors) meaning when
transforming a vector with a matrix the matrix goes on the left.

```
use glam::{Mat3, Vec3};
let m = Mat3::IDENTITY;
let x = Vec3::X;
let v = m * x;
assert_eq!(v, x);
```

Matrices are stored in memory in column-major order.

All angles are in radians. Rust provides the `f32::to_radians()`

and `f64::to_radians()`

methods to
convert from degrees.

### Direct element access

Because some types may internally be implemented using SIMD types, direct access to vector elements
is supported by implementing the `Deref`

and `DerefMut`

traits.

```
use glam::Vec3A;
let mut v = Vec3A::new(1.0, 2.0, 3.0);
assert_eq!(3.0, v.z);
v.z += 1.0;
assert_eq!(4.0, v.z);
```

### glam assertions

`glam`

does not enforce validiity checks on method parameters at runtime. For example methods that
require normalized vectors as input such as `Quat::from_axis_angle(axis, angle)`

will not check
that axis is a valid normalized vector. To help catch unintended misuse of `glam`

the
`debug-glam-assert`

or `glam-assert`

features can be enabled to add checks ensure that inputs to
are valid.

### Vector swizzles

`glam`

vector types have functions allowing elements of vectors to be reordered, this includes
creating a vector of a different size from the vectors elements.

The swizzle functions are implemented using traits to add them to each vector type. This is
primarily because there are a lot of swizzle functions which can obfuscate the other vector
functions in documentation and so on. The traits are `Vec2Swizzles`

, `Vec3Swizzles`

and
`Vec4Swizzles`

.

Note that the `Vec3Swizzles`

implementation for `Vec3A`

will return a `Vec3A`

for 3 element
swizzles, all other implementations will return `Vec3`

.

```
use glam::{swizzles::*, Vec2, Vec3, Vec3A, Vec4};
let v = Vec4::new(1.0, 2.0, 3.0, 4.0);
// Reverse elements of `v`, if SIMD is supported this will use a vector shuffle.
let wzyx = v.wzyx();
assert_eq!(Vec4::new(4.0, 3.0, 2.0, 1.0), wzyx);
// Swizzle the yzw elements of `v` into a `Vec3`
let yzw = v.yzw();
assert_eq!(Vec3::new(2.0, 3.0, 4.0), yzw);
// To swizzle a `Vec4` into a `Vec3A` swizzle the `Vec4` first then convert to
// `Vec3A`. If SIMD is supported this will use a vector shuffle. The last
// element of the shuffled `Vec4` is ignored by the `Vec3A`.
let yzw = Vec3A::from(v.yzwx());
assert_eq!(Vec3A::new(2.0, 3.0, 4.0), yzw);
// You can swizzle from a `Vec4` to a `Vec2`
let xy = v.xy();
assert_eq!(Vec2::new(1.0, 2.0), xy);
// And back again
let yyxx = xy.yyxx();
assert_eq!(Vec4::new(2.0, 2.0, 1.0, 1.0), yyxx);
```

### SIMD and scalar consistency

`glam`

types implement `serde`

`Serialize`

and `Deserialize`

traits to ensure
that they will serialize and deserialize exactly the same whether or not
SIMD support is being used.

The SIMD versions implement the `core::fmt::Debug`

and `core::fmt::Display`

traits so they print the same as the scalar version.

```
use glam::Vec4;
let a = Vec4::new(1.0, 2.0, 3.0, 4.0);
assert_eq!(format!("{}", a), "[1, 2, 3, 4]");
```

### Feature gates

All `glam`

dependencies are optional, however some are required for tests
and benchmarks.

`std`

- the default feature, has no dependencies.`approx`

- traits and macros for approximate float comparisons`bytemuck`

- for casting into slices of bytes`libm`

- required to compile with`no_std`

`mint`

- for interoperating with other 3D math libraries`num-traits`

- required to compile`no_std`

, will be included when enabling the`libm`

feature`rand`

- implementations of`Distribution`

trait for all`glam`

types.`serde`

- implementations of`Serialize`

and`Deserialize`

for all`glam`

types. Note that serialization should work between builds of`glam`

with and without SIMD enabled`scalar-math`

- disables SIMD support and uses native alignment for all types.`debug-glam-assert`

- adds assertions in debug builds which check the validity of parameters passed to`glam`

to help catch runtime errors.`glam-assert`

- adds assertions to all builds which check the validity of parameters passed to`glam`

to help catch runtime errors.

### Minimum Supported Rust Version (MSRV)

The minimum supported Rust version is `1.45.0`

.

## Modules

`bool`

vector mask types.`f32`

vector, quaternion and matrix types.`f64`

vector, quaternion and matrix types.`i32`

vector types.- Traits adding swizzle methods to all vector types.
`u32`

vector types.

## Macros

- Creates a
`DMat2`

from two column vectors that can be used to initialize a constant value. - Creates a
`DMat3`

from three column vectors that can be used to initialize a constant value. - Creates a
`DMat4`

from four column vectors that can be used to initialize a constant value. - Creates a
`DQuat`

from`x`

,`y`

,`z`

and`w`

values that can be used to initialize a constant value. - Creates a
`DVec2`

that can be used to initialize a constant value. - Creates a
`DVec3`

that can be used to initialize a constant value. - Creates a
`DVec4`

that can be used to initialize a constant value. - Creates a
`IVec2`

that can be used to initialize a constant value. - Creates a
`IVec3`

that can be used to initialize a constant value. - Creates a
`IVec4`

that can be used to initialize a constant value. - Creates a
`Mat2`

from two column vectors that can be used to initialize a constant value. - Creates a
`Mat3`

from three column vectors that can be used to initialize a constant value. - Creates a
`Mat3A`

from three column vectors that can be used to initialize a constant value. - Creates a
`Mat4`

from four column vectors that can be used to initialize a constant value. - Creates a
`Quat`

from`x`

,`y`

,`z`

and`w`

values that can be used to initialize a constant value. - Creates a
`UVec2`

that can be used to initialize a constant value. - Creates a
`UVec3`

that can be used to initialize a constant value. - Creates a
`UVec4`

that can be used to initialize a constant value. - Creates a
`Vec2`

that can be used to initialize a constant value. - Creates a
`Vec3`

that can be used to initialize a constant value. - Creates a
`Vec3A`

that can be used to initialize a constant value. - Creates a
`Vec4`

that can be used to initialize a constant value.

## Structs

- A 2D affine transform, which can represent translation, rotation, scaling and shear.
- A 3D affine transform, which can represent translation, rotation, scaling and shear.
- A 2-dimensional boolean vector.
- A 3-dimensional boolean vector.
- A 3-dimensional SIMD vector mask.
- A 4-dimensional boolean vector.
- A 4-dimensional SIMD vector mask.
- A 2D affine transform, which can represent translation, rotation, scaling and shear.
- A 3D affine transform, which can represent translation, rotation, scaling and shear.
- A 2x2 column major matrix.
- A 3x3 column major matrix.
- A 4x4 column major matrix.
- A quaternion representing an orientation.
- A 2-dimensional vector.
- A 3-dimensional vector.
- A 4-dimensional vector.
- A 2-dimensional vector.
- A 3-dimensional vector.
- A 4-dimensional vector.
- A 2x2 column major matrix.
- A 3x3 column major matrix.
- A 3x3 column major matrix.
- A 4x4 column major matrix.
- A quaternion representing an orientation.
- A 2-dimensional vector.
- A 3-dimensional vector.
- A 4-dimensional vector.
- A 2-dimensional vector.
- A 3-dimensional vector without SIMD support.
- A 3-dimensional vector with SIMD support.
- A 4-dimensional vector.

## Enums

- Euler rotation sequences.

## Traits

- Swizzle methods for 2-dimensional vector types.
- Swizzle methods for 3-dimensional vector types.
- Swizzle methods for 3-dimensional vector types.

## Functions

- Creates a 2x2 matrix from two column vectors.
- Creates a 3x3 matrix from three column vectors.
- Creates a 4x4 matrix from four column vectors.
- Creates a quaternion from
`x`

,`y`

,`z`

and`w`

values. - Creates a 2-dimensional vector.
- Creates a 3-dimensional vector.
- Creates a 4-dimensional vector.
- Creates a 2-dimensional vector.
- Creates a 3-dimensional vector.
- Creates a 4-dimensional vector.
- Creates a 2x2 matrix from two column vectors.
- Creates a 3x3 matrix from three column vectors.
- Creates a 3x3 matrix from three column vectors.
- Creates a 4x4 matrix from four column vectors.
- Creates a quaternion from
`x`

,`y`

,`z`

and`w`

values. - Creates a 2-dimensional vector.
- Creates a 3-dimensional vector.
- Creates a 4-dimensional vector.
- Creates a 2-dimensional vector.
- Creates a 3-dimensional vector.
- Creates a 3-dimensional vector.
- Creates a 4-dimensional vector.