A linear algebra and mathematics library for computer graphics.

```
# Change Log
All notable changes to this project will be documented in this file, following
the format defined at [keepachangelog.com](http://keepachangelog.com/).
This project adheres to [Semantic Versioning](http://semver.org/).
## [Unreleased]
## [v0.13.1] - 2017-04-22
### Changed
- Update `serde` and `serde_derive` to version `1.0`.
## [v0.13.0] - 2017-04-14
### Added
- Add optional `use_simd` feature to improve the performance of `Vector4<f32>`,
`Matrix4<f32>` and `Quaternion<f32>`. According to @DaseinPhaos in #394, under
the given benchmark certain operations were able to become up to 60% faster.
- Add component wise casting for the matrix and point types
### Changed
- Update `serde` to version `0.9`, and use `serde_derive` instead of `serde_macros`.
## [v0.12.0] - 2016-09-14
### Changed
- Use [approx](https://github.com/brendanzab/approx/) for approximate equality
comparisons
- Remove `#[repr(packed)]` from all structs where it was specified
- Update serde to 0.8
## [v0.11.0] - 2016-08-17
### Added
- `Quaternion::from_arc`
### Changed
- Change the angle types to be tuple structs
- Make from-angle constructors take generic `Into<Rad<S>>` values
- Fix `Decomposed::concat` implementation
## [v0.10.0] - 2016-05-11
### Added
- A `MetricSpace` trait for types that have a distance between elements.
- `EuclideanSpace::{midpoint, centroid}` functions with default
implementations.
- `Vector1` and `Point1` structs.
- Serde support behind the `eders` feature flag.
- An `ApproxEq` implementation for `Decomposed`.
### Changed
- Depend on the `num-traits` crate rather than `num`, seeing as we only use the
traits in `num`. `num_traits` has also been re-exported so that you can more
easily use these in your project.
- Use an `Euler` type for euler angle conversions.
- Constrain `InnerSpace` by `MetricSpace`.
- Constrain `Rotation` by `One`
- Implement `Transform` and `Transform3` for `Matrix4`.
- Implement `Transform`, `Transform2`, and `Transform3` for `Matrix4`.
- Fix `Euler`-`Quaternion` and `Quaternion`-`Euler` conversions. The axes are
now correct, and the angles are applied in _x_-_y_-_z_ order. The conversion now
matches the conversion from axis angle.
- Fix `Euler`-`{Matrix3, Matrix4}` conversions.
## Removed
- `Rotation::transform_as_point`
- `AffineMatrix3`
- `Rotation::invert_self`
- `Matrix::invert_self`
## [v0.9.1] - 2016-04-20
### Changed
- Fix angle assignment operators so that they actually mutate `self`.
## [v0.9.0] - 2016-04-19
### Changed
- Assignment operators implementations have been stabilised, to coincide with
their [stabilisation in Rust 1.8](http://blog.rust-lang.org/2016/04/14/Rust-1.8.html).
- Renames `Vector` trait to `VectorSpace`.
- Renames `EuclideanVector` to `InnerSpace`.
- Renames `Point` to `EuclideanSpace`, and `Point::Vector` to `EuclideanSpace::Diff`.
- `Quaternion`s now implement `VectorSpace` and `InnerSpace` for the functions
they share.
- The `Matrix` trait is now constraint by `VectorSpace`, with `Matrix::Element`
removed in favor of `VectorSpace::Scalar`.
## [v0.8.0] - 2016-04-06
### Added
- Implements `fmt::Debug` for `Basis2`, `Basis3`, and `AffineMatrix3`
- A `prelude` module for easy importing of common traits.
- Constrained conversion functions for assisting in situations where type
inference is difficult.
- An `ElementWise` trait for non-mathematical element-wise operations.
- A default implementation for `EuclideanVector::angle`.
### Changed
- Improves the `fmt::Debug` impls for `Vector`, `Matrix`, `Point`, `Decomposed`,
`Quaternion` and `Angle` to make them easier to derive, and have clearer
formatting.
- Marks vectors, points, matrices, and angles as `#[repr(C, packed)]`.
- Renames the `Vector::{length, length2}` functions to `Vector::{magnitude, magnitude2}`.
- Move `Angle::new` to be directly implemented on the `Rad` and `Deg` types.
- Move `Vector::dot` to `EuclideanVector` trait.
- Move `Vector::from_value` to `Array` trait.
### Removed
- The non-mathematical operator trait implementations have been removed from
the `Vector` trait, in favor of the `ElementWise` trait.
- `Angle::equiv`.
- Remove `neg_self` method on vectors and matrices.
## [v0.7.0] - 2015-12-23
### Added
- Add missing by-ref and by-val permutations of `Vector`, `Matrix`, `Point`,
`Quaternion` and `Angle` operators.
- Ease lifetime constraints by removing `'static` from some scalar type
parameters.
- Weaken type constraints on `perspective` function to take an `Into<Rad<S>>`.
- Add `Angle::new` for constructing angles from a unitless scalar.
- Implement assignment operators for nightly builds, enabled by the `"unstable"`
feature.
### Changed
- `Vector`, `Matrix`, `Point`, and `Angle` are now constrained to require
specific operators to be overloaded. This means that generic code can now use
operators, instead of the operator methods.
- Take a `Rad` for `ProjectionFov::fovy`, rather than arbitrary `Angle`s. This
simplifies the signature of `PerspectiveFov` from `PerspectiveFov<S, A>` to
`PerspectiveFov<S>`.
- The following trait constraints were removed from `Angle`: `Debug`,
`ScalarConv`, `Into<Rad<S>>`, `Into<Deg<S>>`.
- `Angle` no longer requires `One`, and the implementations have been removed
from `Deg` and `Rad`. This is because angles do not close over multiplication,
and therefore cannot have a multiplicative identity. If we were truly accurate,
`Angle * Angle` would return an `Angle^2` (not supported by the current api).
- Make remainder operators on `Angle`s make sense from the perspective of
dimensional analysis.
- Moved free trigonometric functions onto `Angle`.
### Removed
- Remove redundant `Point::{min, max}` methods - these are now covered by the
`Array::{min, max}` methods that were introduced in 0.5.0.
- Removed `ToComponents`, `ToComponents2`, and `ToComponents3`. If you were
relying on `ToComponents::decompose`, you can produce the same effect by
accessing the fields on `Decomposed` directly. To create the scale vector,
use: `Vector::from_value(transform.scale)`.
- Removed `CompositeTransform`, `CompositeTransform2`, and `CompositeTransform3`.
- Remove `Vector::one`. Vectors don't really have a multiplicative identity.
If you really want a `one` vector, you can do something like:
`Vector::from_value(1.0)`.
- Remove operator methods from `Vector`, `Matrix`, `Point`, and `Angle` traits
in favor of operator overloading.
- Remove `*_self` methods from `Vector`, `Matrix`, `Point`, and `Angle`. The
operator methods can be used via the unstable assignment operators.
- Remove `#[derive(Hash)]` from `Deg` and `Rad`. This could never really be used
these types, because they expect to be given a `BaseFloat` under normal
circumstances.
## [v0.6.0] - 2015-12-12
### Added
- This CHANGELOG for keeping track of notable changes.
- `Matrix4::{from_scale, from_nonuniform_scale}` for easily constructing
homogeneous scale matrices.
### Changed
- Renamed `SquareMatrix::one` to `SquareMatrix::identity`. `identity` is easier
to search for,
and the more common name for the multiplicative identity for matrices.
- Matrix impls have now been constrained to `S: BaseFloat`.
## [v0.5.0] - 2015-11-20
### Changed
- Take many point and vector parameters by value.
- Take point and vector operator overloads by value.
- Divide `Matrix` trait into `Matrix` and `SquareMatrix`, opening the door for
non-square matrices in the future.
- Make many trait type parameters associated types.
- Move element-wise methods from `Vector` and `Point` onto the `Array1` trait,
and rename it to `Array`.
- Make pointer access methods on `Array` match the naming scheme of those in the
standard library.
### Removed
- Removed collision types: `Ray`, `Plane`, `Frustum`, `Aabb2`, `Aabb3` `Obb2`,
`Obb3` `Sphere`, `Cylinder`. These can now be found at
[csherratt/collision-rs](https://github.com/csherratt/collision-rs).
- Remove `Array2` trait, moving methods onto the `Matrix` trait.
## [v0.4.0] - 2015-10-25
## [v0.3.1] - 2015-09-20
## [v0.3.0] - 2015-09-20
## [v0.2.0] - 2015-05-11
## [v0.1.6] - 2015-05-10
## [v0.1.5] - 2015-04-25
## [v0.1.4] - 2015-04-24
## [v0.1.3] - 2015-04-06
## [v0.1.2] - 2015-04-01
## [v0.1.1] - 2015-03-25
## [v0.1.0] - 2015-03-15
## [v0.0.8] - 2015-03-09
## [v0.0.7] - 2015-03-01
## [v0.0.6] - 2015-02-21
## [v0.0.5] - 2015-02-16
## [v0.0.4] - 2015-02-11
## [v0.0.3] - 2015-02-08
## v0.0.1 - 2014-06-24
[Unreleased]: https://github.com/brendanzab/cgmath/compare/v0.13.1...HEAD
[v0.13.1]: https://github.com/brendanzab/cgmath/compare/v0.13.0...v0.13.1
[v0.12.0]: https://github.com/brendanzab/cgmath/compare/v0.12.0...v0.13.0
[v0.12.0]: https://github.com/brendanzab/cgmath/compare/v0.11.0...v0.12.0
[v0.11.0]: https://github.com/brendanzab/cgmath/compare/v0.10.0...v0.11.0
[v0.10.0]: https://github.com/brendanzab/cgmath/compare/v0.9.1...v0.10.0
[v0.9.1]: https://github.com/brendanzab/cgmath/compare/v0.9.0...v0.9.1
[v0.9.0]: https://github.com/brendanzab/cgmath/compare/v0.8.0...v0.9.0
[v0.8.0]: https://github.com/brendanzab/cgmath/compare/v0.7.0...v0.8.0
[v0.7.0]: https://github.com/brendanzab/cgmath/compare/v0.6.0...v0.7.0
[v0.6.0]: https://github.com/brendanzab/cgmath/compare/v0.5.0...v0.6.0
[v0.5.0]: https://github.com/brendanzab/cgmath/compare/v0.4.0...v0.5.0
[v0.4.0]: https://github.com/brendanzab/cgmath/compare/v0.3.1...v0.4.0
[v0.3.1]: https://github.com/brendanzab/cgmath/compare/v0.3.0...v0.3.1
[v0.3.0]: https://github.com/brendanzab/cgmath/compare/v0.2.0...v0.3.0
[v0.2.0]: https://github.com/brendanzab/cgmath/compare/v0.1.6...v0.2.0
[v0.1.6]: https://github.com/brendanzab/cgmath/compare/v0.1.5...v0.1.6
[v0.1.5]: https://github.com/brendanzab/cgmath/compare/v0.1.4...v0.1.5
[v0.1.4]: https://github.com/brendanzab/cgmath/compare/v0.1.3...v0.1.4
[v0.1.3]: https://github.com/brendanzab/cgmath/compare/v0.1.2...v0.1.3
[v0.1.2]: https://github.com/brendanzab/cgmath/compare/v0.1.1...v0.1.2
[v0.1.1]: https://github.com/brendanzab/cgmath/compare/v0.1.0...v0.1.1
[v0.1.0]: https://github.com/brendanzab/cgmath/compare/v0.0.8...v0.1.0
[v0.0.8]: https://github.com/brendanzab/cgmath/compare/v0.0.7...v0.0.8
[v0.0.7]: https://github.com/brendanzab/cgmath/compare/v0.0.6...v0.0.7
[v0.0.6]: https://github.com/brendanzab/cgmath/compare/v0.0.5...v0.0.6
[v0.0.5]: https://github.com/brendanzab/cgmath/compare/v0.0.4...v0.0.5
[v0.0.4]: https://github.com/brendanzab/cgmath/compare/v0.0.3...v0.0.4
[v0.0.3]: https://github.com/brendanzab/cgmath/compare/v0.0.1...v0.0.3
```