# The nalgebra-glm crate

The **nalgebra-glm** crate is a GLM-like interface for the **nalgebra** general-purpose linear algebra library.
GLM itself is a popular C++ linear algebra library essentially targeting computer graphics. Therefore
**nalgebra-glm** draws inspiration from GLM to define a nice and easy-to-use API for simple graphics application. All the types
of **nalgebra-glm** are actually aliases of types from **nalgebra**. Therefore there is a complete and seamless inter-operability
between both crates.

## #

Getting startedFirst of all, you should start by taking a look at the official GLM API documentation
since **nalgebra-glm** implements a large subset of it. To use **nalgebra-glm** to your project, you
should add it as a dependency to your `Crates.toml`

:

Then, you must add an `extern crate`

statement to your `lib.rs`

or `main.rs`

file. It is **strongly
recommended** to add a crate alias to `glm`

as well so that you will be able to call functions of
**nalgebra-glm** using the module prefix `glm::`

. For example you will write `glm::rotate(...)`

instead
of the more verbose `nalgebra_glm::rotate(...)`

:

### #

Main differences compared to GLMWhile **nalgebra-glm** follows the feature line of the C++ GLM library, quite a few differences
remain and they are mostly syntactic. The main ones are:

- All function names use
`snake_case`

, which is the Rust convention. - All type names use
`CamelCase`

, which is the Rust convention. - All function arguments, except for scalars, are all passed by-reference.
- The most generic vector and matrix types are
`TMat`

and`TVec`

instead of`mat`

and`vec`

. - Some feature are not yet implemented and should be added in the future. In particular, no packing functions are available.
- A few features are not implemented and will never be. This includes functions related to color spaces, and closest points computations. Other crates should be used for those. For example, closest points computation can be handled by the ncollide project.

In addition, because Rust does not allows function overloading, all functions must be given a unique name.
Here are a few rules chosen arbitrarily for **nalgebra-glm**:

- Functions operating in 2d will usually end with the
`2d`

suffix, e.g.,`glm::rotade2d`

is for 2D while`glm::rotate`

is for 3D. - Functions operating on vector will often end with the
`_vec`

suffix, possibly followed by the dimension of vector, e.g.,`glm::rotate_vec2`

. Similar functions operating on scalar numbers only often end with the`_scalar`

suffix. - Every function related to quaternions start with the
`quat_`

prefix, e.g.,`glm::quat_dot(q1, q2)`

. - All the conversion functions have unique names as described below.

### #

Should I use nalgebra or nalgebra-glm?That depends on your tastes and your background. **nalgebra** is more powerful overall since it allows stronger typing,
and goes much further than simple computer graphics math. However, it has a bit of a learning curve for
those not used to the abstract mathematical concepts for transformations. **nalgebra-glm** however
have more straightforward functions and can benefit from the various tutorials already existing on the internet
for the original C++ GLM library.

Overall, if you are already used to the C++ GLM library, or to working with homogeneous coordinates (like 4x4
matrices for 3D transformations, or 3x3 matrices for 2D transformations), then you may enjoy **nalgebra-glm** more.
If on the other hand you prefer more rigorous treatments of transformations, with type-level restrictions, then go for **nalgebra**.
If you need dynamically-sized matrices, you should go for **nalgebra** as well.

##### info

Keep in mind that **nalgebra-glm** is just a different API for **nalgebra**! You can very well use both
and benefit from both their advantages: use **nalgebra-glm** when type-level restrictions are not important,
and **nalgebra** itself when you need more expressive types, and more powerful linear algebra operations like
matrix factorizations and slicing. Remember that all the **nalgebra-glm** types are just aliases to **nalgebra** types,
and keep in mind it is possible to convert, e.g., an `Isometry3`

to a `Mat4`

and vice-versa (see the conversions section).

# #

Features overview**nalgebra-glm** supports most linear-algebra related features of the C++ GLM library. You may find their exhaustive list
on the rustdoc-generated documentation. Mathematically
speaking, **nalgebra-glm** supports all the common transformations like rotations, translations, scaling, shearing,
and projections but operating in homogeneous coordinates. This means all the 2D transformations are
expressed as 3x3 matrices, and all the 3D transformations as 4x4 matrices. This is less computationally-efficient
and memory-efficient than nalgebra's transformation types,
but this has the benefit of being simpler to use.

### #

Vector and matrix constructionVectors, matrices, and quaternions can be constructed using several approaches:

- Using functions with the same name as their type in lower-case. For example
`glm::vec3(x, y, z)`

creates a 3D vector. - Using the
`::new`

constructor. For example`Vec3::new(x, y, z)`

creates a 3D vector. - Using the functions prefixed by
`make_`

to build a vector a matrix from a slice. For example`glm::make_vec3(&[x, y, z])`

will create a 3D vector. - Using a geometric construction function. For example
`glm::rotation(angle, axis)`

will build a 4x4 homogeneous rotation matrix from an angle (in radians) and an axis. - Using swizzling and conversions as described in the next sections.

##### caution

Keep in mind that matrices are laid out in column-major order in memory. Thus, constructing a matrix from a slice
with the `glm::make_`

functions requires the components to be arranged in column-major order too.

### #

SwizzlingVector swizzling is a native feature of **nalgebra** itself. Therefore, you can use it with all
the vectors of **nalgebra-glm** as well. Swizzling is supported as methods and works only up to
dimension 3, i.e., you can only refer to the components `x`

, `y`

and `z`

and can only create a
2D or 3D vector using this technique. Here is some examples, assuming `v`

is a vector with float
components here:

`v.xx()`

is equivalent to`glm::vec2(v.x, v.x)`

and to`Vec2::new(v.x, v.x)`

.`v.zx()`

is equivalent to`glm::vec2(v.z, v.x)`

and to`Vec2::new(v.z, v.x)`

.`v.yxz()`

is equivalent to`glm::vec3(v.y, v.x, v.z)`

and to`Vec3::new(v.y, v.x, v.z)`

.`v.zzy()`

is equivalent to`glm::vec3(v.z, v.z, v.y)`

and to`Vec3::new(v.z, v.z, v.y)`

.

##### info

Any combination of two or three components picked among `x`

, `y`

, and `z`

will work. The possibility to manipulate
the `w`

components as well will be added in the future.

### #

ConversionsIt is often useful to convert one algebraic type to another. The two main approaches for conversions in `nalgebra-glm`

are:

- Functions with the form
`glm::type1_to_type2`

in order to convert an instance of`type1`

into an instance of`type2`

. For example`glm::mat3_to_mat4(m)`

will convert the 3x3 matrix`m`

into a 4x4 matrix by appending one column on its right and one row on its bottom. Diagonal elements added this way are set to`1`

. - Using one of the
`glm::convert`

,`glm::try_convert`

, or`glm::convert_unchecked`

functions. These functions are directly re-exported from**nalgebra**and are extremely versatile as described below.

The `glm::convert`

function can convert any type into another algebraic type which equivalent but more general. For example,
`let mat: Mat4 = glm::convert(isometry)`

will convert an `Isometry3`

(from the **nalgebra** crate) to a 4x4 matrix.
This will also convert scalar types, therefore the following works:

However, conversion will not work the other way round: you can't convert a `Matrix4`

to an `Isometry3`

using `glm::convert`

because that could cause unexpected results if the matrix does not complies to the requirements of the isometry.
If you need this kind of conversions anyway, you can use `glm::try_convert`

which tests if the object being converted complies
with the algebraic requirements of the target type. This will return `None`

if the requirements are not satisfied.

##### caution

The `convert_unchecked`

will ignore those tests and always perform the conversion, even if that breaks the invariants of the target type.
This must be used with care! This is actually the recommended method to convert between homogeneous transformations generated by `nalgebra-glm`

and
specific transformation types from **nalgebra** like `Isometry3`

. Just be careful you know your conversions make sense.