# nalgebra-glm, an easy mode for nalgebra§

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 started§

First 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:

[dependencies]
nalgebra-glm = "0.1"

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(...):

extern crate nalgebra_glm as glm;

### Main differences compared to GLM§

While 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.

Note

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 construction§

Vectors, 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.

Warning

Keep in mind that matrices are laid out in column-major order in merory. Thus, constructing a matrix from a slice with the glm::make_ functions requires the components to be arranged in column-major order too.

### Swizzling§

Vector 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).

Note

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.

### Conversions§

It 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:

let m = Mat4::identity(); // 4x4 matrix with f32 elements.
let mat: DMat4 = glm::convert(m);  // 4x4 matrix with f64 elements. 

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.

Warning

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.