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Linear algebra library for the Rust programming language.

lib.rs:

nalgebra-glm − nalgebra in easy mode

nalgebra-glm 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 aliases of types from nalgebra. Therefore there is a complete and seamless inter-operability between both.

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 = "0.3"

Then, you should 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;

Features overview

nalgebra-glm supports most linear-algebra related features of the C++ GLM library. Mathematically speaking, it 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.

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::rotate2d() is for 2D while glm::rotate() is for 3D.
• Functions operating on vectors will often end with the _vec suffix, possibly followed by the dimension of vector, e.g., glm::rotate_vec2().
• 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.

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) will create a 3D vector.
• Using the ::new constructor. For example Vec3::new(x, y, z) will create 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. Keep in mind that constructing a matrix using this type of functions require its components to be arranged in column-major order on the slice.
• 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.

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).

Any combination of two or three components picked among x, y, and z will work.

Conversions

It is often useful to convert one algebraic type to another. There are two main approaches for converting between types in nalgebra-glm:

• Using function with the form 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 to a 4x4 matrix by appending one column on the right and one row on the left. Those now row and columns are filled with 0 except for the diagonal element which is set to 1.
• Using one of the convert, try_convert, or convert_unchecked functions. These functions are directly re-exported from nalgebra and are extremely versatile:

1. The convert function can convert any type (especially geometric types from nalgebra like Isometry3) into another algebraic type which is equivalent but more general. For example, let sim: Similarity3<_> = na::convert(isometry) will convert an Isometry3 into a Similarity3. In addition, let mat: Mat4 = glm::convert(isometry) will convert an Isometry3 to a 4x4 matrix. This will also convert the scalar types, therefore: let mat: DMat4 = glm::convert(m) where m: Mat4 will work. 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.
2. If you need this kind of conversions anyway, you can use try_convert which will test if the object being converted complies with the algebraic requirements of the target type. This will return None if the requirements are not satisfied.
3. 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.

Should I use nalgebra or nalgebra-glm?

Well 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, 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 benefit from the various tutorials 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 4D matrices for 3D transformations), then you will have more success with nalgebra-glm. 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.

Keep in mind that nalgebra-glm is just a different API for nalgebra. So you can very well use both and benefit from both their advantages: use nalgebra-glm when mathematical rigor is not that important, and nalgebra itself when you need more expressive types, and more powerful linear algebra operations like matrix factorizations and slicing. Just 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).