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Configurable Math Library (CML)

This is a free library designed for games, graphics, and computational geometry applications. Listed features include:

  • Vector, matrix, and quarternion classes
  • Templated headers so can be used for arbitrary types
  • Arbitrary sized vectors and matrices (fixed or dynamically resizable)
  • Conversions between polar, cylindrical, spherical, and Cartesian coordinates
  • A large library of functions for the construction and manipulation of transforms in 2D and 3D

CML's design notes state that it is meant to be cross-platform and portable and therefore doesn't contain any platform specific optimisations, but it is possible to include them in the future if there is specific interest.

There's only one header file to include, cml/cml.h.

CML contains quite a nice way of creating an abstraction layer between existing math library objects and CML objects, allowing the use of other math library data types in CML library functions. See here.

CML only has a few examples. Hasn't been updated in a while. Contains useful functions for working with OpenGL or DirectX though, including replacements for things like gluLookAt().

CML is released under the Boost Software License. This means that you're allowed to use and profit from the library as long as when distributing CML or any modifications you have made to CML, you keep the Boost Software License text in each file.

Eigen

This library has by far the most detailed and descriptive tutorial section with many code samples. It is also worth noting that it seems to be the most frequently updated and the most up-to-date (at the time of writing the most recent release, 3.0.4, was 3.5 weeks ago).

Like GLM, it is very easy to pass the class objects directly to OpenGL, although in Eigen this is performed by an unsupported OpenGL module which provides a few functions such as glTranslate and glRotate.

// You need to add path_to_eigen/unsupported to your include path.
#include <Eigen/OpenGLSupport>
// ...
Vector3f x, y; Matrix3f rot;
glVertex(y + x * rot);

Quaternion q;
glRotate(q);

Provides a large number of array, matrix, and vector types with many operators.

Eigen is licensed under the LGPL which is quite restrictive and usually would exclude a library based on my requirements. However, Eigen has a large Licensing FAQ which tries to answer any licensing questions people might have. Their main point is that as Eigen is a header only library, it does not count as a "Combined Work" under the LGPL it can be therefore used entirely under Section 3. This states that to use Eigen you must:

  • Give prominent notice with each copy of the object code that the Library is used in it and that the Library and its use are covered by this License. The Eigen FAQ states that 'the bottom of a README file or of a website would be prominent enough for us'.
  • Accompany the object code with a copy of the GNU GPL and this license document.

This assumes that you're using Eigen unmodified. If you are planning to make changes to Eigen and release it, then you must also make the modifications available under the LGPL.

OpenGL Math Library (GLM)

GLM's main design to be very familiar to those who know GLSL as it uses classes and functions that use the GLSL naming conventions. It also seems to provide all of the functionality that I might need in the future.

Includes several code samples, more than CML. Many more located in the manual.

Includes features such as:

  • Math for splines
  • Math for colour spaces
  • Random numbers
  • Simplex noise generation
  • Conversion of Euler angles

There's only one header file to include, glm/glm.hpp. glm/ext.hpp can be included to add extended features (non GLSL features).

The design choice to follow GLSL conventions allows the library to be intuitive and easy to use, especially given that data alignment is compatible with gl functions. E.g:

glm::vec4 v(0);
glm::mat4 m(0);
glVertex3fv(glm::value_ptr(v))
glLoadMatrixfv(glm::value_ptr(m));

The manual pdf file link is broken but a slightly out of date version can be found here. I've sent the maintainer an email and hopefully this will be fixed shortly.

GLM is licensed under the MIT License (Expat License) which is very permissive and means GLM is a good candidate for any project requiring a math library.