Mathematics is core to all of computer graphics. In earlier versions, OpenGL provided support for managing coordinate transformations and projections using the standard matrix stacks (`GL_MODELVIEW`

and `GL_PROJECTION`

). In recent versions of core OpenGL however, all of the functionality supporting the matrix stacks has been removed. Therefore, it is up to us to provide our own support for the usual transformation and projection matrices, and then to pass them into our shaders. Of course, we could write our own matrix and vector classes to manage this, but some might prefer to use a ready-made, robust library.

One such library is **GLM** (**OpenGL Mathematics**) written by *Christophe Riccio*. Its design is based on the GLSL specification, so the syntax is very similar to the mathematical support in GLSL. For experienced GLSL programmers, this makes GLM very easy to use and familiar. Additionally, it provides extensions that include functionality similar to some of the much-missed OpenGL functions such as `glOrtho`

, `glRotate`

, or `gluLookAt`

.

Since GLM is a header-only library, installation is simple. Download the latest GLM distribution from http://glm.g-truc.net. Then, unzip the archive file, and copy the `glm`

directory contained inside to anywhere in your compiler's include path.

To use the GLM libraries, it is simply a matter of including the core header file, and headers for any extensions. For this example, we'll include the matrix transform extension as follows:

#include <glm/glm.hpp> #include <glm/gtc/matrix_transform.hpp>

Then the GLM classes are available in the `glm`

namespace. The following is an example of how you might go about making use of some of them:

glm::vec4 position = glm::vec4( 1.0f, 0.0f, 0.0f, 1.0f ); glm::mat4 view = glm::lookAt( glm::vec3(0.0,0.0,5.0),glm::vec3(0.0,0.0,0.0),glm::vec3(0.0,1.0,0.0) ); glm::mat4 model(1.0f); // The identity matrix model = glm::rotate( model, 90.0f, glm::vec3(0.0f,1.0f,0.0) ); glm::mat4 mv = view * model; glm::vec4 transformed = mv * position;

The GLM library is a header-only library. All of the implementation is included within the header files. It doesn't require separate compilation and you don't need to link your program to it. Just placing the header files in your include path is all that's required!

The previous example first creates a `vec4`

(four coordinate vector) representing a position. Then it creates a 4 x 4 view matrix by using the `glm::lookAt `

function. This works in a similar fashion to the old `gluLookAt`

function. Here, we set the camera's location at (0, 0, 5), looking towards the origin, with the "up" direction in the direction of the y-axis. We then go on to create the model matrix by first storing the identity matrix in the variable `model`

(via the single argument constructor), and multiplying by a rotation matrix using the `glm::rotate`

function. The multiplication here is implicitly done by the `glm::rotate`

function. It multiplies its first parameter by the rotation matrix (on the right) that is generated by the function. The second parameter is the angle of rotation (in degrees), and the third parameter is the axis of rotation. Since before this statement, `model`

is the identity matrix, the net result is that `model`

becomes a rotation matrix of 90 degrees around the y-axis.

Finally, we create our modelview matrix (`mv`

) by multiplying the `view`

and `model`

variables, and then using the combined matrix to transform the position. Note that the multiplication operator has been overloaded to behave in the expected way.

It is not recommended to import all of the GLM namespace by using the following command:

using namespace glm;

This will most likely cause a number of namespace clashes. Instead, it is preferable to import symbols one at a time, as needed. For example:

#include <glm/glm.hpp> using glm::vec3; using glm::mat4;

GLM supports directly passing a GLM type to OpenGL using one of the OpenGL vector functions (with the suffix `v`

). For example, to pass a `mat4`

named `proj`

to OpenGL we can use the following code:

glm::mat4 proj = glm::perspective( viewAngle, aspect, nearDist, farDist ); glUniformMatrix4fv(location, 1, GL_FALSE, &proj[0][0]);

The Qt SDK includes many classes for vector/matrix mathematics, and is another good option if you're already using Qt

The GLM website http://glm.g-truc.net has additional documentation and examples