Mathematics is the 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 modern 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 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 OpenGL Mathematics (GLM), written by Christophe Riccio. Its design is based on the GLSL specification, so the syntax will be familiar to anyone using GLSL. Additionally, it provides extensions that include functionality similar to some of the much-missed OpenGL utility functions, such as glOrtho, glRotate, or gluLookAt.
Since GLM is a header-only library, the 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, include the core header file, and headers for any extensions. For this example, we'll include the matrix transform extension:
#include <glm/glm.hpp> #include <glm/gtc/matrix_transform.hpp>
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(0.0f, 0.0f, 5.0f),
glm::vec3(0.0f, 0.0f, 0.0f),
glm::vec3(0.0f, 1.0f, 0.0f)
);
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 vec4 (a four-component vector), which represents 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 toward the origin, with the up direction in the direction of the positive y axis. We then go on to create the model matrix by first storing the identity matrix in the modelvariable (via the single-argument constructor), and multiplying it 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 model-view matrix (mv) by multiplying the view and model variables, and then use the combined matrix to transform the position. Note that the multiplication operator has been overloaded to behave in the expected way.
Note
The order is important here. Typically, the model matrix represents a transformation from object space to world space, and the view matrix is a transformation from world space to camera space. So to get a single matrix that transforms from object space to camera space, we want the model matrix to apply first. Therefore, the model matrix is multiplied on the right-hand side of the view matrix.
It is not recommended to import all of the GLM namespaces 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 with the using statements 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 v suffix). For example, to pass 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]);
Alternatively, rather than using the ampersand operator, we can use the glm::value_ptr function to get a pointer to the content of the GLM type:
glUniformMatrix4fv(location, 1, GL_FALSE, glm::value_ptr(proj));
The latter version requires including the header file glm/gtc/type_ptr.hpp. The use of value_ptr is arguably cleaner, and works for any GLM type.
- 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