The ModelView Matrix

The modelView matrix defines the coordinate system that is used to place and orient objects. This 4x4 matrix can either transform vertices, or it can be transformed its-self by other matrices.

Before you can do anything, you must specify if you are going to be working with the modelView or projection matrix. You can do this with the GL.MatrixMode function. This is the signature:

void GL.MatrixMode(MatrixMode);

The MatrixMode enum has two values we use, but the enum its-self has 5 values

  • MatrixMode.Modelview
  • MatrixMode.Projection
  • MatrixMode.Color - we don't use this
  • MatrixMode.Texture - we don't use this
  • MatrixMode.Modelview0Ext

Usually (99% of the time) you want to set your modelView matrix to identity. So that you start around origin. you can achieve this by calling the GL.LoadIdentity function. This function loads the identity matrix into the OpenGL state machines active matrix. (You specified the active matrix with GL.MatrixMode)

This snippet resets the modelview matrix:

GL.LoadIdentity(); // Reset modelview matrix
// Do other transformation

Multiplying OpenGL matrices

We're about to talk about 3 functions:

  • GL.Translate
  • GL.Rotate
  • GL.Scale

Before we discuss how these functions work, i want you to be aware of what they actually do. When you call GL.MatrixMode with MatrixMode.Modelview as an argument, you select the modelView matrix of the OpenGL state machine as the active matrix.

Once you have a matrix set as the active matrix, all further matrix operations will be performed to that matrix. GL.LoadIdentity is one such operation. It takes the current matrix and sets it to identity.

The three functions above will generate an appropriate matrix and multiply the current matrix! GL.Rotate for instance will make a rotation matrix and multiply the current matrix by it.

The following OpenGL snippet

// Set the currently active matrix

// Reset modelview matrix

// Create a rotation matrix
// then multiply the active matrix by it
GL.Rotate(90.0f, 0.0f, 0.0f, 1.0f);

Is the equivalent of:

void Render(ref Matrix4 modelView, ref Matrix4 projection) {
    // Set the currently active matrix
    Matrix4 currentMatrix = modelView;

    // Reset modelview matrix
    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < 4; ++j) {
            currentMatrix[i, j] = (i == j)? 1.0f : 0.0f;

    // Create a rotation matrix
    Matrix4 rotation = Matrix4.AngleAxis(90.0f, 0.0f, 0.0f, 1.0f);

    // then multiply the active matrix by it
    currentMatrix = rotation * currentMatrix;

OpenGL just wraps all the math up for you. But the following function create and multiply matrices for you!

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