Working with the Model Matrix

The model matrix is the accumulation of the multiplications of the transformation matrices that are to be applied to a point or vector. As we discovered in Chapter 13, Understanding the Importance of Matrices, the order in which the transformations are multiplied is important to the final outcome. Also, at the end of the same chapter, you discovered that in OpenGL, you can obtain the contents of the modelview matrix with the following code:

glGetDoublev(GL_MODELVIEW_MATRIX)

Rather than using OpenGL’s own methods for moving, resizing, and orienting an object, you can set the matrix manually, and then perform matrix multiplication to apply the transformation to a model as long as you keep in mind the format of the modelview matrix.

These transformations were performed in Chapter 13, Understanding the Importance of Matrices:

glTranslatef(0, 0, -3)
glRotated(45, 1, 0, 0)
glScalef(0.5, 2, 1)

The result of performing these transformations...