Transformation

Eye Coordinates
Eye coordinates are from your viewpoint, regardless of any transformation. It is the absolute screen coordinates. It represents a virtual fixed coordiante system that is used as a common frame of reference. In the abscence of any transformation, the observer (us) will look towards the -z (perpendicular to the monitor).

Modelview Transformation

glMatrixMode(GL_MODELVIEW);

The Modelview transformation allows us to translate, rotate and scale our objects. The coordinates of the modelview transformation (using functions such as glTranslate, glRotatef, glScalef) are in reference to the Projection matrix (GL_PROJECTION)

The modelview transformationBy default the point of observation in a perspective projection is at the origin (0, 0, 0) looking down toward the negative z-axis (“into the monitor”). The modelview transformation allows us to place our objects, rotate and scale them. New transformations are performed with respect to the last transformation.

Projection Transformation

glMatrixMode(GL_PROJECTION);

This projection defines the viewing volumne and establishes clipping planes. Clipping planes are plane equations in 3D space that openGL uses to determine whether geometry can be seen by the viewer.

There are two types of projections: orthographic (using glOrtho) and perspective (using gluPerspective) .

Orthograhpic
All the polygons are drawn onscreen with exactly the relative dimensions specified. No matter how far they are, lines and polygons are mapped directly to the 2D screen using parallel lines.

Perspective
Shows scenes more as they appear in real life. It makes distant objects appear smaller than nearby objects of the same size. (Using railroad tracks for example, they are parallel using orthographic projection but converges to a point using perspective.)

Viewport Transformation
This is the final transformation that maps all the 3D objects to 2D screen pixels.

You use the function glViewport to do that transformation.