1. 3D Computer Graphics (3080/GV10) Week 5-6 Tutorial 3
Andrew Cox

2. OpenGL Transformation Pipeline
ModelView Matrix
Camera Space
Projection Matrix
Object Space
Homogeneous Clip Space
Perspective Divide
Normalized Device
Coordinates
Viewport Transform
Viewport
Coordinates
Slide adapted from Eric Lengyel [1]

3. OpenGL Perspective Projection Matrix
n, f = distances to near, far planes
e = focal length = 1 / tan(FOV / 2)
a = viewport height / width
Picks up viewspace z and places negated in w: division by Z gives perspective
Slide adapted from Eric Lengyel [1]

4. Slide courtesy of Eric Lengyel [1]

5. Matrix Multiplication and Concatenation

6. Order of OpenGL Transformations
OpenGL calls define a matrix, then concatenate it with existing one
Transformations applied in reverse of lexical program order

7. Matrix Modes GL tracks two matrix stacks
Projection
ModelView
The matrix applied to vertices is
The matrix commands apply to the current mode:
glMatrixMode(GL_PROJECTION);
glMatrixMode(GL_MODELVIEW);

8. glLoadIdentity()
Matrix commands are concatenated with matrix of current mode
Includes gluPerspective () etc.
Clear out current matrix with glLoadIdentity()

9. References
Eric Lengyel, Projection Matrix Tricks, Game Developers Conference 2007, <