1. Projections

2. Learning Objectives Understand how projection transforms work
Understand how clipping works
Understand how a z-buffer operates
Be able to describe the rendering process from vectors to pictures on the screen

3. Projection Mathematicsy d
Image
Plane z x

4. The Math
(x,y,z)
[x/(z/d), y/(z/d), z/(z/d)]

5. Clipping
Sometimes objects are larger than, or outside of the region in the viewing frustum.
Sometimes objects are closer or farther away than you want to view them.
Objects outside the edges are easily recognized after projected to the image plane (i.e., if x < -1, y>+1, etc.)

6. The Z-Buffer
All the useful imaging information is in the x and y coordinates after the image transformation. What can you do with the z coordinate?
The z coordinate can be used to determine the relative depth (z/d) of the objects in space. This allows you to find out which objects are in front of other objects.

7. For Example
Z/d is big for
These points
Z/d is small
For these
points

8. The Rendering Process
Transform the viewed geometry so you are looking down the z axis (or negative z axis on some systems). Sometimes this is two transformations – the model and the viewing position
Define the projection transformation (specify the image plane distance, near and far clipping).
Project the points into the viewing plane and clip the ones that are outside the field of view.
Fill in the z-buffer and draw things that have a smaller z-buffer value than whatever was there previously.

9. Learning Objectives Understand how projection transforms work
Understand how clipping works
Understand how a z-buffer operates
Be able to describe the rendering process from vectors to pictures on the screen