Projections

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

Projection Mathematics y d Image Plane z x

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

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.)

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.

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

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.

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