1. CS 450: Computer Graphics PIXEL AdDRESSING AND OBJECT GEOMETRY
Spring 2015
Dr. Michael J. Reale

2. PIXELS AND COORDINATES
So far, we’ve been talking about coordinates and locations on the screen using the mathematical definition
Point = infinitely small location in space
Pixels, however, actually do take up space
So, given a coordinate (x,y), how do we interpret it? Which pixel do we fill in?

3. COORDINATE = LOWER-lEFT CORNER OF PIXEL
If we treat a coordinate as the lower-left coordinate of a pixel, then a point plotted at (2,3) would look like this:
The true center of the pixel is, in fact, at (2.5, 3.5)

4. COORDINATE = LOWER-lEFT CORNER OF PIXEL
Advantages:
Allows for precise object representations
Avoids half-integer pixel boundaries
Simplifies many scan-conversion algorithms and other raster procedures

5. PROBLEM: TRUE GEOMETRIC SIZE
Because pixels have size, it means that we run into some problems when we draw lines and shapes
For example, if we blindly draw a line from (0,0) to (2,0):
Our line is actually 3 pixels wide!
Solution: don’t draw the last pixel  only draw pixels “inside” coordinates (0,0) to (2,0)

6. PROBLEM: TRUE GEOMETRIC SIZE
We have a similar issue with shapes like squares and rectangles
Example: rectangle from (0,0) to (4,3)
Solution: plot pixels “interior” to object boundaries

7. PROBLEM: OTHER CURVES/SHAPES
Again, same issue with circles and ellipses (otherwise, radius is too big)
Solution: shorten by 1 in x and/or y for appropriate octants