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

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?

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)

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

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)

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

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