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