Each year the author has begun an introductory class in computer graphics with the following problem:

Take a piece of graph paper, and select any two squares. Design an algorithm to fill in intervening squares in such a way that the filled squares give the best possible approximation to a straight line joining the two squares.

Rarely do introductory classes begin at such an elementary level -- most classes (and consequently most students) begin with the presumption that the computer "knows" how to draw a straight line, and that the problem in computer graphics is to build up from that point. This paper argues that this elementary problem is very powerful in a variety of ways:

1. It helps to introduce the concept of algorithms.
2. It familiarizes the student with the nature of the discrete space in which computation and graphics occur.
3. Many different algorithms can solve this problem, and after struggling hopefully to discover or invent one, students are afforded the opportunity to compare many solutions from the point of view of efficiency, clarity, generality, etc. Many solutions are characteristic of broad classes of algorithms (e.g. "Divide and Conquer").
4. After considering the strengths and weak nesses of different algorithms, two algorithms which result in identical implementations but have different derivations, Bresenham's and Weiman's, are examined. The derivation of Bresenham's is algebraic, while Weiman's is combinatorial. The students are shown that the combinatoric approach leads to a great many generalizations which are applicable to other, often radically different, problems in computer graphics.

Not surprisingly, students often think of this problem as trivial until they try it. Even when they appreciate the difficulty involved in deriving a good algorithm, they presume it is an "academic" exercise which once they complete they will never use again and which they can replace with canned versions. To emphasize its ongoing utility, the students are then required to use the algorithms to animate objects, to move through RGB color space, to rotate and scale images, and to complete a variety of other operations not generally available in graphics packages.