Programming Interviews Exposed: Secrets to Landing Your Next Job, 3rd Edition

Graphics Problems

Graphics problems typically focus on your ability to implement primitive graphics functions rather than using a high-level API as you would in most programming projects.

Eighth of a Circle

PROBLEM Write a function that draws the upper-eighth of a circle centered at (0, 0) with a given radius, where the upper-eighth is defined as the portion starting at 12 and going to 1:30 on a clock face. Use the following prototype:

void drawEighthOfCircle( int radius );

The coordinate system and an example of what you are to draw are shown in Figure 13-1. You can use a function with the following prototype to draw pixels:

void setPixel( int xCoord, int yCoord );

Figure 13-1

This problem is not as contrived as it seems. If you were trying to implement a full-circle drawing routine, you would want to do as little calculation as possible to maintain optimum performance. Given the pixels for one-eighth of a circle, you can easily determine the pixels for the remainder of the circle from symmetry.

NOTE If a point (x, y) is on a circle, so are the points (–x, y), (x, –y), (–x, –y), (y, x), (–y, x), (y, –x), and (–y, –x).

This problem is an example of a scan conversion, converting a geometric drawing to a pixel-based raster image. You need an equation for a circle before you can calculate anything. The common mathematical function that produces a circle is: