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# Chapter 9. Areas

Modern calculus has its origin in two old mathematical problems: find a line tangent to a given curve, and find the area enclosed by a given curve. The first problem was solved by differential calculus, the second by integral calculus. In the Windows graphics API, line and curve API handles layering pixels along lines and curves; area-filling API handles painting the areas enclosed by closed figures formed by lines and curves.

We discussed line and curve drawing in great depth in the last chapter. In this chapter, we're moving up a grade to explore a new dimension: area filling. More specifically, we're going to examine the basic tools in area fill: brushes; basic data structures: rectangles and regions; common shapes: rectangles, ...

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