I have a series of 'images' described by a mixture of connected lines and curves. Users will draw on the screen, free hand, and my goal is to break their drawing down into a series of lines and curves that can be matched with the 'images' in my set.

For the sake of simplicity, let's assume this is occurring on a touch screen. These lines will be connected. Each time the user's finger moves, the dx and dy is recorded. The drawing is considered complete and analyzed when the user's finger leaves the screen.

I'm having trouble figuring out a good way to break the user's drawing down into lines. Is there any well known approach to this problem, a C++ library that solves it, or any good articles/technical papers on how to achieve this?