The new area of discrete differential geometry is solving problems in computer graphics, such as creating more lifelike hair in animation. I became aware of this from an article in the New York Times (see http://www.nytimes.com/2010/12/30/movies/30animate.html). An excerpt: "... the images on screen are not the result of a patchwork of technical tricks, but of precise mathematical equations based on the way the world actually looks and operates — in a word, physics. They use what is known as discrete differential geometry, a field so new that the first textbook on the subject was published only two years ago.ago. [...] The uses of discrete differential geometry go far beyond animation. Johns Hopkins Medical Center, for instance, is using Mr. Grinspun’s computer simulations to predict how needles move through human flesh, so that doctors can train to do laparoscopic surgery on virtual bodies instead of the real thing."
Here is a link to a book: http://www.amazon.com/Discrete-Differential-Geometry-Graduate-Mathematics/dp/0821847007.