ScienceDaily (Apr. 14, 2010) — Whether it's an exploding fireball in "Star Wars: Episode 3," a swirling maelstrom in "Pirates of the Caribbean: At World's End," or beguiling rats turning out gourmet food in "Ratatouille," computer-generated effects have opened a whole new world of enchantment in cinema. All such effects are ultimately grounded in mathematics, which provides a critical translation from the physical world to computer simulations.Mathematics provides the language for expressing physical phenomena and their interactions, often in the form of partial differential equations. These equations are usually too complex to be solved exactly, so mathematicians have developed numerical methods and algorithms that can be implemented on computers to obtain approximate solutions. The kinds of approximations needed to, for example, simulate a firestorm, were in the past computationally intractable. With faster computing equipment and more-efficient architectures, such simulations are feasible today -- and they drive many of the most spectacular feats in the visual effects industry.
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