Discovery Helps Computers Draw Intricate Two-Dimensional Animations

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A new algorithm solves the long-standing “hidden line problem” of computer graphics

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Nearly 60 years ago computer scientist Ruth Weiss of Bell Labs published a pioneering algorithm to turn three-dimensional objects into two-dimensional drawings from any angle. But she ran into a problem with depicting outlines—an issue that has remained a computational geometry riddle for decades. With the ubiquity of computer animation today, this “hidden line problem” is now even more pressing.

It has proved impossible to generate a triangle mesh fine enough to avoid every error of this kind. As Meta Reality Labs researcher Stéphane Grabli, an Oscar nominee for visual effects, explains, “The feeling was that with enough subdivision, it should be possible to create a mesh that allows exact visibility computation for these contours. This turned out to be wrong.” The resulting errors limit the complexity of nonphotorealistic illustration styles, Grabli adds.

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