Hair Modeling

The modeling of fiber patterns, including those of hair, grass and fur, is recurrent in the Computer Graphics literature. The reproduction of the extensive variety of fiber arrangements, and their generation from scarce information, remains a challenge for computational fiber models. This project introduces a novel mathematical representation of fibers based on a class of minimal surfaces called generalized helicoids, characterized by intuitive parameters that control the curvature of a fiber along its tangent, normal and binormal directions, and its elevation angle. This representation equips a fiber with information not only about its own geometry but also about the geometric behavior of other fibers in its vicinity. An implicit surface sampling method based on interacting particles is used for determining fiber root locations. Algorithms for interpolating generalized helicoids from sparse fiber samples are introduced as well as a fitting algorithm for modeling fiber datasets of arbitrary origin. The usefulness of the generalized helicoid is motivated via several applications including the generation of different types of hair geometry, hair interpolation, hair fitting and wisp generation.

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