Braiding Hair by Braid Theory

In this paper, we propose a system based on braid theory that help users to generate customized hair braiding, which is a function that is lacking in most existing hair design software. Our user interface for braid design is built upon braid theory, which is a subarea of knot theory in mathematics. The user designs braid patterns using braid index, and specifies the amount of hair for each braid as well as the area over the head where the braid is to be made. Then, the system automatically braids the hair of the character and generates a realistic image of the designed hair style. Theoretically, our system can produce arbitrary kinds of braids. Our system can also judge if two braids are equivalent or not by making use of the transition rules of braid index, which helps to register designed braids to the database. The system is implemented as a Maya plugin, and can be combinedly used with various functions including physical simulation, hair rendering and hair texturing. Our user study shows that our toolkit is easy-to-use for novice users as well as experienced users.