Cyclic twill-woven objects

Classical (or biaxial) twill is a textile weave in which the weft threads pass over and under two or more warp threads, with an offset between adjacent weft threads to give an appearance of diagonal lines. This paper introduces a theoretical framework for constructing twill-woven objects, i.e., cyclic twill-weavings on arbitrary surfaces, and it provides methods to convert polygonal meshes into twill-woven objects. It also develops a general technique to obtain exact triaxial-woven objects from an arbitrary polygonal mesh surface.

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► We develop a theoretical framework for constructing twill-woven objects.
► We provide methods to convert polygonal meshes into twill-woven objects.
► We develop methods to obtain exact and approximate biaxial twill-woven objects.
► We obtain characteristic diagonal pattern of classical twill weaving for biaxial cases.
► We introduce and obtain exact triaxial twill-woven objects from triangular meshes.