gTangle: a Grammar for the Procedural Generation of Tangle Patterns

摘要

Tangles are a form of structured pen-and-ink 2D art characterizedrnby repeating, recursive patterns. We present a method to procedurallyrngenerate tangle drawings, seen as recursively split sets of arbitraryrn2D polygons with holes, with anisotropic and non-stationaryrnfeatures. We formally model tangles with group grammars, an extensionrnof set grammars, that explicitly handles the grouping ofrnshapes necessary to represent tangle repetitions. We introduce arnsmall set of expressive geometric and grouping operators, showingrnthat they can respectively express complex tangles patterns andrnsub-pattern distributions, with relatively simple grammars. We alsornshow how users can control tangle generation in an interactive andrnintuitive way. Throughout the paper, we show how group grammarsrncan, in few tens of seconds, produce a wide variety of patterns thatrnwould take artists hours of tedious and time-consuming work. Wernthen validated both the quality of the generated tangles and the efficiencyrnof the control provided to the users with a user study, runrnwith both expert and non-expert users.