Tangles are complex patterns, which are often used to decorate the surface of real-world artisanal objects. They consist of arrangements of simple shapes organized into nested hierarchies, obtained by recursively splitting regions to add progressively finer details. In this article, we show that 3D digital shapes can be decorated with tangles by working interactively in the intrinsic metric of the surface. Our tangles are generated by the recursive application of only four operators, which are derived from tracing the isolines or the integral curves of geodesics fields generated from selected seeds on the surface. Based on this formulation, we present an interactive application that lets designers model complex recursive patterns directly on the object surface without relying on parametrization. We reach interactive speed on meshes of a few million triangles by relying on an efficient approximate graph-based geodesic solver.

中文翻译：

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geoTangle : 表面上测地线缠结图案的交互设计

缠结是复杂的图案，通常用于装饰现实世界的手工物品的表面。它们由组织成嵌套层次结构的简单形状的排列组成，通过递归分割区域以逐步添加更精细的细节来获得。在本文中，我们展示了 3D 数字形状可以通过在表面的内在度量中交互工作来装饰缠结。我们的缠结是由仅四个运算符的递归应用生成的，这些运算符是通过跟踪表面上选定种子生成的测地线场的等值线或积分曲线得出的。基于这个公式，我们提出了一个交互式应用程序，让设计人员可以直接在对象表面上对复杂的递归模式进行建模，而无需依赖参数化。