geoTangle : Interactive Design of Geodesic Tangle Patterns on Surfaces

Abstract

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.

MoMaS: Mold Manifold Simulation for real‐time procedural texturing

“…For many applications, such as landscape generation or tile synthesis, procedural texturing has become very useful and effective [MSC12, Ols04, LN03, Par14]. Nevertheless, most of the literature is devoted to the generation of complex textures on planar domains, and only a few works deal with general manifold meshes [NPP21, MNPP21, FPSG21]. The ability to generate a broader range of complex patterns that follow the shape of a mesh is of fundamental importance in generating a large variety of contents.…”

“…The only few exceptions are simulation based approaches [Tur91, Sta03], which makes them similar in spirit to our method. Only recently, some works have shown procedural generation of complex patterns directly on surfaces [NPP21, FPSG21], but these works are limited to recursive structures or repetitive patterns and do not explore other possibilities. Another work following a similar fashion is [MNPP21], where the authors propose a method for drawing Bézier curves on manifold meshes.…”