Motivated by the emergence of rough surfaces in various areas of design, we address the computational design of triangle meshes with controlled roughness. Our focus lies on small levels of roughness. There, roughness or smoothness mainly arises through the local positioning of the mesh edges and faces with respect to the curvature behavior of the reference surface. The analysis of this interaction between curvature and roughness is simplified by a 2D dual diagram and its generation within so-called isotropic geometry, which may be seen as a structure-preserving simplification of Euclidean geometry. Isotropic dihedral angles of the mesh are close to the Euclidean angles and appear as Euclidean edge lengths in the dual diagram, which also serves as a tool for visualization and interactive local design. We present a computational framework that includes appearance-aware remeshing, optimization-based automatic roughening, and control of dihedral angles.

中文翻译：

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设计具有受控粗糙度的三角形网格


在各个设计领域出现粗糙表面的推动下，我们解决了具有受控粗糙度的三角形网格的计算设计问题。我们的重点在于小程度的粗糙度。在那里，粗糙度或平滑度主要通过网格边和面相对于参考曲面曲率行为的局部定位而产生。曲率和粗糙度之间这种相互作用的分析通过二维对偶图及其在所谓的各向同性几何中生成来简化，这可以被视为欧几里得几何的结构保持简化。网格的各向同性二面角接近欧几里得角，在对偶图中显示为欧几里得边长，该对偶图也用作可视化和交互式局部设计的工具。我们提出了一个计算框架，其中包括外观感知的重新网格划分、基于优化的自动粗化和二面角控制。