We present a method for direction field design on surface and volumetric meshes supporting non-orthogonality. Our approach is a generalization of the representation of 3D cross fields in spherical harmonic basis. As such it induces a geometrically meaningful measure of smoothness, allows orthogonality control by a simple parameter and enables orientation constraints of a single direction. To the best of our knowledge this is the first work to propose non-orthogonal 3D frame field design. We demonstrate the applicability of our method to generate anisotropic quadrangular and hexahedral meshes which are particularly useful for remeshing CAD models.

中文翻译：

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设计 2D 和 3D 非正交框架场

我们提出了一种在支持非正交性的表面和体积网格上进行方向场设计的方法。我们的方法是在球谐基础上对 3D 交叉场表示的概括。因此，它引入了几何上有意义的平滑度测量，允许通过简单参数进行正交控制，并实现单个方向的定向约束。据我们所知，这是第一个提出非正交 3D 帧场设计的工作。我们证明了我们的方法在生成各向异性四边形和六面体网格方面的适用性，这对于重新划分 CAD 模型特别有用。