We introduce a construction of subspaces of the spaces of tangential vector, n‐vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangential fields. Important features of our construction are that it is based on a general principle, from which constructions for different types of tangential fields can be derived, and that it is scalable, making it possible to efficiently compute and store large subspace bases for large meshes. Moreover, the construction is adaptive, which allows for controlling the distribution of the degrees of freedom of the subspaces over the surface. We evaluate our construction in several experiments addressing approximation quality, scalability, adaptivity, computation times and memory requirements. Our design choices are justified by comparing our construction to possible alternatives. Finally, we discuss examples of how subspace methods can be used to build interactive tools for tangential field design and processing tasks.

中文翻译：

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局部支持的切向向量、n 向量和张量场

我们引入了表面上切向向量、n 向量和张量场空间的子空间的构造。得到的子空间可用作涉及切向场的设计和处理问题的快速逼近算法的基础。我们构造的重要特征是它基于一个通用原理，从中可以导出不同类型的切向场的构造，并且它是可扩展的，从而可以有效地计算和存储大型网格的大型子空间基。此外，该构造是自适应的，这允许控制子空间在表面上的自由度分布。我们在解决近似质量、可扩展性、适应性、计算时间和内存要求的几个实验中评估了我们的构造。通过将我们的结构与可能的替代方案进行比较，我们的设计选择是合理的。最后，我们讨论了如何使用子空间方法为切向场设计和处理任务构建交互式工具的示例。