Visualization of Tensor Invariant Spaces

张量场在一些科学学科中起着重要作用，特别是结构力学。这导致了更大的张量场可视化方法。但是张量场的结构视觉分析仍然强烈关注方向信息，即特征向量。相比之下，工程师通常首先关注各向同性应力或冯米塞斯应力等不变量。该项目希望开发所有张量不变量的结构可视化来填补这一空白。它将集中在二维或三维的二阶张量，因为这些情况在实践中是最常见的。结构力学中的典型示例可作为测试用例。

Tensor fields play a major role in several scientific disciplines, especially structural mechanics. This has led to a larger set of visualization approaches for tensor fields. But the structural visual analysis of tensor fields has still a strong focus on the directional information, i.e. the eigenvectors. In contrast, engineers often focus first on invariants like isotropic stress or von Mises stress. This project wants to develop a structural visualization of all tensor invariants to fill this gap. It will focus on second-order tensors in two or three dimensions, because these cases are most common in practice. Typical examples from structural mechanics serve as test cases.