地应力三维张量场的可视化技术研究

分析和研究地应力弹性二阶张量场的可视化技术。根据对地应力二阶张量的数学分析，得出了地应力场对应于二阶对称张量，导出了二阶对称张量在空间几何学中对应的二次曲面。结果表明，求取对称二阶张量问题可以归结为求取特征值与特征向量问题。解决了同时表示二阶对称张量场空间一点多个分量的难题和沿地应力某一主方向对称张量及二维对称张量的可视化问题。

Visualization Techniques of 3D Tensor Field in Geostress

The visualization techniques of 3D tensor field in geostress were analyzed and studied. Based on mathematical analysis, it was showed that the elastic geostress field is a symmetric second order tensor, which can be expressed as symmetric matrix and studied by its eigenvalue and eigenvector, and the quadratic surface corresponding to the second order tensor was derived. The difficulty of displaying six components simultaneously at one point in 3D space was solved. The visualization of second order geostress tensor fields along a principle direction with hyperstreamlines was implemented. The topology of three dimensional symmetric tensor fields was analyzed.