二阶对称张量场可视化的一种新模式

New pattern for visualizing second-order symmetric tensor fields

目前二阶对称张量场的可视化均是基于最大(次大)和最小特征向量场的,但这样定义的特征向量场存在着方向不连续的问题,而应力场的特征向量的方向却是永远连续的,鉴于此,提出了基于特征向量方向连续的一种可视化的新模式。从原理上阐述了问题产生的机理,提出了特征向量场的新定义——根据特征向量方向的连续性将特征向量场定义为第一和第二(第三)特征向量场,并对新定义的特征向量场在每一点包括退化点处的取值问题进行了研究。新定义克服了传统定义方向不连续的缺点,保持了特征向量场在每一点包括退化点处的方向上的连续性,同时,基于新定义的可视化从本质上体现了应力场及其他对称张量场本身具有的属性。

Second-order symmetric tensor fields are visualized based on major（medium） and minor eigenvector fields,but there is a problem of discontinuity in direction with these eigenvector fields.On the other hand, the directions of eigenvectors of stress ＂fields are always continuous.In consideration of these facts, a new pattern for visualizing second-order symmetric tensor fields based on the continuity of eigenvectors in direction is presented.Firstly the problem is clarified in theory,and a new definition for eigenvector fields is given.According to the continuity of eigenvectors in direction they are defined as the first（second） and third ones,and the values of the new eigenvector fields at all points including degenerate ones are then studied.New definition overcomes the drawback of discontinuity in direction under traditional definition with the continuity of eigenvector fields in direction preserved at all points including degenerate ones, at the same time, the visualization based on the new definition displays the property of such symmetric tensor fields as stress fields in essence.