Derived Metric Tensors for Flow Surface Visualization

Harald Obermaier, Kenneth I. Joy
2012 IEEE Transactions on Visualization and Computer Graphics  
Fig. 1 . Visualizations of the inverse metric tensor field of a flow surface in surface parameter space (left and right) gives an overview of surface stretching. The middle image demonstrates different surface visualizations made possible by metric tensor field processing. Abstract-Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface
more » ... ring techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.
doi:10.1109/tvcg.2012.211 pmid:26357122 fatcat:q7k7u2swkvfldktf6msflm23na