Asymmetric Tensor Visualization with Glyph and Hyperstreamline Placement on 2D Manifolds

Asymmetric tensor fields present new challenges for visualization techniques such as hyperstreamline placement and glyph packing. This is because the physical behaviors of the tensors are fundamentally different inside real domains where eigenvalues are real and complex domains where eigenvalues are complex. We present a hybrid visualization approach in which hyperstreamlines are used to illustrate the tensors in the real domains while glyphs are employed for complex domains. This enables an effective visualization of the flow patterns everywhere and also provides a more intuitive illustration of elliptical flow patterns in the complex domains. The choice of the types of representation for different types of domains is motivated by the physical interpretation of asymmetric tensors in the context of fluid mechanics, i.e., when the tensor field is the velocity gradient tensor. In addition, we encode the tensor magnitude to the size of the glyphs and density of hyperstreamlines. We demonstrate the effectiveness of our visualization techniques with real-world engine simulation data.