Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, altho...Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously character- ize the local tensor details - anisotropy - on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be inter- actively adjusted by changing some given parameters. The second one generates a dense LIC （line integral convolution） texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.展开更多
Second-order tensors are widely existed in engineering,physical science and biomechanics. Examples arestresses and strains in solids and velocity gradients in fluid flows. This paper takes the Boussinesq' s proble...Second-order tensors are widely existed in engineering,physical science and biomechanics. Examples arestresses and strains in solids and velocity gradients in fluid flows. This paper takes the Boussinesq' s problem as an ex-ample which is typical in Elasticity Mechanics ,and visualizes the second-order real symmetric tensor fields by ellipsoidicons and hyperStreamlines. The results are reasonable. The visualization methods adopted in this paper are also suit-able for other second-order symmetric tensor fields such as electromagnetic field.展开更多
基金Supported by the National Natural Science Foundation of China(61070233)the Natural Science Foundation of Shaanxi Province,China(2011JM1006)
文摘Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously character- ize the local tensor details - anisotropy - on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be inter- actively adjusted by changing some given parameters. The second one generates a dense LIC （line integral convolution） texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.
文摘Second-order tensors are widely existed in engineering,physical science and biomechanics. Examples arestresses and strains in solids and velocity gradients in fluid flows. This paper takes the Boussinesq' s problem as an ex-ample which is typical in Elasticity Mechanics ,and visualizes the second-order real symmetric tensor fields by ellipsoidicons and hyperStreamlines. The results are reasonable. The visualization methods adopted in this paper are also suit-able for other second-order symmetric tensor fields such as electromagnetic field.
