Streamsurfaces in diffusion tensor fields are used to represent structures with primarily 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 medically 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 characterize 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 interactively 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.