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28 February 2000 Direct tensor rendering using a bidirectional reflectance model
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For the multi variable volumetric tensor field visualization, an efficient direct rendering technique without using geometrical primitive is proposed. The bi- directional reflectance shading model is used to map the anisotropy stress shear tensor components in direct volume rendering. We model the sub-pixel-sized microfacet at tensor sampling points. The nine component of 3D tensor field are mapped onto grid deformation, opacity mapping, color specification, and normal directions of these microfacets. The ray integration is executed though these irregular infinitesimal microfacets distribution. This direct tensor rendering was applied for at-a-glance tensor visualization of earthquake simulation. That realized a view of deformed structure, stress distribution, local shear discontinuity and the shock front, integrated in a single image. The characteristic P- and S-wave modes are distinguished in the rendered earthquake simulations. Compared with the glyph representation of tensor features, the direct tensor rendering gives the general and total image of tensor field even for the low resolution pixel planes, because the sampling object is assumed as infinitesimally small. the computational cost of direct tensor rendering is not so high than that of scalar volume rendering because the modifications are only ins hading calculation but not in the ray integration.
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Mikio Nagasawa and Yoshio Suzuki "Direct tensor rendering using a bidirectional reflectance model", Proc. SPIE 3960, Visual Data Exploration and Analysis VII, (28 February 2000);

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