Anisotropic volume rendering for extremely dense, thin line data

Abstract

Many large scale physics-based simulations which take place on PC clusters or supercomputers produce huge amounts of data including vector fields. While these vector data such as electromagnetic fields, fluid flow fields, or particle paths can be represented by lines, the sheer number of the lines overwhelms the memory and computation capability of a high-end PC used for visualization. Further, very dense or intertwined lines, rendered with traditional visualization techniques, can produce unintelligible results with unclear depth relationships between the lines and no sense of global structure. Our approach is to apply a lighting model to the lines and sample them into an anisotropic voxel representation based on spherical harmonics as a preprocessing step. Then we evaluate and render these voxels for a given view using traditional volume rendering. For extremely large line based datasets, conversion to anisotropic voxels reduces the overall storage and rendering for O(n) lines to O(1) with a large constant that is still small enough to allow meaningful visualization of the entire dataset at nearly interactive rates on a single commodity PC.

Illuminated Lines Revisited

“…Schussman and Ma [13] calculate diffuse and specular reflection by integrating the reflection from the infinitesimally thin facets of a cylinder. The range of integration consists of those facets which are both visible and lit.…”

“…An equivalent but less compact expression was published in [13]. Our expression lets us recognize the square root term as obtained with the maximum reflection principle (Eq.…”

“…Therefore, we follow [13] and use the Phong/Blinn model leading to simpler expressions and finally to 2D textures only. From V and L we first compute the halfway vector…”

“…More recently, a texture-based method exploiting programmable graphics hardware was presented by Li et al [8]. For the visualization of tensor fields, methods based on anisotropic volume rendering have been developed by Sigfridsson et al [14] and by Schussman and Ma [13], the latter being also applicable to general sets of lines. In other areas of computer graphics, the display of lines in space is of much less importance nowadays.…”

“…Diffuse and specular reflection are calculated by integrating over the visible part of the perimeter. Such a lighting model has been used by Schussman and Ma [13]. The diffuse component of their model is a view dependent version of the one introduced by Kajiya and Kay [7].…”