5.6 Volume Visualization



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5.6 Volume Visualization

     

The terms volume rendering and volume visualization refer to techniques for displaying scalar functions of three spatial coordinates known as volume data (or volumetric data). The most general known approach to generate images from such data is to simulate the interaction of light rays with a semitransparent, absorbing and emitting material, according to linear transport theory. There is a wide variety of possible mappings of scalar function values to the optical properties of the simulated material. Almost all volume rendering techniques are covered by this general concept.

Although the primary impact of these rather new techniques has been on the visualization of intrinsically three-dimensional experimental data (generated, e.g., by nuclear magnetic resonance tomography or seismic explorations) the application to three-dimensional simulated data is no less attractive. An increasing number of volume rendering applications can also be found in traditional CAE areas, some of them even in process and device simulation [91] [90].

Most existing methods operate on data given on regular tensor-product grids and hence have to re-sample the data if it is given on an irregular grid. The volume rendering module of VISTA [93] does not re-sample the data but works directly on the tetrahedral tessellation of the volume data, given as set of 3-simplexes, .

The algorithm to obtain the intensity of the red, green, and blue ``light components'' at a given point of the resulting image is based on the casting of a ray through the three-dimensional simplex set. Figure 5.5 shows a simple two-dimensional equivalent. The ray originates at a source point in the background where it consists of the initial components , , and and intersects the simplex structures at certain points (labeled 1 to 4). During the transition through the absorbing and emitting medium the intensities are modified according to the optical properties of this region and finally the observer at the point is reached by the ray.

  
Figure 5.5: A ray passing through the simplexes

The light intensities of color arrivinggif at point is

where the integral is approximated as

is the amount of C-colored light emmitted by the virtual ``fog-like'' medium. is the density of this medium. The optical parameters and depend on the value of the visualized quantity and can be chosen by the user to obtain the desired visualization effect.

  
Figure 5.6: Tetrahedral simplex set used for volume rendering

  
Figure 5.7: Volume-rendered image of the doping concentration in a three-dimensional trench structure

Figure 5.7 shows the doping concentration in a three-dimensional trench structure that has been created by the simulation of ion implantation with Monte Carlo methods [94]. The resulting volumetric data ( in PIF, the struture of the simplex set can be seen in Figure 5.6) has been transferred into the visualization system using an input module and the resulting simplex set has been volume-rendered to create Figure 5.7. The colorgif bar on the right side shows the combined effect of , , and for increasing from bottom to top.



next up previous contents index
Next: 5.7 Ray-Tracing Interface Up: 5 Visualization Previous: 5.5.4 Deficiencies



Martin Stiftinger
Thu Oct 13 13:51:43 MET 1994