Volume visualization

It is possible to perform volume visualization with different color and opacity tables, which can be designed by the user out of the samples intensity histogram. 

Figure 2 Volume visualization of the three-dimensional volume representing the PVC-enriched phase of the polymer blend (a) the whole volume rendered, (b) three orthogonal slices showing the interior of the volume, (c) single isosurface showing 5/95 PVC/PMMA composition of the blend, and (d) multiple isosurfaces displaying three compositions 5/95, 12/88, and 22/78 of the blend. Reproduced from Artyushkova and Fulghum [9].

Figure 13.2 Instantaneous volume visualizations of the vorticity magnitude for the M = 0.6 square jet [9] 1 — hairpin (braid) vortices, 2 — vortex rings, and 3 — worm vortices...

Schulze D. J., Wiese D., and Steude J. (1996) Abundance and distribution of diamonds in eclogite revealed by volume visualization of CT X-ray scans. J. Geol. 104(1), 109-113. 

R. Q. Topper, this volume. Visualizing Molecular Phase Space Nonstatistical Effects in Reac-... 

Visualization of CT, MRI, and nuclear medicine images can greatly benefit fi om specialized visualization techniques, since they are series of two-dimensional cross sections. Instead of having the surgeon mentally correlate consecutive slices and create a mental three-dimensional view, it is desirable to directly reconstruct the three-dimensional information and show it as a new computed image. There are two families of visualization algorithms volume visualization and surface visualization. We describe them briefly next. 

Figure 2 Sample-volume visualizations that would be expected to produce 95% of detector response. Linear attenuation coefficients for soil and air have been estimatedfor energy level 662 keV...

T. McReynolds. Programming with OpenGL Advanced rendering. C.13. Volume visualization with texture, SIGGRAPH 99 Course 1999... 

For presenting the results of the 3D-CT measurements the software tool 3D-CTViewer [12] was designed and developed under the visualization developer language IDL [13]. In this package both typical methods for 3D-visualization, the surface and the volume rendering technique [14], are implemented. 

The method of volume rendering uses the whole sample volume for visualization. Therefor semitransparent representations of the samples inner structure are possible and the detection of small cracks or faults is much easier compared to the surfaces based techniques (Fig. 4 b). From its principle volume rendering is more time consuming compared to surface representation. 

Here a - surface tension pa - atmospheric pressure 9 - contact angle of crack s wall wetting by penetrant n - coefficient, characterizing residual filling of defect s hollow by a penetrant before developer s application IT and h - porosity and thickness of developer s layer respectively W - minimum width of crack s indication, which can be registered visually or with the use of special optical system. The peculiarity of the case Re < H is that the whole penetrant volume is extracted by a developer. As a result the whole penetrant s volume, which was trapped during the stage of penetrant application, imbibes developer s layer and forms an indication of a defect. 

The space filling model developed by Corey, Pauling, and Koltun is also known as the CPK model, or scale model [197], It shows the relative volume (size) of different elements or of different parts of a molecule (Figure 2-123d). The model is based on spheres that represent the "electron cloud . These atomic spheres can be determined from the van der Waals radii (see Section 2.10.1), which indicate the most stable distance between two atoms (non-bonded nuclei). Since the spheres are all drawn to the same scale, the relative size of the overlapping electron clouds of the atoms becomes evident. The connectivities between atoms, the bonds, are not visualized because they are located beneath the atom spheres and are not visible in a non-transparent display (see Section 2.10). In contrast to other models, the CPK model makes it possible to visualize a first impression of the extent of a molecule. 

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

Accordingly, the product 6A is about the same as Vj, the volume of the hole. For liquids of low molecular weight, is on the order of 0.5% the volume of the liquid at room temperature, increasing to 2-3% at the boiling point, and larger yet at still higher temperatures. This identification makes 6 A easier to visualize, but it still leaves us with four parameters kj, 6, X, and. ... 

It is possible to derive an expression equivalent to Eq. (4.67) starting from entropy rather than free volume concepts. We have emphasized the latter approach, since it is easier to visualize and hence to use for qualitative predictions about Tg. 

There are a variety of ways to describe the droplet population. Figures 14-88 and 14-90 illustrate one of the most common methods, the plot of cumulative volume against droplet size on log-normal graph paper. This satisfies the restraint of not extrapolating to a negative drop size. Its other advantages are that it is easy to plot, the results are easy to visualize, and it yields a nearly straight line at lower drop sizes. 

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