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7.1 CAD

A few mesh examples are shown which are not related to semiconductor process or device simulation. A wide field of applications exists ranging from computational fluid dynamics or stress mechanics to computer tomography, anthropology, or computer graphics. Models were obtained from some of these areas to show the versatility of the implemented mesh generator.

The modified advancing front algorithm allows to pause the meshing process to take a snapshot of the incomplete mesh. The advantage is that such a snapshot reveals those parts of the mesh which are finished and those parts which were not yet touched at all. The finished parts will stay unchanged in the final mesh. In such a way it can be quickly determined where faults in the surface description exist. If the program runs into problems or shows unexpected behavior, the developer can halt the process and view the current state of the front and the problem region.

Scientific visualization is a challenging task and is important to grasp the results from a three-dimensional simulation [51]. To provide a meaningful feedback to the user different techniques must be developed to appropriately prepare scalar or vector data and to expose the interior of a mesh which becomes inherently difficult in three dimensions [57]. A powerful visualization toolkit [150] was used to render some of the more complex images shown in this chapter.

The first example is a model of a hand. Snapshots of the advancing front are shown in Fig. 7.1. The second example is a model of Beethoven's bust. The surface mesh is depicted in Fig. 7.2. Extracting all structural edges results in a contour plot (Fig. 7.3). Figure 7.4 shows the model of a cow. The meshes for all three examples are depicted in Fig. 7.5, Fig. 7.6, and Fig. 7.7. The edges and points of the mesh of the hand rendered as tubes and spheres can be seen in Fig. 7.6. Computation time is minimal (less than a minute) and the mesh contains 4344 tetrahedra. For the example of the cow and Beethoven's bust the tetrahedral elements are itself visualized by shrinking them (Fig. 7.5, Fig. 7.7). The mesh of Beethoven's bust contains 17665 tetrahedra and the mesh of the cow 11608 tetrahedra.

Figure 7.1: The advancing front at several moments during the meshing process. It separates the meshed region from the empty parts of the volume.
\includegraphics [height=0.35\textheight]{ppl/hand.sps}

Figure 7.2: Surface mesh of Beethoven's bust.
\includegraphics [width=0.36\textwidth]{ppl/bhovenorg.eps}

Figure 7.3: Structural edges form a contour plot.
\includegraphics [width=0.36\textwidth]{ppl/bhovengline.eps}

Figure 7.4: The model of a cow.
\includegraphics [width=0.7\textwidth]{ppl/}

Figure 7.5: The mesh of a cow with 11608 elements.
\includegraphics [width=0.7\textwidth]{ppl/}

Figure 7.6: Edges and points of the final mesh.
\includegraphics [width=0.8\textwidth]{ppl/handvtk.eps}

Figure 7.7: Final mesh of Beethoven's bust with 17665 elements.
\includegraphics [width=0.8\textwidth]{ppl/}

The tetrahedralization domain for a quite different example, a human skull (Fig. 7.8), is extremely non-convex. In fact, only the outer shell has been tetrahedralized and the region of the brain itself was never processed. Figure 7.9 shows cross-sections of the mesh at interesting parts of the skull. It can be seen that the meshed volume is much smaller than the volume covered by the convex hull. The top left picture in Fig. 7.9 shows the cross-section of the jaw area. In the following pictures one can see the nasal cavity, nasal bone, and nasal septum. The bottom right picture contains the cross-section of the skull above the nose and eye area.

Figure 7.8: Human skull, mesh with 28512 elements.
\includegraphics [height=0.8\textheight]{ppl/}

Figure 7.9: Crossections of the human skull mesh.
\includegraphics [height=0.8\textheight]{ppl/}

next up previous contents
Next: 7.2 Interconnects Up: 7. Examples Previous: 7. Examples
Peter Fleischmann