Interpolation



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Interpolation

Figure 6.40 shows a result of the application of VORONOI to a geometry which has the shape of the VISTA logo. Three inner gridpoints labeled , , and are given in Figure 6.40. The specified attribute values are , , and . For this example, VORONOI performed both triangulation and interpolation (by solving the biharmonic equation), which led to the solution shown in Figure 6.40 (the shaded quasi-three-dimensional surface) along with the initial geometry.

  
Figure: Application of VORONOI to the complex singly connected geometry of the VISTA logo. Attribute values have only been defined on the three inner grid points , , . All other grid points are boundary points with interpolated values.

The example shown in Figure 6.40 exceeds the complexity and requirements of current TCAD problems, but it clearly proofs the ability of VORONOI to construct a smooth (``physically reasonable'') interpolation in very complex geometries from a minimum of information required (in this case just three points). VORONOI processes this example in 1.8 CPU seconds (including PIF output) on a PC 486 (DX2, 66Mhz) running Linux 1.0.



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