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Parametric Patch Model

Many electromagnetic scattering modeling approaches represent the scatterer's surface by a set of flat patches. The most popular one is that of Rao, Wilton, and Glisson [14], which uses flat triangles. The disadvantages of the flat patch model are in the following two important areas. One is that using flat patches to discretize a curved surface is an approximate surface model which introduces discretization error in the solution. Next, the flat patch surface model requires a relatively larger number of elements to represent a complex surface to a desired accuracy than would a parametric surface model. The motivation for using curved patches rather than flat ones is to avoid any surface modeling errors. This allows one to get accurate RCS predictions with a minimum number of surface patches. Figure 5.30 and Figure 5.31 in Chapter 5 demonstrate that the parametric surface model is superior to the flat patch surface model. As the density of the surface patches increases, the difference in accuracy between curvilinear patches and flat patches (facets) decreases. However, for the large 3D target in which we are interested, it is almost impossible to increase the number of surface patches because of the limitation of both the physical memory and the CPU time of the modern computer.

We will only consider a special class of surfaces which only depend on two surface parameters. This class of surface is very useful in the course of RCS prediction applications. Figure 2.1 shows an example of this type of surface, where and are the surface parameters, and is a position vector which can be represented as a function of these two surface parameters as:

where has the following form

and , , and are constants, and is a simple function of . The tangent vectors of the position vector along constant u and v are defined by:

where and are, respectively, the metrical coefficients or the scalar factors along and , and and are the unit vectors of and , respectively. The Jacobian of the surface is defined as a function of and by:

To generate this model, lines along constants u and v are first used to divide the surface into four sided patches. Then curved diagonal lines are used to form curved triangular patches.

The geometric model utilizes the parametric description to map the physical surface into the parametric space shown in Figure 2.2, where the physical surface is decomposed into a collection of curved triangles as shown in Figure 2.2(a). Figure 2.2(b) shows a two-dimensional parametric space (-) representation of the physical surface. In the physical space, the surface is closely modeled by an appropriate set of curved triangles. In the corresponding two-dimensional parametric (-) space, these triangles will have straight edges.



Next: Basis Functions Up: Parametric Modeling and Previous: Parametric Modeling and


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Sat Dec 3 17:51:03 EST 1994