Usual geometrical optics based syntheses of shaped reflectors provide numerically defined surfaces which must be interpolated for subsequent evaluation of the antenna secondary field to check against design specifications. The implementation of three techniques capable of performing global interpolations of numerically defined (3D) surfaces, namely, the quintic pseudosplines, polynomial Fourier series, and Jacobi polynomial-sinusoidal expansions, is explored. The relative superior stability of the first is demonstrated for the synthesis of shaped reflectors presenting critical behavior of their principal curvatures.>
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Bergmann et al. (1994) studied this question.
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