NDLI: The 'clamshell problem'-interpolation of shaped reflectors and other smooth surfaces

Content Provider	IEEE Xplore Digital Library
Author	Baker, L.A.
Copyright Year	1963
Abstract	An interpolation method for shaped reflector antennas and similar smooth surfaces is developed using cubic spline interpolants in a parametric representation. Ordinary one-dimensional splines are combined in tensor products to give a two-dimensional interpolant for each cartesian component of points of the surface. The two independent variables are the polar coordinates of rays traced from an aperture disk. This ray tracing maps a grid of lines from the aperture to the surface being interpolated and gives a general-purpose method for interpolating smooth surfaces. The polar coordinates are partitioned into uniform intervals, which simplifies the calculations. The interpolant is differentiated to provide partial derivatives of the surface coordinates, and these derivatives are combined to give surface normals and Jacobians. The bicubic spline is also integrated to give a general-purpose two-dimensional integration routine. The parametric form makes it easy to find a variety of cross sections, boundaries, inflection points, and other characteristics of the surface.<>
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	1560
Ending Page	1565
Page Count	6
File Size	591360
File Format	PDF
ISSN	0018926X
Volume Number	36
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1988-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Interpolation Spline Apertures Reflector antennas Ray tracing Tensile stress Equations Geometrical optics Nonlinear optics Jacobian matrices
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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