Showing papers on "Regular polygon published in 1976"

On convex lattice polygons

Abstract: Let π be a convex lattice polygon with b boundary points and c (≥ 1) interior points. We show that for any given c, the number b satisfies b ≤ 2c + 7, and identify the polygons for which equality holds.

Self-consistent GTD formulation for conducting cylinders with arbitrary convex cross section

Abstract: A user-oriented computer program has been developed for high frequency radiation and scattering from infinitely-long perfectly. conducting convex cylinders. The analysis is based on the self-consistent geometrical theory of diffraction (GTD). The cylinder is modeled as an N -sided polygon. Two cylindrical waves with unknown amplitudes are assumed to travel in opposite directions on each face of the polygon. The boundary conditions for the corners are applied to set up a matrix equation for 2N unknowns (the amplitudes associated with the traveling cylindrical waves). Crout's method is used to solve the matrix equation. Once the amplitudes for the traveling waves are determined, the radiation or scattered field is readily obtained via the usual GTD techniques. Numerical results are presented for radiation and scattering from rectangular, semi-circular, circular, and elliptic cylinders for both principal polarizations. The results show excellent agreement with GTD, moment, and eigenfunction solutions.

A decomposition theorem form-convex sets

Abstract: LetS be a closedm-convex subset of the plane,m≧2,Q the set of points of local nonconvexity ofS, with convQ ⊆S. If there is some pointp in [(bdryS) ∩ (kerS)] ∼Q, thenS is a union ofm−1 closed convex sets. The result is best possible for everym.

On the number of sides necessary for polygonal approximation of black-and-white figures in a plane

Abstract: A bound on the number of extreme points or sides necessary to approximate a convex planar figure by an enclosing polygon is described. This number is found to be proportional to the fourth root of the figure's area divided by the square of a maximum Euclidean distance approximation parameter. An extension of this bound, preserving its fourth root quality, is made to general planar figures. This is done by decomposing the general figure into nearly convex sets defined by inflection points, cusps, and multiple windings. A procedure for performing actual encoding of this type is described. Comparisons of parsimony are made with contemporary figure encoding schemes.