scholarly journals Non-Periodic Rhomb Substitution Tilings that Admit Order n Rotational Symmetry

2005 ◽  
Vol 34 (3) ◽  
pp. 523-536 ◽  
Author(s):  
E. O. Harriss
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tilings

A Computer Search for Planar Substitution Tilings with $$n$$ n -Fold Rotational Symmetry

2015 ◽  
Vol 53 (2) ◽  
pp. 445-465 ◽  
Author(s):  
Franz Gähler ◽  
Eugene E. Kwan ◽  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Computer Search ◽  
Substitution Tilings

scholarly journals On substitution tilings of the plane with n-fold rotational symmetry

2015 ◽  
Vol Vol. 17 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tiling ◽  
Computer Assistance ◽  
Discrete Algorithms ◽  
Special Cases ◽  
International Audience ◽  
Substitution Tilings

Discrete Algorithms International audience A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with elevenfold symmetry appearing in the literature.

Primitive substitution tilings with rotational symmetries

2018 ◽  
Vol 74 (4) ◽  
pp. 388-398
Author(s):  
April Lynne D. Say-awen ◽  
Ma. Louise Antonette N. De Las Peñas ◽  
Dirk Frettlöh
Keyword(s):  
Rotational Symmetry ◽  
Primitive Substitution ◽  
Substitution Tilings

This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six- and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.

scholarly journals Substitution tilings with dense tile orientations and n-fold rotational symmetry

2017 ◽  
Vol 28 (1) ◽  
pp. 120-131 ◽  
Author(s):  
D. Frettlöh ◽  
A.L.D. Say-awen ◽  
M.L.A.N. De Las Peñas
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tilings

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals On the Reconstruction of the Center of a Projection by Distances and Incidence Relations

2020 ◽  
Author(s):  
András Pongrácz ◽  
Csaba Vincze
Keyword(s):  
Algebraic Surface ◽  
Basic Problem ◽  
Rotational Symmetry ◽  
Image Plane ◽  
Equivalent Condition ◽  
Central Projection ◽  
Profile Curve ◽  
Reconstruction Process ◽  
Restricted Area ◽  
Photographic Images

AbstractUp to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.

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