The best method for investigating moiré phenomena in the superposition of periodic layers is based on the Fourier approach. However, superposition moiré effects are not limited to periodic layers, and they also occur between repetitive structures that are obtained by geometric transformations of periodic layers. We present in this paper the basic rules based on the Fourier approach that govern ...

Seemingly distant areas of symmetry, such as mentioned in the title, are closely related to each other on an abstract level. The unified treatment is made possible by some common features of the symmetry groups used in the mathematical description of these types of symmetries. The key property is the way as a two-element group generated by an involutory transformation can extend a geometric sym...

This paper addresses the numerical estimation of the principal curvature of pattern transformation manifolds. When a visual pattern undergoes a geometric transformation, it forms a (sub)manifold in the ambient space, which is usually called the transformation manifold. The manifold curvature is an important property characterizing the manifold geometry, with several applications in manifold lea...

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used...

We provide a geometric interpretation of a new rational Landen transformation and establish the convergence of its iterates.

A geometric separator for a set U of n geometric objects (usually balls) is a small (sublinear in n) subset whose removal disconnects the intersection graph of U into roughly equal sized parts. These separators provide a natural way to do divide and conquer in geometric settings. A particularly nice geometric separator algorithm originally introduced by Miller and Thurston has three steps: comp...

This paper presents a survey of past transformation functions for image registration and introduces a new transformation function for registration of images containing rigid as well as nonrigid regions. Included in the survey are similarity transformation, linear transformation, and nonlinear transformation. Nonlinear transformation itself includes thin-plate splines, radial basis functions, ap...

based on description and nature of geomorphology, the geomorphologists must be have specific tendency to form of earth crust's landforms and their transformation. but some of related specialists in iran, believe that questa have relationship to old (paleo) geology formations, and by this reason say that questa there is not in iran. whereas anothers such as the writer (author) of this articl, wi...

Preserving the privacy of individuals when data are shared for clustering is a complex problem. The challenge is how to protect the underlying data values subjected to clustering without jeopardizing the similarity between objects under analysis. In this short paper, we revisit a family of geometric data transformation methods (GDTMs) that distort numerical attributes by translations, scalings,...

For a certain class of varieties X, we derive a formula for the valuation dX on the arc space L(Y ) of a smooth ambient space Y , in terms of an embedded resolution of singularities. A simple transformation rule yields a formula for the geometric Poincaré series. Furthermore, we prove that for this class of varieties, the arithmetic and the geometric Poincaré series coincide. We also study the ...