Radius Vector Function Research Articles

Determination of used textiles drape characteristics for circular economy

In the present work, the drape characteristics of second-hand textile fabrics were determined. The results can be used to implement the concepts of the circular economy. Automated software tools have been adapted and researched to apply the proposed methods and procedures for digital image analysis of used textile drape, which will be utilized to describe their shapes and predict their characteristics, as well as their classification into groups and assessment of classification accuracy in recognizing their elements. A radius-vector function was used to determine the main drape characteristics, such as the number of peaks, their size, and their location. Analytical models have been created for automated forecasting of the drape characteristics from used textiles, which can be applied to predict changes in these characteristics. It obtained an accuracy of 68–92% in the prediction of the main drape characteristics of used textiles. Due to changes in their main characteristics, the errors in classification and prediction increased by 10–15%. More complex computational procedures have been implemented to obtain a higher predictive power for second-hand textile fabrics. The results can be applied in the manufacture of new products such as curtains, tablecloths, napkins and fashion accessories.

Implementation of image processing techniques as a tool for form analysis of Romanian folk elements

The present paper proposes a method for an effective analysis of Romanian folk motifs using two basic algorithms – Radius-Vector function (RV) and Principal Component Analysis (PCA). For a better accuracy of the analysis, a combination of these methods has been proposed. The authors selected few Romanian folk motifs (embroidered on blouses, skirts called “poale”, front aprons called “zadii”, sleeveless vest) from Bihor, Arad, and Maramures Counties. The vectorization of traditional motifs was made by GIS software.

Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

Based on complex function methods and a multipolar coordinate system, the scattering induced by a cylindrical cavity in a radially inhomogeneous half-space is investigated. Mass density of the half-space varies depending on the distance from the centre of the cavity while the shear modulus is always constant. The wave velocity is expressed as a function of radius vector and the Helmholtz equation is a partial differential equation with a variable coefficient. By means of a conformal mapping technique, the Helmholtz equation with a variable coefficient is transferred into its normal form. Then, displacement fields and corresponding stress components are deduced. Applying the boundary conditions, dynamic stress concentration factors around the cavity are obtained and analyzed. Typical numerical results are presented to demonstrate the distribution of dynamic stress concentration factors when influencing parameters are assumed.

Identification of radius-vector functions of interface evolution for star-shaped crystal growth

This article introduces a new method based on a radius-vector function for identifying the spatio-temporal transition rule of star-shaped crystal growth directly from experimental crystal growth imaging data. From the morphology point of view, the growth is decomposed as initial conditions, uniform growth and directional growth, which is represented by a static polynomial model based on the Fourier expansion. A recursive model is also introduced to help understand the dynamic characteristics of the observed systems. The applicability of the proposed approach is demonstrated using data from a simulation and from a real crystal growth experiment.

A microcontact model developed for sphere- and cylinder-based fractal bodies in contact with a rigid flat surface

The present study examines sphere- and cylinder-based fractal bodies in contact with a smooth and rigid flat surface. The generalized Weierstrass–Mandelbrot function (the W–M function) is employed in combination with the radius–vector function method (the (r, θ) method) to derive the formulae of fractal surface asperities formed on a smooth spherical surface and a smooth cylindrical surface. The size distribution functions used to calculate the contact load and the real contact area of an apparent area were derived for the three deformation regimes of microcontacts. The non-Gaussian probability density functions for two contact forms (cylindrical and spherical) were developed by combining the probability density functions developed for all small elements in the contact area using the superposition technique. In the present model, the deformation behavior demonstrated in the elastic, elastoplastic, and fully plastic deformation regimes is consistent with that described by classical (statistical) theories. Both the contact load and the real contact area results predicted by the present fractal model at various minimum separations show very good agreement with the results obtained using the statistical method. However, the results also exhibited properties very different from the results predicted by the unmodified fractal model, which showed the microcontact behavior demonstrated in the three deformation regimes to be exactly opposite to that predicted by the classical theories.

A continuous parametric shape model

In this paper we propose a flexible continuous parametric shape model for star-shaped planar objects. The model is based on a polar Fourier expansion of the normalized radius-vector function. The expected phase amplitudes are modelled by a simple regression with parameters having nice geometric interpretations. The suggestedgeneralized p-order model is an extension of first- and second-order Gaussian shape models, and in particular the Gaussian assumption is relaxed. The statistical analysis is straightforward, as demonstrated by an application concerning shape discrimination of two cell nuclei populations.

A Deformable Template Model, with Special Reference to Elliptical Templates

This paper suggests a high-level continuous image model for planar star-shaped objects. Under this model, a planar object is a stochastic deformation of a star-shaped template. The residual process, describing the difference between the radius-vector function of the template and the object, is allowed to be non-stationary. Stationarity is obtained by a time change. A parametric model for the residual process is suggested and straightforward parameter estimation techniques are developed. The deformable template model makes it possible to detect pathologies as demonstrated by an analysis of a data set of cell nuclei from a benign and a malignant tumour, using stochastic deformations of ellipses.

Shift x, y-coordinate detection of line figures and the extraction of particle shape information

Several theories are used for particle shape analysis. Among these are the Fourier transform (full range) methods for the angular bend function and radius vector function. However these contain methodological weaknesses, not only in the functions themselves, such as the re-entrant nature or irregular asymmetricity apt to provide noisy information, but also in the Fourier transform with the phase angle for further extended shape analyses. In this report, these two main elements are reconsidered, introducing the shift x, y-coordinate detection method for contour curves and the Fourier sine transformation in the half-range. Their application to measurement of particle size contraction and shape information was examined via image (contour) reconstruction and estimations of projected area and elongation for real sand particles.