New cubic rational basis with tension shape parameters

By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.

Circular object recognition based on shape parameters

To recognize circular objects rapidly in satellite remote sensing imagery, an approach using their geometry properties is presented. The original image is segmented to be a binary one by one dimension maximum entropy threshold algorithm and the binary image is labeled with an algorithm based on recursion technique. Then, shape parameters of all labeled regions are calculated and those regions with shape parameters satisfying certain conditions are recognized as circular objects. The algorithm is described in detail, and comparison experiments with the randomized Hough transformation （RHT） are also provided. The experimental results on synthetic images and real images show that the proposed method has the merits of fast recognition rate, high recognition efficiency and the ability of anti-noise and anti-jamming. In addition, the method performs well when some circular objects are little deformed and partly misshapen.

Generate mesh with shape parameters

In CAD/CAM, mesh rather than smooth surface is only needed sometimes. A mesh-generating method from permanence principle of Coons patch is developed. A new mesh point is defined through local small subpatch and all mesh points are computed by a linear system with special symmetric block tridiagonal coefficient matrix. By simplification, the determinant of coefficient matrix is determined by determinants of submatrices. Condition of existence of solution is given. Whether coefficient matrix is singular can be judged by a simple polynomial function with the eigenvalue of submatrix as variable. Numerical examples demonstrate the effects of shape parameters.

MODIFIABLE QUARTIC AND QUINTIC CURVES WITH SHAPE-PARAMETERS

This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.

Research on shape parameters of circular arc disc teeth for three-cone bit

Through the single row drilling experiment,this paper studied the regularity of the tooth shape parameter's influence to the disc teeth's rock-breaking effect,which provided some basis for the composite teeth type roller bit's combined experimental study and the structure design of the tooth type.This experimental research is only for the circular arc disc teeth which is arranged on the composite teeth type roller bit's main tooth.The experiments were designed using the method of orthogonal design and the results were analyzed by the fuzzy optimization method.The results show that the disc tooth's drilling effect is the best when the tip diameter is 2 mm,taper angle is 30
and the groove number is 8,and the disc tooth's drilling effect is the second best when the tip diameter is 3 mm,taper angle is 30
and the groove number is 7.The above two combined ways of drilling effect's difference is very small(the difference of the degree of the membership is 0.003).

Non-uniform B-spline curves with multiple shape parameters

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence.These curves not only have the many valued properties of the usual non-uniform B-spline curves,but also are shape adjustable under fixed control polygons.Our method is based on the degree elevation of B-spline curves,where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline.We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms,which are indispensable from the user's perspective.

NEW TRIGONOMETRIC BASIS POSSESSING EXPONENTIAL SHAPE PARAMETERS

Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced．

A Class of Spline Curves with Four Local Shape Parameters

A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.

A New Local Control Spline with Shape Parameters for CAD/CAM

A new local control spline based on shape parameters with G^2 continuity,called BLC-spline,is pro- posed.Not only is BLC-spline very smooth,but also the spline curve's characteristic polygon has only three control vertices,and the characteristic polyhedron has only nine control vertices.The behavior of lo- cal control of BLC-spline is better than that of the other splines such as cubic Bezier,B and Beta-spline.The three shape parameters β_0,β_1 and β_2 of BLC-spline,which are independent of the con- trol vertices,may be altered to change the shape of the curve or surface.It is shown that BLC-spline may be used to construct a space arc spline for DNC machining directly.That is a powerful tool for the design and manufacture of curves and surfaces in integrated CAD/CAM systems.

Influence of the roughness and shape of quartz particles on their flotation kinetics

Surface roughness and shape play an important role on the behavior of particles in various processes such as flotation. In this re- search, the influence of different grinding methods on the surface roughness and shape characteristics of quartz particles as well as the effect of these parameters on the flotation of the particles was investigated. The surface roughness of the particles was determined by measuring their specific surface area via the gas adsorption method. The shape characteristics of the particles were measured and calculated by images obtained by scanning electron microscopy via an image analysis system. The flotation kinetics was determined using a laboratory flotation cell. The results showed that the particles of rod mill products have higher roughness and elongation ratio and lower roundness than the parti- cles of ball mill products. The flotation kinetics constant of the particles increased with their surface roughness increasing. Particles with higher elongation and lower roundness indicated higher floatability. In addition, the influence of the surface roughness on the flotation kinet- ics was greater than that of shape parameters.

Bézier curves with shape parameter

In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface.

Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter

In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.

The Importance of the Shape Parameter in a Bulk Parameterization Scheme to the Evolution of the Cloud Droplet Spectrum during Condensation

The shape parameter of the Gamma size distribution plays a key role in the evolution of the cloud droplet spectrum in the bulk parameterization schemes. However, due to the inaccurate specification of the shape parameter in the commonly used bulk double-moment schemes, the cloud droplet spectra cannot reasonably be described during the condensation process. Therefore, a newly-developed triple-parameter condensation scheme with the shape parameter diagnosed through the number concentration, cloud water content, and reflectivity factor of cloud droplets can be applied to improve the evolution of the cloud droplet spectrum. The simulation with the new parameterization scheme was compared to those with a high-resolution Lagrangian bin scheme, the double-moment schemes in a parcel model, and the observation in a 1.5D Eulerian model that consists of two cylinders. The new scheme with the shape parameter varying with time and space can accurately simulate the evolution of the cloud droplet spectrum. Furthermore, the volume-mean radius and cloud water content simulated with the new scheme match the Lagrangian analytical solutions well, and the errors are steady, within approximately 0.2%.

Subtle Influence of the Weibull Shape Parameter on Homer Optimization Space of a Wind Diesel Hybrid Gen Set for Use in Southern Brazil

Wind power is an increasingly important alternative for obtaining energy supplies, both in large interconnected power systems and in smaller hybrid systems and even in backup systems. The temporal and spatial variability of the winds represent an obstacle to be overcome so that wind energy can be increasingly used. The capacity factor of wind farms shows how this variability impacts the operation of the plants and its value is of the order of 30% to 35%. The variability of the wind speed is influenced if the point of interest is on land or on sea, the shape of the surface, the proximity of water bodies, among other factors. The availability of wind is best described by the Weibull probability distribution, which has as one of its defining parameters one which is termed as shape parameter. This parameter is much higher as higher is the variability of the wind speed. This paper studies the subtle influence of Weibull shape parameter on the optimal combination of components in a wind diesel hybrid system, by means of computer simulations with the well known software Homer. The results indicate a relatively small influence (as expected) in the studied system, which appears particularly when the cost of diesel is higher and the availability of wind is lower.

Cognition,Application and Discussion on Shaped Charge Hydraulic Smooth Blasting Technology

In the past,the main method of tunnel excavation in China was drilling and blasting,but the biggest shortcoming of the traditional drilling and blasting method is that it is easy to cause serious overexcavation and underexcavation.At the same time,the operation cycle time of this method is long,which leads to a serious waste of resources.Not only that,a large number of toxic gases and dust produced after blasting also do harm to the health of construction workers.So this is an urgent need for a new construction technology to solve this worldwide problem.In this situation,the leading experts in the field of tunnel,"The survey and design master of China"Shi Yuxin,Liu Pei,and well-known expert in explosion field,yan-sheng ding,professor Chen Chengguang and Gu Yicheng,the experts group,cooperate with The Fifth Branch of China Railway 18th Bureau in northwest project management department,developed a new technology.This technology has passed the appraisal of scientific and technological achievements organized by Tianjin Science and Technology Commission,which is shaped hydraulic smooth blasting technology.The comprehensive evaluation of the technology is"international leading"level.This paper is mainly aimed at the drawbacks of drilling and blasting construction,combined with the author's cognition and discussion on the introduction of the new technology of cumulative hydraulic blasting and the practical application effect in the tunnel excavation process of the fourth company of China Railway 14th Bureau Group in the second division of the 9th bid section of Zhangjihuai Railway in Huainan Province.

Dendritic tip selection during solidification of alloys:Insights from phase-field simulations

The effect of undercooling DT and the interface energy anisotropy parameter e4 on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys.It was found that the tip radius r increases and the tip shape amplitude coefficient A4 decreases with the increase of the fitting range for all cases.The dendrite tip shape selection parameter sdecreases and then stabilizes with the increase of the fitting range,and sincreases with the increase of e4.The relationship between sand e4 follows a power-law function sµea 4,and a is independent of DT but dependent on the fitting range.Numerical results demonstrate that the predicted sis consistent with the curve of microscopic solvability theory(MST)for e4<0.02,and sobtained from our phase-field simulations is sensitive to the undercooling when e4 is fixed.

A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems

Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.

Development of a mass model in estimating weight-wise particle size distribution using digital image processing

Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.

A UNIFIED THREE POINT APPROXIMATING SUBDIVISION SCHEME

In this paper, we propose a three point approximating subdivision scheme, with three shape parameters, that unifies three different existing three point approximating schemes. Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed. The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.

The Mean Deviation from the Median of the Dagum Distribution

The Dagum model is particularly suitable for the analysis of the distributions of economic quantities, such as income, assets and consumption. The purpose of this note is to derive the expression of the mean deviation from the median of the Dagum distribution to study the behavior of the scale and shape parameters in terms of absolute variability and in terms of relative variability.