We use the matrices of transformations between Chebyshev and Bernstein basis and the matrices of degree elevation and reduction of Chebyshev polynomials to present a simple and efficient method for r times degree elevation and optimal r times degree reduction of Bézier curves with respect to the weighted L2-norm for the interval [0,1], using the weight function wðxÞ 1⁄4 1= ffiffiffiffiffiffiffi...

introduction snow is a kind of precipitation that is formed by the condensation of moist air mass and in the condition that temperature is below freezing point. although small areas of the world are mountainous regions, these small territories play an important role in the hydrological context of river basins. in some areas snow covers and glaciers supply drinking water. monitoring and forecast...

A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...

Given the fact that, in the ‘constricting differential . . . ’, the successful management hinged crucially on the identification of the constrictive component of pericarditis, the latter component typically characterized by marked elevation of the jugular venous pressure (JVP), it would be useful to know how elevated that parameter was in the subject of the case report. In one series, 75% of 62...

ABSTRACT In previous work, a periodic surface model for computeraided nano-design (CAND) was developed. This implicit surface model can construct Euclidean and hyperbolic nano geometries parametrically and represent morphologies of particle aggregates and polymers. In this paper, we study the characteristics of degree elevation and reduction based on a generalized periodic surface model. Method...

Theoretical study shows that Said-Bézier generalized Ball curves (SBGB curves) are distinctly superior to Bézier curves in evaluation, degree elevation and reduction. However in practical engineering, there is no effective algorithm for explicit multi-degree reduction of SBGB curves with endpoints constraints in the world. It is going against designing and applying generalized Ball curves. In o...

purpose: to determine the sensitivity and specificity of posterior corneal elevation in discriminating keratoconus and subclinical keratoconus from normal corneas by galilei and orbscan ii diagnosed on the basis of topography. methods: three groups (keratoconus, subclinical keratoconus and normal) were evaluated with galilei and orbscan ii and results were compared to those obtained by gold sta...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...