This paper introduces a B ezier curve-based mechanism for constructing membership functions of convex normal fuzzy sets. The mechanism can fit any given data set with a minimum level of discrepancy. In the absence of data, the mechanism can be intuitively manipulated by the user to construct membership functions with the desired shape. Some numerical experiments are included to compare the perf...

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curve or surface). In this paper, we characterize a new family of compactly supported piecewise-exponential basis functions that are smooth and s...

An explicit method to compute algebraic equations of curves constant width and Zindler generated by a family middle hedgehogs is given thanks property Chebyshev polynomials. This extends the methodology used Rabinowitz Martinez-Maure in particular generate full equations, both curves, defined trigonometric polynomials as support functions.

This article presents a generalized B-spline surface subdivision scheme of arbitrary order with a tension parameter.We first propose a tensor-product subdivision scheme that produces ku×kv order generalized B-spline limit surfaces. Generalized B-spline surface is the unified and extended form of B-splines, trigonometric B-splines and hyperbolic B-splines (Fang et al. 2010). The tensor product s...

Three methods of determining the actual size of objects on the living fundus were utilized to measure the horizontal disc diameter (H) in 68 volunteers. H1 was calculated from fundus photographs based on the refractive power of the eye and according to the formula of Bengtsson and Krakau. H2 was derived from Littmann's trigonometric curves based on the anterior corneal curvature and the refract...

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dyn...

In this article we define a new class of Pythagorean-Hodograph curves built-upon a sixdimensional mixed algebraic-trigonometric space, we show their fundamental properties and compare them with their well-known quintic polynomial counterpart. A complex representation for these curves is introduced and constructive approaches are provided to solve different application problems, such as interpol...

The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation. 1. Outline and introduction Recently, in an attempt to prove, through the Cauchy residue method, Dougall’s theorem (Dougall [6, 1907], se...

We present a new method for implicitization of parametric curves, surfaces and hypersurfaces using essentially numerical linear algebra. The method is applicable for polynomial, rational as well as trigonometric parametric representations. The method can also handle monoparametric families of parametric curves, surfaces and hypersurfaces with a small additional amount of human interaction. We i...