In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

In this paper we present a novel method of simulating the elegant brushstrokes found in calligraphic lettering and painting. Such simulations have earlier been attempted with physically based or texture-mapped approaches, methods that succeeded in producing aesthetic, but also computationally intensive, results. We introduce a brushstroke model based on a parametric curve, the interval spline. ...

A method is described whereby a G* planar curve consisting of clothoid (Comu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically. and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restric...

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. Th...

This paper generalizes the classical spline using a new construction of spline coalescence hidden variable fractal interpolation function (CHFIF). The derivative of a spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of a nondiagonal iterated function system. Our construction generalizes the construction of Barnsley and Harrington (198...

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to L are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule. Key...

In this paper, we propose to re-size images using an oblique projection operator instead of the orthogonal one in order to obtain faster, simpler, and more general algorithms. The main advantage is that it becomes perfectly feasible to use higher order models (e.g, splines of degree n≥3). We develop the theoretical background and present a simple and practical implementation procedure that uses...

Battle-Lemarie wavelet systems of natural orders are established in the paper. The main result work is decomposition theorem Besov and Triebel-Lizorkin spaces with local Muckenhoupt weights, which performed terms bases generated by such a type. wavelets splines suit very well for study integration operators.

Image subtraction is essential for transient detection in time-domain astronomy. The point spread function (PSF), photometric scaling, and sky background generally vary with time across the field-of-view imaging data taken ground-based optical telescopes. algorithms need to match these variations of flux variability. An algorithm that can be fully parallelized highly desirable future surveys. H...

A computationally inexpensive algorithm for signal interpolation using B-spline functions is presented in this work. Speciically, the convolution between the B-spline coeecients and the B-spline function itself, widely acknowledged as the most costly aspect of B-spline interpolation, is reformulated such that it is directly amenable to implementation at a much lower computational cost (16.25% o...