Quadratice Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and...

This paper proposes an optimization technique for the outline capture of planar images. This is inspired by a global optimization algorithm based on multilevel coordinate search (MCS). By starting a search from certain good points (initially detected corner points), an improved convergence result is obtained. The overall technique has various phases including extracting outlines of images, dete...

In this work, we proposed an effective method based on cubic and pantic B-spline scaling functions to solve partial differential equations of fractional order. Our method is based on dual functions of B-spline scaling functions. We derived the operational matrix of fractional integration of cubic and pantic B-spline scaling functions and used them to transform the mentioned equations to a syste...

Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programs of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution hav...

Spline curves are useful in a variety of geometric modeling and graphics applications and covering problems abound in practical settings. This work defines a class of covering decision problems for shapes bounded by spline curves. As a first step in addressing these problems, this paper treats translational spline covering for planar, uniform, cubic B-splines. Inner and outer polygonal approxim...

Presented paper describes the method for finding the intersection of class space rational Bezier curves. The problem curve/curve intersection belongs among basic geometric problems and the aim of this article is to describe the new technique to solve the problem using relief perspective and Bezier clipping.

In this paper, a new approach to solve the cubic B-spline curve fitting problem is presented based on a meta-heuristic algorithm called “dolphin echolocation”. The method minimizes the proximity error value of the selected nodes that measured using the least squares method and the Euclidean distance method of the new curve generated by the reverse engineering. The results of the proposed method...

This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated...

Introduction Relative dose computation is a necessary step in radiation treatment planning. Therefore, finding an approach that is both fast and accurate seems to be necessary. The purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. Materials and Met...