by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

A method of generating cubic blending spline curves based on weighted trigonometric and hyperbolic polynomial is presented in this paper. The curves inherit nearly all properties of cubic B-splines and enjoy some other advantageous properties for modeling. They can represent some conics and some transcendental curves exactly. Here weight coefficients are also shape parameters, which are called ...

A class of cubic Bézier-type curves based on the blending of algebraic and trigonometric polynomials, briefly CAT Bézier curves, is presented in this paper. The CAT Bézier curves retain the main superiority of cubic Bézier curves. The CAT Bézier curves can approximate the Bézier curves from the both sides, and the shapes of the curves can be adjusted totally or locally. With the shape parameter...

We provide su cient conditions for the Bernstein-B ezier (BB) form of an implicitly de ned bivariate polynomial over a triangle, such that the zero contour of the polynomial de nes a smooth and single sheeted real algebraic curve segment. We call a piecewise G-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree ...

A new technique and an algorithm have been designed which are meant to automatically capture the outlines of fonts. A more flexible class of B! ezier cubic (generalized Hermite cubic) functions are the basis of this technique. This class of functions involves two families of control parameters, to produce more flexible shapes than ordinary Hermite or B! ezier cubics, in each segment. These func...

The purpose of this study is to investigate the impact of using Trigonometric Graphs, a teacher created web-based simulation, and asynchronous online discussion on students’ understanding of and performance in sketching transformation of trigonometric curves. The participants of the study were 29 Grade 9 students from a Singapore school. The students worked in groups of three or four in experim...