We analyze an alternative to classical Zernike fitting based on the cubic B-spline model, and compare the strengths and weaknesses of each representation over a set of different wavefronts that cover a wide range of shape complexity. The results obtained show that a Zernike low-degree polynomial expansion or a cubic B-spline with a low number of breakpoints are the best choices for fitting simp...

We generalize the univariate divided difference to a multivariate setting by considering linear combinations of point evaluations that annihilate the null space of certain differential operators. The relationship between such a linear functional and polynomial interpolation resembles that between the divided difference and Lagrange interpolation. Applying the functional to the shifted multivari...

A sphere is a fundamental geometric object widely used in (computer aided) design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal approximation of equilateral spherical triangles by patches if measure quality (simplified) radial error. As consequence, approximations unit spline underlying on par...

In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method. Keyw...

This paper points out that the fundamental partial differential equation (PDE) implies that the drifts of the underlying processes are irrelevant, regardless whether the state factors are tradable or not. Since the simple boundary condition for default-free discount bonds can be satisfied by a linear discount function, the variances and covariances of the underlying processes are also irrelevan...

In this paper we address the issue of designing developable surfaces with Bézier patches. We show that developable surfaces with a polynomial edge of regression are the set of developable surfaces which can be constructed with Aumann’s algorithm. We also obtain the set of polynomial developable surfaces which can be constructed using general polynomial curves. The conclusions can be extended to...

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...

Polynomial Pythagorean hodograph (PH) curves form a remarkable subclass of polynomial parametric curves; they are distinguished by having a polynomial arc length function and rational offsets (parallel curves). Many related references can be found in the article by Farouki and Neff on C1 Hermite interpolation with PH quintics. We extend the C1 Hermite interpolation scheme by taking additional c...

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative that geometrically constructed and form convex of unity. With the help control polynomial theory introduced herein, Marsden identity ...