We study the smoothness of the limit function for one dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midway as is usually the case. For the natural generalization of the four point scheme introduced by Dubuc and Dyn, Levin, and Gregory, we show th...

We consider the problem of thin plate spline interpolation to n equally spaced points on a circle, where the number of data points is suuciently large for work of O(n 3) to be unacceptable. We develop an iterative multigrid-type method, each iteration comprising ngrid stages, and n being an integer multiple of 2 ngrid?1. We let the rst grid, V 1 , be the full set of data points, V say, and each...

A method to compute the scattering solutions of a spinless Salpeter equation ~or a Schrödinger equation! with a central interaction is presented. This method relies on the three-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same ...

A method to compute the bound state eigenvalues and eigenfunctions of a Schrödinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the Fourier grid Hamiltonian method for one-dimensional Schrödinger equation. It requires only the evaluation of the potential at equally spaced grid points and yield...

We construct a fast method, OðN logNÞ, for the computation of discrete Gauss transforms with complex parameters, capable of dealing with unequally spaced grid points. The method is based on Fourier techniques, and in particular it makes use of a modified unequally spaced fast Fourier transform algorithm, in combination with previously suggested divide and conquer strategies for ordinary fast Ga...

Digital Terrain Modeling, the Triangulated Irregular Network (TIN) is a representation of a surface derived from irregularly spaced sample points and break line features. Paper deals with the basic concept of Delauney’s triangulation method with its practical approach in ArcGIS. The next section describes the process to convert mass points to TIN model and explores some of the basics of TIN Mod...

Realistic simulation of smoke is used in the special effects industry to produce smoke in both feature films and video games. Traditional simulations utilize uniformly spaced rectangular computational grids to perform the smoke simulation. Various changes had been proposed to improve different aspects of the simulation, including level of details, memory usage and simulation speed. In this thes...

Given finite sets P and T of points in the Euclidean space R, the point pattern matching problem studied in this paper is to find all translations f ∈ R such that P + f ⊆ T . A fast search algorithm with some variants is presented for point patterns P that have regular grid–like geometric shape. The algorithm is analogous to the Knuth–Morris–Pratt algorithm of string matching. The time requirem...

The n-grid En consists of n equally spaced points in [−1,1] including the endpoints ±1. extremal polynomial pn∗ is that maximizes uniform norm ‖p‖[−1,1] among polynomials p degree ≤αn are bounded by one absolute value on En. For every α∈(0,1), we determine limit 1nlog‖pn∗‖[−1,1] as n→∞. interest this comes from a connection with an impossibility theorem stable approximation n-grid.

We propose a novel multiresolution-multigrid based signal reconstruction method from arbitrarily spaced samples. The signal is reconstructed on a uniform grid using B-splines basis functions. The computation of spline weights is formulated as a variational problem. Specifically, we minimize a cost that is a weighted sum of two terms: (i) the sum of squared errors at the specified points; (ii) a...