Basis functions of biquadratic polynomial spline spaces over hierarchical T-meshes are constructed. The basis functions are all tensor-product B-splines, which are linearly independent, nonnegative and complete. To make basis functions more efficient for geometric modeling, we also give out a new basis with the property of unit partition. Two preliminary applications are given to demonstrate th...

We analyze the space Sr m,m (T ) of bivariate functions that are piecewise polynomial of bi-degree 6 (m,m) and of smoothness r along the interior edges of a planar T-mesh T . We give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques. We relate this dimension to the weight of the maximal interior segments of the T-mesh, defined for an o...

A T-conic (rational cubic with a quadratic denominator) spiral spline, with shape control parameters, will be discussed with the view to its application in Computer Graphics. An efficient scheme is presented which constructs a curve interpolating a set of given data points and allows subsequent interactive alteration of the shape of the curve by changing the shape control and shape preserving p...

We present a new method, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects a...

Yuanxin Liu: Computations of Delaunay and higher order triangulations, with applications to splines. (Under the direction of Jack Snoeyink.) Digital data that consist of discrete points are frequently captured and processed by scientific and engineering applications. Due to the rapid advance of new data gathering technologies, data set sizes are increasing, and the data distributions are becomi...

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

Some new results on univariate interpolation by weak Cheby-shev spaces, using conditions of Schoenberg-Whitney type and the concept of almost interpolation sets, are given. x1. Introduction Let U denote a nite-dimensional subspace of real-valued functions deened on some set K. We are interested in describing those conngurations T = dimU jT = s: T is called an interpolation set (I-set) w.r.t. U....

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar non-planar meshes arbitrary topology), we present the construction quadratic splines mixed smoothness — C1 smooth away from regions T C0 otherwise. The have several useful B-spline-like properties – partition unity, non-negativity, local support linear independence for straightforward imposition boundary...

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...