In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

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In this paper results from a forthcoming paper are presented concerning the convexity of multivariate spline functions built from B patches Conditions are given under which it is possible to de ne a control net for such spline functions The control net is understood as a piecewise linear function If it is convex then so is the underlying spline

We develop a rational biquadratic G analogue of the non-uniform C B-spline paradigm. These G splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, and combine them into one smoothly-connected structure. This enables a design process that starts with basic shapes, re-pepresents them in spline form and uses the spline form to provide shape handles for locali...

This paper discusses the dimension of spline spaces S(m,n,m−1, n−1,T ) over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space S(m,n,m− 1, n− 1,T ) and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory...

In this work, we present a generalized method for analysis of data series based on shape constraint spline fitting which constitutes the first step towards a statistically optimal method for qualitative analysis of trends. The presented method is based on a branch-and-bound (B&B) algorithm which is applied for globally optimal fitting of a spline function subject to shape constraints. More spec...

The effect of the modification of knot values on the shape of B-spline curves is examined in this paper. The modification of a knot of a Bspline curve of order k generates a one-parameter family of curves.This family has an envelope which is also a B-spline curve with the same control polygon and of order k 2 1: Applying this theoretical result, three shape control methods are provided for cubi...

We first review B-splines and splines constructed using B-splines as the basis functions.