in this work, we proposed an efective method based on cubic and pantic b-spline scaling functions to solve partial differential equations of frac- tional order. our method is based on dual functions of b-spline scaling func- tions. 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 ...

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...

In this paper we present a new method for the model of interpolation sweep surfaces by the C-continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control point...

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

Although B-spline curves and surfaces have enjoyed a long established place in the graphics community as constructive modeling tools, the use of B-spline approximation techniques has received relatively little attention in rendering. In this work we explore the use of 4D and 5D tensor product B-spline functions to represent surface radiance, and establish that, when appropriately applied, they ...

This paper presents a non-uniform cubic C spline framework that unifies three scenarios for incorporating data from basic curves, such as spirals and conics. In the first scenario, no parameterization of the basic curves is available, only well-spaced samples; in the second, a parameterization is available but cannot be used directly in a spline framework; only in the third scenario can pieces ...

This paper presents an integrated set of tools to facilitate the manipulation and reuse of motion capture data. A functional representation in terms of nonuniform B-splines provides a compact and eecient description of motion sequences. A collection of B-spline curves attached to a hierarchical structure is used to represent the animation of articulated gures. A set of primitive operators actin...

This paper addresses the problem of joint rate-distortion optimization of spline curves for optimal video object shape coding. It proposes a B-spline snake model which minimizes rate-distortion energy to find optimal spline coefficients. A continous model of a contour distortion is used which models the shape reconstruction error. A continous model of a coding bitrate is based on the relative i...

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...