New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify thèbad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorith...

In this paper, a new smooth slideshow transition effect, Sewing Photos, is proposed while considering both of smooth content transition and smooth camera motion. Comparing to the traditional photo browsing and displaying work, which all focused on presenting splendid visual effects, Sewing Photos emphasizes on the smooth transition process between photos while taking the photo contents into acc...

In this paper, reference trajectory is designed according to minimum energy consumed for multi-robot system, which nonlinear programming and cubic spline interpolation are adopted. The control strategy is composed of two levels, which lower-level is simple PD control and the upper-level is based on the internal average kinetic energy for multi-robot system in the complex environment with veloci...

In this paper, we develop a new cubic spline method for computing approximate solution of a system of fourth-order boundary value problems associated with obstacle, unilateral and contact problems. It is shown that the present method is of order two and gives approximations which are better than those produced by some other collocation, finite difference and spline methods. Numerical examples a...

We construct a generalized Cr-Fractal Interpolation Function (Cr-FIF) f by prescribing any combination of r values of the derivatives f (k), k = 1, 2, . . . , r, at boundary points of the interval I = [x0, xN ]. Our approach to construction settles several questions of Barnsley and Harrington [J. Approx Theory, 57 (1989), pp. 14–34] when construction is not restricted to prescribing the values ...

The Problem: Pixel representations for images do not have resolution independence. When we zoom into a bitmapped image, we get a blurred image. Figure 1 shows the problem for a teapot image, rich with real-world detail. We know the teapot’s features should remain sharp as we zoom in on them, yet standard pixel interpolation methods, such as pixel replication (b, c) and cubic spline interpolatio...

According to the characteristics of the map images, a practical data compression system was introduced in this paper. The main idea of this system is to segment the map image into two images: long-line image and the rest short-line image. For the first one, we use the cubic spline interpolation method to compress it; for the other image, we use arithmetic coding. It is proved by the experiments...

The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...

The currently adopted strategy of EOP estimation from VLBI is to estimate six parameters: UT1, UT1 rate, pole positions and nutation o sets for each 24-hour session independently. Then the resulting time series of raw Earth orientation parameters are ltered and a regression analysis is performed in order to obtain nutation coe cients, polhode of the pole and other physical parameters. Thus, the...

We construct cubic spline approximations of a circle which are four times continuously differentiable and converge with order six.