In this article, we address the problem of interpolating data points lying on a regular grid by C 1-continuous L1-bicubic spline surfaces. Our algorithm is based on a local univariate L1 minimization method which enable us to calculate first derivative values for C 1-cubic spline curves. In order to construct the interpolation surface, we calculate four derivative values at each data point usin...

The color filter array (CFA) captures only one-third of the necessary color intensities and the full color image is generated from the captured data by interpolation. In recent years, the algorithm of Bayer patterned image compression based on “structure separation” has achieved better image quality. On the basis of previous work, the algorithm based on the all phase biorthogonal transform (APB...

“The NURBS Book” [L. Piegl, W. Tiller, The NURBS Book, second edn, Springer, 1997] is very popular in the fields of computer aided geometric design (CAGD) and geometric modeling. In Section 9.5.2 of the book, the well-known problem of the local cubic spline approximation is discussed. The key in local cubic spline approximation is cubic polynomial interpolation. In this short paper, we present ...

The purpose of this paper is to provide sufficient geometric conditions that imply the existence of a cubic parametric polynomial curve which interpolates six points in the plane. The conditions turn out to be quite simple and depend only on certain determinants derived from the data points.

A piecewise rational cubic spline [5] has been used to visualize the positive data in its natural form. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of a rational cubic have been constrained in such a way that they preserve the shape of the positive data in the view of positive curve. As far as visual smoothness is ...

We describe an algorithm for constructing point sets which admit unique Lagrange and Hermite interpolation from the space S 1 3 (() of C 1 splines of degree 3 deened on a general class of triangulations. The triangulations consist of nested polygons whose vertices are connected by line segments. In particular, we have to determine the dimension of S 1 3 (() which is not known for arbitrary tria...

In this paper, geometric Hermite interpolation by planar cubic G1 splines is studied. Three data points and three tangent directions are interpolated per each polynomial segment. Sufficient conditions for the existence of such G1 spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data a...

An algorithm for the local interpolation of a mesh of cubic curves with 3-and 4-sided facets by a piecewise cubic C ~ surface is stated and illustrated by an implementation. Precise necessary and sufficient conditions for oriented tangent-plane continuity between adjacent patches are derived, and the explicit constructions are characterized by the degree of the three scalar weight functions tha...

An explicit representation of a C1 piecewise rational cubic spline has been developed, which can produce a monotonic interpolant to given monotonic data. The explicit representation is easily constructed, and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant is given.

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 ...