Monotone cubic interpolation

About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.

Numerical Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System

Abstract: In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing and error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.

An algorithm for computing shape-preserving cubic spline interpolation to data

Abstract: We present an algorithm for the construction of shape-preserving cubic splines interpolating a set of data point. The method is based upon some existence properties recently developed. Graphical examples are given.

Lagrange and hermite interpolation by bivariate splines

Abstract: We develop methods for constructing sets of points which admit Lagrange and Hermite type interpolation by spaces of bivariate splines on rectangular and triangular partitions which are uniform, in general. These sets are generated by building up a net of lines and by placing points on these lines which satisfy interlacing properties for univariate spline spaces.

Matrix Cubic Splines for Progressive 3D Imaging

Abstract: Mathematical theory of matrix cubic splines is introduced, then adapted for progressive rendering of images. 2D subsets of a 3D digital object are transmitted progressively under some ordering scheme, and subsequent reconstructions using the matrix cubic spline algorithm provide an evolving 3D rendering. The process can be an effective tool for browsing three dimensional objects, and effectiveness is illustrated with a test data set consisting of 93 CT slices of a human head. The procedure has been implemented on a single processor PC system, to provide a platform for full 3D experimentation; performance is discussed. A web address for the complete, documented Mathematica code is given.

Quadratic B-spline curve interpolation☆

Abstract: Traditional approach in performing even-degree B-spline curve/surface interpolation would generate undesired results. In this paper, we show that the problem is with the selection of interpolation parameter values, not with even-degree B-spline curves and surfaces themselves. We prove this by providing a new approach to perform quadratic B-spline curve interpolation. This approach generates quadratic B-spline curves whose quality is comparable to that of cubic interpolating B-spline curves. This makes quadratic B-spline curves better choices than cubic B-spline curves in some applications in graphics and geometric modeling, since it is cheaper to render/subdivide a quadratic curve and it is easier to find the intersection of two quadratic curves.