Topic
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.
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TL;DR: An algorithm for creating tangent continuous splines from segments of algebraic cubic curves, which naturally contains conic splines as a subfamily is presented.
Abstract: We present an algorithm for creating tangent continuous splines from segments of algebraic cubic curves. The curves used are cubic ovals, and thus are guaranteed convex. Each segment is given by an equation which has five coefficients, thus four degrees of freedom available for shape control. We describe shape handles that work via the coet%cients ta control the curve. Each segment can be chosen to interpolate one more point and slope and has two additional fullness parameters to control the shape. This family of curves naturally contains conic splines as a subfamily.
19 citations
TL;DR: In this article, the shape preserving C1-interpolation of data sets given on rectangular grids was studied and rational biquadratic splines were derived which are sufficient for the positivity, monotonicity, and S-convexity.
Abstract: This paper is concerned with shape preservingC1-interpolation of data sets given on rectangular grids. Using special rational biquadratic splines, criteria are derived which are sufficient for the positivity, monotonicity, andS-convexity and which, in addition, are satisfied for sufficiently large rationality parameters.
18 citations
01 Jan 2002
TL;DR: In this article, the authors used cubic spline interpolation to represent the centerline of a road, for curves in both R and R, and proposed algorithms to create a representation based on arc length and evenly spaced nodes along the center line.
Abstract: We study the use of cubic spline interpolation to represent the centerline of a road, for curves in both R and R . We look at algorithms to create a representation based on arc length and evenly spaced nodes along the centerline. We also consider methods for moving between rectangular coordinates and coordinates based on distance along the centerline and the offset from that centerline (in R) and a related decomposition in R .
18 citations
15 Apr 2015
TL;DR: In this article, the authors apply hidden variable fractal interpolation to associate a class of R-valued continuous fractal functions with a prescribed continuous function, and obtain positive C-cubic spline interpolation functions corresponding to a prescribed set of positive data.
Abstract: The notion of hidden variable fractal interpolation provides a method to approximate functions that are self-referential or non-self-referential, and consequently allows great flexibility and diversity for the fractal modeling problem. The current article intends to apply hidden variable fractal interpolation to associate a class of R-valued continuous fractal functions with a prescribed continuous function. Suitable values of the parameters are identified so that the fractal functions retain positivity and regularity of the germ function. As an application of the developed theory, we obtain positive C-cubic spline hidden variable fractal interpolation functions corresponding to a prescribed set of positive data, thus initiating a new approach to shape preserving approximation via hidden variable fractal function. Depending on the values of the parameters, these positive interpolants can reflect the self-referentiality or non-self-referentiality of the original data defining function and fractality of its derivative. Therefore, the present scheme outperforms the traditional nonrecursive positivity preserving C-cubic spline interpolation scheme and its fractal extension studied recently in the literature. Mathematics Subject Classification (2010). Primary: 28A80; Secondary: 41A05, 41A10, 41A29, 41A30.
18 citations
26 Nov 2007
TL;DR: An efficient local cubic spline interpolation curve modeling algorithm is proposed and an approach to apply the algorithm to model arbitrary shape built from free form curves is provided.
Abstract: We present an approach to model handwriting like curves with the cubic spline interpolation function. Different from NURBS such as Bezier and B-spline curve modeling, the huge complexity of the traditional spline interpolation have been obstructed and limited the application of spline curve modeling. We propose an efficient local cubic spline interpolation curve modeling algorithm and provide an approach to apply the algorithm to model arbitrary shape built from free form curves.
18 citations