Paper Info
Title
Monotonic Cubic Spline Interpolation
Abstract
This paper describes the use of cubic splines for interpolating monotonic data sets. Interpolating cubic splines are popular for fitting data because they use low-order polynomials and have $C^2$ continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity.The goal of this work is to determine the smoothest possible curve that passes through its control points while simultaneously satisfying the monotonicity constraint. We first describe a set of conditions that form the basis of the monotonic cubic spline interpolation algorithm presented in this paper. The conditions are simplified and consolidated to yield a fast method for determining monotonicity.This result is applied within an energy minimization framework to yield linear and nonlinear optimization-based methods. We consider various energy measures for the optimization objective functions. Comparisons among the different techniques are given, and superior monotonic cubic spline interpolation results are presented.
Year
DOI
Venue
1999
10.1109/CGI.1999.777953
Computer Graphics International
Keywords
Field
DocType
superior monotonic cubic spline,monotonic cubic spline interpolation,monotonicity constraint,desirable smoothness constraint,interpolation result,energy minimization framework,cubic spline,desirable property,fitting data,monotonic data set,satisfiability,optimization,interpolation,polynomials,computational geometry,objective function,nonlinear optimization,curve fitting,cubic splines
Spline (mathematics),Mathematical optimization,Box spline,Spline interpolation,Mathematical analysis,Interpolation,Smoothing spline,Bicubic interpolation,Monotone cubic interpolation,Cubic Hermite spline,Mathematics
Conference
ISBN
Citations 
PageRank 
0-7695-0185-0
15
2.78
References 
Authors
1
2
Name
Order
Citations
PageRank
George Wolberg1783100.30
Itzik Alfy2152.78