On monotone and convex spline interpolation
Mathematics of Computation
Co-Monotone interpolating splines of arbitrary degree—a local approach
SIAM Journal on Scientific and Statistical Computing
An algorithm for computing shape-preserving interpolating splines of arbitrary degree
Journal of Computational and Applied Mathematics
Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Post-processing piecewise cubics for monotonicity
SIAM Journal on Numerical Analysis
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Accurate monotone cubic interpolation
SIAM Journal on Numerical Analysis
Fundamentals of numerical computing
Fundamentals of numerical computing
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Digital Image Warping
Monotonic Cubic Spline Interpolation
CGI '99 Proceedings of the International Conference on Computer Graphics
Pocketing toolpath computation using an optimization method
Computer-Aided Design
Multiple-cue saliency measurement and optimized image composition for image retargeting
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
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 C2 continuity, a property that permits them to satisfy a desirable smoothness constraint. Unfortunately, that same constraint often violates another desirable property: monotonicity. It is possible for a set of monotonically increasing (or decreasing) data points to yield a curve that is not monotonic, i.e., the spline may oscillate. In such cases, it is necessary to sacrifice some smoothness in order to preserve 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 C2 cubic spline interpolation results are presented. Extensions to shape preserving splines and data smoothing are described.