Error analysis for piecewise quadratic curve fitting algorithms
Computer Aided Geometric Design
On monotone and convex spline interpolation
Mathematics of Computation
Local control of interval tension using weighted splines
Computer Aided Geometric Design
Interpolation with exponential B-splines in tension
Geometric modelling
Two dimensional spline interpolation algorithms
Two dimensional spline interpolation algorithms
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline
ACM Transactions on Mathematical Software (TOMS)
Algorithm 574: Shape-Preserving Osculatory Quadratic Splines [E1, E2]
ACM Transactions on Mathematical Software (TOMS)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Convexity-Preserving Piecewise Rational Quartic Interpolation
SIAM Journal on Numerical Analysis
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In this paper we discuss the design of algorithms for interpolating discrete data by using weighted C1 quadratic splines in such a way that the monotonicity and convexity of the data are preserved. The analysis culminates in two algorithms with automatic selection of the shape control parameters: one to preserve the data monotonicity and other to retain the data convexity. Weighted C1 quadratic B-splines and control point approximation are also considered.