Estimating Lorenz Curve of Income by Cubic Spline with Multiple Knots

Least Squares Cubic Spline Approximation I Fixed Knots

Constrained shape modification of cubic B-spline curves by means of knots

The effect of the modification of knot values on the shape of B-spline curves is examined in this paper. The modification of a knot of a Bspline curve of order k generates a one-parameter family of curves.This family has an envelope which is also a B-spline curve with the same control polygon and of order k 2 1: Applying this theoretical result, three shape control methods are provided for cubi...

A fast algorithm for cubic B-spline curve fitting

Based on the matrix perturbation technique. a fast-fitting algorithm using uniform cubic B-spline curves is presented. Our algorithm entails much less floating-point operations when compared with Gaussian elimination method. In addition, our result can be applied to solve the closed cubic B-spline curve-fitting problem. Experimental results are included for a practical version. These experiment...

Spline Curve Approximation and Design by Optimal Control over the Knots Using Genetic Algorithms

In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [23] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control ove...

Modelling Lorenz curve

There has been a large number of studies in which the scientists have built models for income distributions. As an alternative, some have built models for Lorenz curves. The step from Lorenz curve to distribution function is more difficult than the step from distribution function to Lorenz curve. There is a difference between advanced and simple Lorenz models. Advanced models with several param...