Evolution-based least-squares fitting using Pythagorean hodograph spline curves

Evolution-based least-squares fitting using Pythagorean hodograph spline curves

The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general representations of shapes. In order to solve the highly nonlinear curve fitting problem, we formulate an evolution process within the family of PH ...

Least-Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process

The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. In order to solve this highly non-linear problem, we formulate an evolution process within the family of PH spline curves. This process generates a one–parameter family of curves which depends on a time–like parameter t. The best approximant is shown to be a stationary ...

On Interpolation by Planar Cubic G Pythagorean-hodograph Spline Curves

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...

Least-Squares Fitting of Data with B-Spline Curves

On interpolation by Planar cubic G2 pythagorean-hodograph spline curves

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...