Abstract
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 spline curves. This process generates a family of curves which depends on a timelike variable t.
The best approximant is shown to be a stationary point of this evolution process, which is described by a differential equation. Solving it numerically by Euler's method is shown to be related to GaussNewton iterations.
Different ways of constructing suitable initial positions for the evolution are suggested.