Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of approximating a given set of data points by splines composed of Pythagorean hodograph (PH) curves is addressed.  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 non-linear curve fitting problem,  formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a time-like 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 Gauss-Newton iterations. Different ways of constructing suitable initial positions for the evolution are suggested.
['Martin Aigner', 'Zbynek Sir', 'Bert Jüttler']
I am writing a research paper on a idea Evolution-based least-squares fitting using Pythagorean hodograph spline curves
[{"from": "human", "value": "I am writing a research paper on a idea Evolution-based least-squares fitting using Pythagorean hodograph spline curves"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem of approximating a given set of data points by splines composed of Pythagorean hodograph (PH) curves is addressed.  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 non-linear curve fitting problem,  formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a time-like 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 Gauss-Newton iterations. Different ways of constructing suitable initial positions for the evolution are suggested."}]