Hermite Interpolation with Rational Splines with Free Weights

Abstract

In this text we present an approach for Hermite interpolation with rational splines without predefined weight factors. We rearrange the equation of the derivative of the rational spline function into a homogeneous linear system of equations in homogeneous space. We use this linear system to formulate different interpolation problems, with the weight factors as well as the control points as a solution. In the first approach, we solve the linear system directly by adding only one inhomogeneous equation to normalise the weights. This approach has some significant constraints. The second approach uses the linear system as a secondary condition for maximizing the minimum weight. This way allows us to obtain method more open regarding the number of interpolation points. In the third approach, we reduce the number of interpolation points to approximate the values of the function between the interpolation points.