A univariate method for plane elastic curves Original Research Article

The problem to interpolate Hermite-type data (i.e., two points with attached tangent vectors) with elastic curves of prescribed tension is known to have multiple solutions. A method is presented that finds all solutions of length not exceeding one period of its curvature function. The algorithm is based on algebraic relations between discrete curvature information which allow to transform the problem into a univariate one. The method operates with curves that by construction interpolate a subset of the given data. Hereby the objective function of the problem is drastically simplified. A bound on the maximum curvature value is established that provides an interval containing all solutions.