Planar cubic \(G^{1}\) interpolatory splines with small strain energy
A classical problem of the construction of a cubic \(G^1\) continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. The tangent directions are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally. The spline is regular, cusp-, loop- and fold-free. Numerical examples demonstrate effectiveness of the considered method.
scientific article; zbMATH DE number 5863174
scientific article