Renner, GaborPochop, VladimirJ. L. Encarnacao2015-09-292015-09-2919811017-4656https://doi.org/10.2312/eg.19811013A new method for interpolation is presented which starts from a given set of data pints. The resulting curve consisting of a set of polynomials has tangent vector continuity in the nodes, and can have straight line sections incorporated in it, with preserved continuity properties. The interpolation is local in the sense, that the shape of the curve at a certain data pint is influenced by five data points in its neighbourhood. First the construction of tangent vectors, then the determination Of the parameter intervals are dealt with. These are selected in such a way that a quasi-natural parametrization is held along the whole curve.10.2312/eg.19811013