Path splines with circle envelopes

The purpose of this paper is to introduce the construction of algebraic splines, using sections of envelopes of quadratic families of circles. Such splines are similar to paths and interpolate ordered sequences of point pairs which lie on the plane. These sequences of point pairs satisfy certain cocircularity conditions. Each section of envelope is controlled through a Bézier conic in 3D and its implicit degree is less or equal than four. The control handles of each segment are four interpolation points, two tangent lines and a weight. The weight can be used to dilate or contract locally any section of the path.