Geometric control of G2-cubic A-splines Original Research Article

A-splines are piecewise algebraic curves, constructed in a control polygon that is a sequence of triangles meeting at the vertices. The arc in a given triangle is a cubic segment that joins these vertices and interpolates also the slope and curvature at each endpoint. This arc in each triangle is controlled by three other shape handles: an interior point that is interpolated, the slope at the interior point, and a tension parameter. The individual arcs can never be singular and are always convex. An inflection point of an A-spline must be placed at a junction point.