The term algebraic spline or A-spline refers to splines which are pieced to gether from algebraic curves. These were introduced by Sederberg [13,14] and were further studied in [1,7,8,9]. They are cubic if each piece is a segment of an algebraic cubic, which means that it has an equation of the form
in Euclidean coordinates, or
in barycentric coordinates, where a,j and a ,^ are real constants and s -h t u = 1. G2-continuity means that adjacent segments of the spline have the same tangent lines and curvatures at the joint points. The algebraic splines discussed here are locally convex; that is, free of inflection points.