Cubic polynomial A-splines:: G1, G2 and inflection point control

We present three results concerning the construction of algebraic splines whose segments are singular cubic and admit a polynomial parameterization. We use the implicit expression of the cubic in barycentric coordinates. We choose each segment of the spline from a monoparametric family of cubic segments that interpolate an additional intermediate point. These splines are of class G 1 (continuous tangent line). We also give, sufficient conditions for the spline to be of class G 2; moreover, in certain cases, the curvature value in the connection points can be prescribed. Also, we offer a method for the design of concavity changing splines. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.