C2 Local convexity-preserving interpolation through the control point form method

C

² continuous convexity-preserving parametric curves in ℝ² is presented. The control point form method, which was developed in the field of numerical grid generation, is used here to construct interpolating curves. Good control over the shape of the curves is obtained thanks to the capability of the proposed approach to interpolate not only the data points, but also some directions suitably associated with them.