Shape-Preserving C 3 Interpolation: The Curve Case

We present a new method for the construction of shape-preserving curves interpolating a given set of 3D data. The interpolating functions are obtained using quintic-like spaces of polynomial splines with variable degrees. These splines are of class C³ and are therefore curvature and torsion continuous and possess a very simple geometric structure, which permits to easily handle the shape-constraints.