The quartic Catmull–Rom spline with local adjustability and its shape optimization

Abstract Parametric interpolatory curves play a vital part in geometric modeling. Cubic Catmull–Rom spline is well-known tool for constructing parametric curves, but it cannot be modified once its control points are fixed. We propose novel quartic with free parameters to tackle this issue. The owns shape adjustability based on inheriting the features of cubic spline. Some modeling examples show that can realize both global adjustment and local by changing parameters. In addition, we give three schemes optimizing spline, which generate minimal internal energy, shape-preserving monotonicity-preserving Numerical indicate proposed effective more practical than data interpolation.