C-1 Hermite Shape Preserving Polynomial Splines in R-3

摘要

The C-2 variable degree splines(1-3) have been proven to be an efficient tool for solving the curve shape-preserving interpolation problem in two and three dimensions. Based on this representation, the current paper proposes a Hermite interpolation scheme, to construct C-1 shape-preserving splines of variable degree. After this, a slight modification of the method leads to a C1 shape-preserving Hermite cubic spline. Both methods can easily be developed within a CAD system, since they compute directly (without iterations) the B-spline control polygon. They have been implemented and tested within the DNV Software CAD/CAE system GeniE.