A class of quintic spline curves whose shape can be controlled via the control net and a pair of tension parameters for each spline segment is the subject of this paper. The authors start with a description of a geometric construction of the Bezier control points for a C4 quintic spline. They introduce the concept of FC4 continuity, then reduce the number of shape parameters from seven to two per segment, and explain how the previous construction can be modified to produce a C2 ∩ FC3 quintic spline, for which the effect of the shape parameters is more intuitive. Several theorems are presented to establish that the curve approaches the piecewise linear curve defined by the control net as the shape parameters tend to zero, hence verifying the shape preservation of these splines. Applications to interpolation and least squares approximation of spatial data are discussed, and several examples of each are presented.
Readers should be familiar with the concept of Frenet continuity (FC), and the associated geometric constructions. Details of some proofs are left to other referenced papers.
This paper is readable, though it is clear that the authors could have used some help with the English language.
