\(C^n\)-continuous \(B\)-type spline curves with its localization interpolation and approximation (Q698386)

The author presents a class of \(C^n\)-continuous \(B\)-type spline curves with length 4 local support and with some parametric factors, and such that each segment of the curves can be generated by 4 control points. In addition, the author shows that, when the parametric factors satisfy certain conditions, the degrees of the curves can be decreased to be optimal. This fact motivates the notion of free-type alternative spline curve. Furthermore, if the parametric factors tends to zero, the curves globally approximate the control polygon.