A new local control spline with shape parameters for CAD/CAM
The authors propose an algorithm for the construction of a spline curve which they call BLC-spline (I guess the abbreviation is coming from best local control spline). The spline is defined by a sequence of \(n\) control vertices \(V_1,\dots, V_n\) in \(\mathbb{R}^3\) and is composed of \(n-2\) curve segments of the form: \(P_j(t)= \sum^2_{j= 0} B_j(t) V_{i+ j}\), \(i= 1,\dots, n- 2\), where \(B_j(t)\) is a quartic polynomial. The curve has \(G^2\) continuity. One of the advantages of the BLC-spline is its best local independence among the splines that have \(G^2\) or \(C^2\) continuity.
scientific article; zbMATH DE number 687924