Shape determination of planar uniform cubic B-spline segments
A parametric uniform cubic B-spline curve in the plane is determined by four control vertices. The authors investigate how the movement of any control vertex affects the shape of the curve segments. \textit{C. Y. Wang} [ibid. 13, 199-206 (1981)] gave conditions on the coefficients of the cubic polynomials such that the corresponding cubic B-spline segment has a corner or cusp, one inflection point, two inflection points, or forms a loop. In this paper, simpler conditions are developed which make it possible to divide the plane into regions such that placing an appropriate control vertex in one of the regions will cause the cubic B-spline segments to have a particular feature according to the above classification.
scientific article; zbMATH DE number 4164005