Although B´ezier control polygons are useful tools to express and control the shape of polynomial curves, they

are not suitable to control Pythagorean hodograph (PH) curves, since any slight modification of a single B´ezier

control points make the curve lose the PH property. To remedy this problem, different types of control polygons

such as the Gauss–Legendre polygon [1, 2] and the Gauss–Lobatto polygon [2] were introduced. In this work,

we analyze the shape control functionality of these polygons from the viewpoint of hodographs. Edges of these

polygons can be understood as points in the hodograph space, and the curve construct process corresponds to

computing the hodograph that interpolates the velocity data followed by integrating it. This approach can be

applied not only to PH curves but also to general polynomial curves.