If there are two links, and , then the C-space can be nicely visualized as a square with opposite faces identified. Each coordinate, and , ranges from 0 to , for which . Suppose that each link has length . This yields . A point is transformed as
To obtain polynomials, the technique from Section 4.2.2 is applied to replace the trigonometric functions using and , subject to the constraint . This results in
Multiplying the matrices in (4.59) yields the polynomials, ,
Steven M LaValle 2020-08-14