On the break-ups of spherical centre- and circle-point curves of the PP-PP case

With a pole and two instant centres specified on a unit sphere, a geometrical construction is proposed to determine the spherical centre- and circle-points. The explicit equations of the corresponding spherical centre- and circle-point curves of the PP-PP case are thus obtained by using spherical trigonometry. All break-ups of these spherical centre- and circle-point curves are directly generated from the explicit equations. Through an exhaustive search, it was found that there are four kinds of degenerated curves, i.e. (1) two points and a great circle, (2) two spherical ellipses and a great circle, (3) three orthogonal great circles and (4) a sphere. Two design examples are presented.