DEGENERATE BURMESTER CURVES OF PP-PP MULTIPLY SEPARATED POSITIONS

A new method is proposed to derive the special cases that the center- and circle-point curves of PP-PP multiply separated positions degenerate into the combinations of points, lines and circles. Analytical equations for the construction of the Burmester curves are presented in a simpler form with four parameters. All conditions that yield degenerate forms of the equations are concluded by investigating the parameters. Degenerate Burmester curves are then thoroughly derived from various combinations of the conditions. The results of this work are more complete than existing papers, and presented concisely in tables. Applications of the degenerate curves are also illustrated by an example.