Assume the position of the *i*th corner is $(\varphi \u2032c,i,rc,i)$ in the PCS and let *n* be the number of the polygon sides in the vertical cross section. We propose a one-to-one mapping from $(\varphi \u2032c,i,\varphi \u2032c,i+1)$ to $((i\u22123/2)\pi ,(i\u22121/2)\pi )$, which is the domain for trigonometric function $cos\u2009\theta $ that all the points in this domain are positive or negative. The mapping is proposed as
Display Formula

(12)$\varphi \u2032\u21a6\theta :\u2009where\u2009\theta =\varphi \u2032\u2212\varphi \u2032c,i\varphi \u2032c,i+1\u2212\varphi \u2032c,i+i\u221232$