Table 1.

Equations of polynomials, cross-sectional area (CSA), surface area (SA) and volume (V) for the Two Curves Method (TCM) and the One Curve Method (OCM). p(x) is the posterior polynomial, a(x) is the anterior polynomial and h(x) is the polynomial representing the contour of a half-meridional section of the lens. The coefficients of the three polynomials are denoted by f_p, f_a and f_h. D, bA and bP are the diameter, anterior thickness and posterior thickness of the lens.

Two Curves Method (TCM)	One Curve Method (OCM)
$p(x)=bP+{\displaystyle \sum _{i=1}^5}{f}_{p(2i)}{(x)}^{2i}$	$h(x)=\frac{D}{2}+{\displaystyle \sum _{i=1}^{10}}{f}_{h(i)}{(x)}^i$
$a(x)=-bA+{\displaystyle \sum _{i=1}^5}{f}_{a(2i)}{(x)}^{2i}$
$\mathit{CSA}={\displaystyle \underset{-D/2}{\overset{D/2}{\int }}}[p(x)-a(x)]dx$	$\mathit{CSA}=2{\displaystyle \underset{-bP}{\overset{bA}{\int }}}h(x)dx$
$\begin{array}{l}SA=2\pi {\displaystyle \underset{0}{\overset{D/2}{\int }}}x\sqrt{1+{\left[p^{\prime }(x)\right]}^2}dx\\ +2\pi {\displaystyle \underset{0}{\overset{D/2}{\int }}}x\sqrt{1+{\left[a^{\prime }(x)\right]}^2}dx\end{array}$	$SA=2\pi {\displaystyle \underset{-bP}{\overset{bA}{\int }}}h(x)\sqrt{1+{[h^{\prime }(x)]}^2}dx$
$V=2\pi {\displaystyle \underset{0}{\overset{D/2}{\int }}}x[p(x)-a(x)]dx$	$V=\pi {\displaystyle \underset{-bP}{\overset{bA}{\int }}}{[h(x)]}^{2}dx$