Table 3.

Mathematical forms for algorithmically generated targets: x = u, y = v, and z(u,v)

Design	Form of $z\left(u,v\right)$
Fig. 6	Row 1	$z=0.2\left(u+v\right)\left(2-u-v\right)$
	Row 2	$z=0.3\left(u+v\right)\left(2-u-v\right)$
	Row 3	$z=0.1{\left(u+v\right)}^2\left(2-u-v\right)$
	Row 4	$z=0.2{\left(u+v\right)}^2\left(2-u-v\right)$
	Row 5	$z=-0.1{\left(2u-1\right)}^2\sin \left[\left(v-0.5\right)\pi \right]+0.1$
Fig. 7b		$\begin{array}{c}\hfill z=0.2\left(u+v\right)\left(2-u-v\right)\left(-\frac{4}{19}u+\frac{15}{59}v\right)\hfill \\ \hfill \cdot \left(-5u^2-\frac{3}{4}u+1\right)\left(\frac{10}{3}{v}^2-\frac{2}{5}v+1\right)\hfill \end{array}$