Chapter 16.6, Problem 16E

Match the equations with the graphs labeled I–VI and give reasons for your answers. Determine which families of grid curves have u constant and which have v constant.

$x=\left(1-u\right)\left(3+\cos v\right)\cos 4\pi u$,

$y=\left(1-u\right)\left(3+\cos v\right)\sin 4\pi u$,

$z=3u+\left(1-u\right)\sin v$