Applet: A parametrized helicoid -- subapplet
The function $\dlsp(\spfv,\spsv) = (\spfv\cos \spsv, \spfv\sin \spsv, \spsv)$ parametrizes a helicoid when $(\spfv,\spsv) \in \dlr$, where $\dlr$ is the rectangle $[0,1] \times [0, 2\pi]$. The region $\dlr$ is shown as the green rectangle floating above the helicoid. You can drag the green point in $\dlr$ to specify both $\spfv$ and $\spsv$. If, for example, you drag the green point along the bottom of the rectangle, you change $\spfv$ while leaving $\spsv=0$. Similarly, if you drag the green point along the right side of the rectangle, you change $\spsv$ while leaving $\spfv=1$. You cannot directly move the red point on the surface as it is moves with $\spfv$ and $\spsv$ to be at the point $\dlsp(\spfv,\spsv)$.
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