I want to create the following animation with Mathematica.

[![Enter image description here][1]][1]

What is the simplest way to do so?

My first effort:

 GenerateLines[a_, b_, r_, n_] :=
 Table[r {Cos[\[Theta]], Sin[\[Theta]], 0}, {\[Theta], a, b, (b - a)/
 n}];
 basePts = GenerateLines[\[Pi]/6, 2 \[Pi] - \[Pi]/6, 3, 200];
 peakPt = {{0, 0, 3}};
 baseLine = Line@basePts;
 slantedLines = Line /@ Tuples[{basePts, peakPt}];
 Graphics3D[{baseLine, slantedLines}]

[![Enter image description here][2]][2]

 [1]: https://i.sstatic.net/mBkFw.gif
 [2]: https://i.sstatic.net/ung5S.png