Imagine I have an arbitrary concave polygon. I need to find/generate a point inside of it, efficiently.

`RandomPoint@Polygon@points` is relatively fast only for simple such polygons.

 n=1;(* toy polygon complexity *)

 points=Join[Transpose[{Range[2*n+1]*5,Drop[Flatten@ConstantArray[{0,45},n+1],-1]}],Transpose[{Reverse@Range[2*n+1]*5-5,Drop[Flatten@ConstantArray[{55,10},n+1],-1]}]];

 insidepoint=RandomPoint@Polygon@points;//RepeatedTiming

 Show[
 Graphics@Thread@Line@Transpose[{points,RotateLeft@points}],
 Graphics@{Red,PointSize[Medium],Point@insidepoint}
 ]

<h2>n=1</h2>
> {0.00244676, Null}


[![enter image description here][1]][1]

<h2>n=100</h2>

> {0.233274, Null}
[![enter image description here][2]][2]

 <h2>n=1000</h2>

> {2.84268, Null}

So, for complex polygons,`RandomPoint@Polygon` is very, very slow.

Is there a method to find a point inside a convex polygon efficiently, no matter the complexity?



 [1]: https://i.sstatic.net/6F8UkEBM.jpg
 [2]: https://i.sstatic.net/VCodWkIt.jpg