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[?] Create a constrained locator inside a polygon?

Dear Community,

I have a closed polygon, and I would like to place a locator into it, so it remains constrained to the interior of the polygon, i.e. it never leaves the polygon when I drag it. How could I do it? My polygon is attached.

Tx for the kind help in advance, Andras

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POSTED BY: Andras Gilicz
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This seems to work:

DynamicModule[{pt = {.5, 10^7}}, 
 Graphics[ {LightBlue, Polygon[pts], 
   Locator[Dynamic[pt, (pt = RegionNearest[Polygon[pts], #]) &]]} , 
  Axes -> True, AspectRatio -> 1]]
POSTED BY: Gianluca Gorni

Dear Gianluca thank you so much, works indeed, yet I get a continuous flow of warnings upon moving the locator to the boundary: 

    LinearSolve::luc: Result for LinearSolve of badly conditioned matrix {{3.71649*10^13,3.71649*10^13},
{3.71649*10^13,3.71649*10^13}} may contain significant numerical errors.      etc.

How could I overcome this?

Tx in advance, best regards Andras
POSTED BY: Andras Gilicz

Now its OK, I've scaled down the polygon by 1.0E6, and now its fine. Tx once again Andras
POSTED BY: Andras Gilicz
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