graphics - How to ensure that Polygon[list] plots a simple polygon?

Consider the following code which plots a triangle.

 p = {{0, 0}, {.2, 0}, {0, .2}};
 {Cyan, Polygon[Dynamic[p]]} // Graphics

Mathematica graphics

Then adding (for example) {.1, -.1} yields a non-simple polygon with intersecting lines.

AppendTo[p, {.1, -.1}]

Mathematica graphics

Question: Given a list of 2D points that are plotted as a polygon by Graphics. Is there a way to re-order the points such that Graphics plots a simple polygon after a point which has been added that resulted in plotting a non-simple polygon?

Answer

The function you may be looking for is FindCurvePath. Its task is to find reasonable curves through disorganized point sets. It is not guaranteed to find the solution that you find most pleasing but if often gets close. You may also end up with several disconnected lines instead of a single one.

(* some points randomly drawn on a sine shape *)
pts = {#, Sin[#]} & /@ RandomReal[{0, 2 \[Pi]}, 30];

Graphics@Line@pts

Mathematica graphics

(* now with FindCurvePath *)
Graphics@GraphicsComplex[pts, Line@FindCurvePath@pts]

Mathematica graphics

In the case of your point set it finds the following:

Graphics@GraphicsComplex[p, {EdgeForm[Black], Polygon@FindCurvePath@p}]

Mathematica graphics

i.e., a polygon and a line.

Comments

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