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

front end - keyboard shortcut to invoke Insert new matrix

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plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

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