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I have a polyline and I want to simplify it with Douglas-Peucker. It's an easy algorithm, but what if there are points with the same distance. What point should I select? Is there a reasonable solution?

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I would consider the curvature in that case too. If the curvature is small - then it is a flat region - so you can safely remove it - your 4th point for example. If the curvature is large (your 5th point for example), even if the distance is the same, you should most likely leave it alone.

I would actually recommend a curvature based method coming before Douglas-Peucker.

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  • $\begingroup$ Could you please suggest a good "curvature based method"? $\endgroup$
    – rr84
    Commented Oct 11, 2019 at 17:17
  • $\begingroup$ You can start by removing points with the smallest curvature (as an approximation, you can use the angle that they form). $\endgroup$
    – lightxbulb
    Commented Oct 11, 2019 at 17:41

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