The centroid of an object is defined as the arithmetic mean of all points of the object. For non-convex objects, the centroid is often not a part of the object itself:
Is there a definition of a centroid-like point which always lies within the object?
A definition that tackles 2 dimensional polygon objects is sufficient. I could think of something like the following, however, I would prefer a well-known definition if there is one:
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Let $s_p(a, b)$ be the shortest path from $a \in p$ to $b \in p$ such that all points of the path are within $p$.
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Let $S_p := \{s_p(a, b) | a, b \in p\}$.
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Let $d$ be the longest path in $S_p$.
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The mid point of $d$ is a centroid-like point and it always lies within $p$.
Best Answer
In geography there is an interesting point called Pole of inaccessibility: the most distant internal point from the polygon outline.
It is found by an iterative method, described in the Methodology section of this paper.
Links of interest:
https://sites.google.com/site/polesofinaccessibility/
https://github.com/mapbox/polylabel