Centroid of contiguous polygonsSay that I know which are the centroids of two polygons. These polygons share a number of edges (they belong to a planar subdivision). I want to compute the union of the two polygons and also to know the centroid of the new polygon which covers the other two. I know I could recompute the centroid taking the points of the new polygon. But, is there a way to obtain the centroid by knowing the other centroids, without the need for recomputing everything from scratch?

Question

falwsay · Accepted Answer

Step 1If, when you computed the centroids, you also computed the polygon areas, then the answer is yes. The new centroid is       c    new    =            A      1                      A        1            +              A        2                  c    1    +            A      2                      A        1            +              A        2                  c    2    ,, where the       A    i   are the areas and the       c    i   are the centroid points.Step 2By the way, you can also compute the new area with the update rule       A    new    =      A    1    +      A    2    ..I know that&#039;s silly, but if you&#039;re hoping to proceed inductively, it&#039;s actually pretty useful.By the way, the two polygons under consideration need not be adjacent. On the other hand, they must not overlap, unless you&#039;re willing to consider the overlap area as counted twice.

Answered question

Answer & Explanation

New Questions in High school geometry