Center of Mass of a Polygon

crosshairs

none

The result is not valid for self-intersecting polygons!

Both the area and the various moments of a simple polygon can be written as simple functions of the coordinates of the vertices. These formulas can then be used to identify the center of mass of the polygon:

{X,Y}={

M

x

,

M

y

}A

. Move or add new locators and watch the center of mass move. Careful: if the polygon boundary intersects itself, the results are invalid!