Center of Mass of a Plane Region
The Center of Mass is the position defined as the mathematical center of mass of a closed polygon (and, by definition, may therefore be located outside the polygon it represents.) e.g., center of mass of a lake, center of mass of an island.
Implementations of the equation of the center of mass are available in C language and in Fortran language.
Center of Mass Equation
By definition, the center of mass of a plane region is given by:
,
where:
- Moment about the x-axis:
- Moment about the y-axis:
- Area of a plane region:
Line Equation
The equation of the line connecting two points:
,
is given by:
where:
- Slope:
- Y-intercept at the y-axis:
