Method to Determine the Centroid of Non-Homogeneous Polygons Based on Suspension Theory

Abstract

The centroid is most often used to describe the average position of an object’s mass and has very important applications in computational geometry, applied physics, and spatial information fields, amongst others. Based on the suspension theory of physics, this paper proposes a new method to determine the centroid of a non-homogeneous polygon by the intersection of the two balance lines. By considering the inside point value and distance to the balance line, the proposed method overcomes the traditional method’s limitation of only considering the geometric coordinates of the boundary points of the polygon. The results show that the consideration of grid distance and grid value is logical and consistent with the calculation of the centroid of a non-homogeneous polygon. While using this method, a suitable value for relative parameters needs to be established according to specific application instances. The proposed method can be applied to aid in solving specific problems such as location assessment, allocation of resources, spatial optimization, and other relative uses.