centroidal

Centroidal is an adjective relating to the centroid, the point that represents the center of mass or geometric center of a region with uniform density. In two-dimensional geometry, the centroid is the balance point of a lamina; in three dimensions, it is the average position of all volume elements. For simple shapes, the centroid has well-known locations: a triangle's centroid is the intersection of its medians; a rectangle's centroid lies at the intersection of its diagonals. In general, the centroid can be found by area- or volume-weighted averages, and for polygons or polyhedra it can be computed by standard summation formulas or integration.

Centroidal concepts are central in statics and rigid-body mechanics. The centroidal axes are coordinate axes that pass through the centroid; moments of inertia calculated about these axes are called centroidal moments of inertia. The parallel axis theorem relates these to moments about axes through other points. Knowing the centroid helps in designing cross-sections so bending and shear responses are predictable and balanced.

In more advanced contexts, centroidal is used in computational geometry and optimization. Centroidal Voronoi tessellations arise when the generating point of each Voronoi cell coincides with the cell's centroid, a property exploited in mesh generation and data quantization.