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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | 1x 1x 11x 11x 11x 11x 45x 45x 45x 45x 45x 45x 45x 45x 11x 11x 11x | import { type Cartesian, type Polygon } from './@types/geometry.ts';
import { modulo } from './modulo.ts';
/**
* Calculates the centroid (geometric center) of a polygon.
*
* The centroid is computed using the formula for the centroid of a non-self-intersecting closed polygon.
* The vertices should be provided in order (either clockwise or counterclockwise).
* @param vertices - An array of points representing the vertices of the polygon.
* @returns The centroid as a Cartesian coordinate.
* @example
* ```typescript
* centroid([
* { x: 0, y: 0 },
* { x: 0, y: 5 },
* { x: 10, y: 5 },
* { x: 10, y: 0 },
* ]);
* // { x: 5, y: 2.5 }
* ```
* @remarks
* The function assumes the polygon is non-self-intersecting.
* @group Geometry
* @category Polygon
*/
export function centroid(vertices: Polygon): Cartesian {
let a = 0;
let x = 0;
let y = 0;
for (let i = 0; i < vertices.length; ++i) {
const j = modulo(i + 1, vertices.length);
const v0 = vertices[i];
const v1 = vertices[j];
const f = v0.x * v1.y - v1.x * v0.y;
a += f;
x += (v0.x + v1.x) * f;
y += (v0.y + v1.y) * f;
}
const d = a * 3;
return { x: x / d, y: y / d };
}
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