Centroid

centroid.dart

import 'dart:math';

num add(num a, num b) => a + b;

num sumPoints(
  List<Point> points,
  num Function(num) generator,
) =>
    List.generate(
      points.length,
      generator,
    ).reduce(add);

num Function(int i) commonPart(List<Point> points) => (int i) =>
    points[i].x * points[(i + 1) % points.length].y -
    points[(i + 1) % points.length].x * points[i].y;

num internalArea(List<Point> points) => sumPoints(
      points,
      commonPart(points),
    );

num xPart(List<Point> points) => sumPoints(
      points,
      (i) =>
          (points[i].x + points[(i + 1) % points.length].x) *
          commonPart(points)(i),
    );

num yPart(List<Point> points) => sumPoints(
      points,
      (i) =>
          (points[i].y + points[(i + 1) % points.length].y) *
          commonPart(points)(i),
    );

double signedArea(List<Point> points) => (internalArea(points) / 2);

double centroidX(List<Point> points) =>
    xPart(points) / (6 * signedArea(points));

double centroidY(List<Point> points) =>
    yPart(points) / (6 * signedArea(points));

Point centroid(List<Point> points) => Point(
      centroidX(points),
      centroidY(points),
    );