ios - 找到 MKPolygon 的精确质心(作为 MKMapPoint)

Question

这意味着排除任何 interiorPolygons 的区域。

一旦有了外部 points 多边形的质心，如何(即以 Objective-C 示例的形式)通过减法 interiorPolygons?或者是否有更优雅的方法来一次计算质心？

如果您帮助代码运行，它将开源 (WIP here)。

可能有帮助:

1. > http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?topic=st&chap_sec=07.2&page=case_sol
2. > https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

Answer 1

今天想想，将每个内部质心按面积加权添加到外部质心会得到合理的结果，这在定性上是有意义的。 (左侧具有内部多边形(孔)的正方形会将质心向右移动，与孔的面积成正比。)

不按比例:

- (MKMapPoint)calculateCentroid
{
    switch (self.pointCount) {
        case 0: return MKMapPointMake(0.0,
                                      0.0);
        case 1: return MKMapPointMake(self.points[0].x,
                                      self.points[0].y);
        case 2: return MKMapPointMake((self.points[0].x + self.points[1].x) / 2.0,
                                      (self.points[0].y + self.points[1].y) / 2.0);

    }

    // onward implies pointCount >= 3

    MKMapPoint centroid;
    MKMapPoint *previousPoint = &(self.points[self.pointCount-1]); // for i=0, wrap around to the last point

    for (NSUInteger i = 0; i < self.pointCount; ++i) {
        MKMapPoint *point = &(self.points[i]);

        double delta = (previousPoint->x * point->y) - (point->x * previousPoint->y); // x[i-1]*y[i] + x[i]*y[i-1]

        centroid.x += (previousPoint->x + point->x) * delta; // (x[i-1] + x[i]) / delta
        centroid.y += (previousPoint->y + point->y) * delta; // (y[i-1] + y[i]) / delta

        previousPoint = point;
    }

    centroid.x /= 6.0 * self.area;
    centroid.y /= 6.0 * self.area;

    // interiorPolygons are holes (subtractive geometry model)
    for (MKPolygon *interiorPoly in self.interiorPolygons) {
        if (interiorPoly.area == 0.0) {
            continue; // avoid div-by-zero
        }

        centroid.x += interiorPoly.centroid.x / interiorPoly.area;
        centroid.y += interiorPoly.centroid.y / interiorPoly.area;
    }

    return centroid;
}