如何从 cgpoints 数组中获取中心点？

Question

我有一个 CGPoints 数组：

let points = [(1234.0, 1053.0), (1241.0, 1111.0), (1152.0, 1043.0)]

我要做的是找到 CGPoints 的中心。所以我可以在所有点的中心放置一个对象。如果这是一个整数数组，我会像这样减少数组：

points.reduce(0, +)

然后除以数组总数得到平均值。但由于它的 CGPoints 这不起作用。关于如何实现这一点的任何想法？

Answer 1

Farhad 已经回答了有关如何平均所有这些数据点的问题。 (+1)

但这真的是你想要的吗？考虑：

这个凸形由蓝点定义，但所有这些点的平均值是红点。但这并不是真的在形状的中心。它是向上倾斜的，因为顶部附近有五个数据点，而下方只有两个。这个凸的形状很好地说明了这个问题，但它不需要是凸的来表现这个问题。任何数据点分布不均的情况都可能表现出这种行为。

绿点是多边形的centroid。您可以看到它落在边界框的中心下方（上图中的十字准线），正如您所期望的那样。对于简单的形状，这可能是放置标签的更好位置。可以这样计算：

extension Array where Element == CGPoint {
    /// Calculate signed area.
    ///
    /// See https://en.wikipedia.org/wiki/Centroid#Of_a_polygon
    ///
    /// - Returns: The signed area

    func signedArea() -> CGFloat {
        if isEmpty { return .zero }

        var sum: CGFloat = 0
        for (index, point) in enumerated() {
            let nextPoint: CGPoint
            if index < count-1 {
                nextPoint = self[index+1]
            } else {
                nextPoint = self[0]
            }

            sum += point.x * nextPoint.y - nextPoint.x * point.y
        }

        return sum / 2
    }

    /// Calculate centroid
    ///
    /// See https://en.wikipedia.org/wiki/Centroid#Of_a_polygon
    ///
    /// - Note: If the area of the polygon is zero (e.g. the points are collinear), this returns `nil`.
    ///
    /// - Parameter points: Unclosed points of polygon.
    /// - Returns: Centroid point.

    func centroid() -> CGPoint? {
        if isEmpty { return nil }

        let area = signedArea()
        if area == 0 { return nil }

        var sumPoint: CGPoint = .zero

        for (index, point) in enumerated() {
            let nextPoint: CGPoint
            if index < count-1 {
                nextPoint = self[index+1]
            } else {
                nextPoint = self[0]
            }

            let factor = point.x * nextPoint.y - nextPoint.x * point.y
            sumPoint.x += (point.x + nextPoint.x) * factor
            sumPoint.y += (point.y + nextPoint.y) * factor
        }

        return sumPoint / 6 / area
    }

    func mean() -> CGPoint? {
        if isEmpty { return nil }

        return reduce(.zero, +) / CGFloat(count)
    }
}

extension CGPoint {
    static func + (lhs: CGPoint, rhs: CGPoint) -> CGPoint {
        CGPoint(x: lhs.x + rhs.x, y: lhs.y + rhs.y)
    }

    static func - (lhs: CGPoint, rhs: CGPoint) -> CGPoint {
        CGPoint(x: lhs.x - rhs.x, y: lhs.y - rhs.y)
    }

    static func / (lhs: CGPoint, rhs: CGFloat) -> CGPoint {
        CGPoint(x: lhs.x / rhs, y: lhs.y / rhs)
    }

    static func * (lhs: CGPoint, rhs: CGFloat) -> CGPoint {
        CGPoint(x: lhs.x * rhs, y: lhs.y * rhs)
    }
}

你会这样计算质心：

let points = [(1234.0, 1053.0), (1241.0, 1111.0), (1152.0, 1043.0)]
    .map(CGPoint.init)

guard let point = points.centroid() else { return }

FWIW，具有复杂的凹形形状，即使质心也不是最佳的。见What is the fastest way to find the "visual" center of an irregularly shaped polygon?

Answer 2

您可以快速重载操作，例如：

func +(lhs: CGPoint, rhs: CGPoint) -> CGPoint {
    CGPoint(x: lhs.x + rhs.x, y: lhs.y + rhs.y)
}
func /(lhs: CGPoint, rhs: CGFloat) -> CGPoint {
    CGPoint(x: lhs.x / rhs, y: lhs.y / rhs)
}


let points = [(1234.0, 1053.0), (1241.0, 1111.0), (1152.0, 1043.0)].map({CGPoint(x: $0.0, y: $0.1)})

let m = points.reduce(.zero, +) / CGFloat(points.count)
print(m)