鞋带配方的最快方法 [英] Fastest way to Shoelace formula

问题描述

我做了一个函数，可以用鞋带方式计算面积多边形.

I have made a function who calculate area polygon with Shoelace way.

这很完美，但是现在我想知道是否没有更快的方法来获得相同的结果. 我想知道，因为此功能必须在具有很多坐标的多边形上更快地工作.

That's works perfectly but right now I wonder if there is not a faster way to have the same result. I want to know that because this function must work faster with polygon with a lot of coordinates.

我的功能:

def shoelace_formula(polygonBoundary, absoluteValue = True):
    nbCoordinates = len(polygonBoundary)
    nbSegment = nbCoordinates - 1

    l = [(polygonBoundary[i+1][0] - polygonBoundary[i][0]) * (polygonBoundary[i+1][1] + polygonBoundary[i][1]) for i in xrange(nbSegment)]

    if absoluteValue:
        return abs(sum(l) / 2.)
    else:
        return sum(l) / 2.

我的多边形:

polygonBoundary = ((5, 0), (6, 4), (4, 5), (1, 5), (1, 0))

结果:

22.

有什么想法吗?

我尝试Numpy: 这是最快的方法，但您必须先转换坐标.

I try with Numpy : It's speedest but you have to convert your coordinates first.

import numpy as np
x, y = zip(*polygonBoundary)

def shoelace_formula_3(x, y, absoluteValue = True):

    result = 0.5 * np.array(np.dot(x, np.roll(y, 1)) - np.dot(y, np.roll(x, 1)))
    if absoluteValue:
        return abs(result)
    else:
        return result

推荐答案

class Point //a new class for an any point a(X,Y), b(X,Y), c(X,Y), d(X,Y)
{
    //private int x, y;
    public int X { get; set; }
    public int Y { get; set; }

}

static class Geometry
{       

    public static void GerArea(Point a, Point b, Point c)
    {

        double area = 0.5 * ( (a.X * b.Y) + (b.X * c.Y) + (c.X * a.Y) - (b.X * a.Y) - (c.X * b.Y) - (a.X * c.Y) );

        Console.WriteLine(Math.Abs(area));
    }
    public static void GerArea(Point a, Point b, Point c, Point d)
    {
        double area = 0.5 * ((a.X * b.Y) + (b.X * c.Y) + (c.X * d.Y) + (d.X * a.Y) - (b.X * a.Y) - (c.X * b.Y) - (d.X * c.Y) - (a.X * d.Y ) );

        Console.WriteLine(Math.Abs(area));
    }
}
class Program
{
    static void Main(string[] args)
    {

        Point a = new Point() { X = -12, Y = 12 }; 
        Point b = new Point() { X = 15, Y = 15 };
        Point c = new Point() { X = -15, Y = -16 };
        Point d = new Point() { X = 16, Y = -15 };

        Console.WriteLine("****Shoelace formula****\n");


        Console.Write("Area of tringle: ");
        Geometry.GerArea(a, b, c);
        Console.Write("Area of quad: ");
        Geometry.GerArea(a, b, c, d);


        Console.ReadLine();

    }
}

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