在MATLAB中,计算多边形的几何中心(又称质心或重心)可以通过以下步骤实现。假设你有一个多边形,其顶点按照顺时针或逆时针顺序排列在一个矩阵中。具体步骤如下:
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定义多边形顶点:首先,你需要将多边形的顶点坐标存储在一个矩阵中。例如,假设你的多边形顶点为,,…,,则可以将它们存储在一个 n×2 的矩阵
vertices
中。 -
计算几何中心:使用多边形顶点的坐标,通过公式计算几何中心。
多边形的几何中心坐标 可以通过以下公式计算:
其中,A 是多边形的面积,计算公式为:
下面是MATLAB代码,用于计算多边形的几何中心:
function [Cx, Cy] = polygonCentroid(vertices) % Number of vertices n = size(vertices, 1); % Ensure the vertices are in a closed polygon (the last vertex should be the same as the first) if ~isequal(vertices(end,:), vertices(1,:)) vertices(end+1, :) = vertices(1, :); n = n + 1; end % Initialize variables for the sums sumCx = 0; sumCy = 0; area = 0; % Loop over vertices for i = 1:n-1 x1 = vertices(i, 1); y1 = vertices(i, 2); x2 = vertices(i+1, 1); y2 = vertices(i+1, 2); % Calculate the area term crossProduct = x1 * y2 - x2 * y1; area = area + crossProduct; % Calculate the sum for Cx and Cy sumCx = sumCx + (x1 + x2) * crossProduct; sumCy = sumCy + (y1 + y2) * crossProduct; end % Calculate the scaled area area = area / 2; % Ensure the area is not zero (to avoid division by zero) if area == 0 error('The polygon area is zero, check the vertices.'); end % Calculate the centroid coordinates Cx = sumCx / (6 * area); Cy = sumCy / (6 * area);
end
使用方法
clc;close all;clear all;warning off;%清除变量
rand('seed', 100);
randn('seed', 100);
format long g;p =[27.6177681446901 24.427185391493126.9564380155505 27.210020771650122.7866669489879 26.987227127588422.4598242645914 26.038317261603523.6707146140053 22.206973156027527.6177681446901 24.4271853914931];[Cx, Cy] = polygonCentroid(p);
figure;
plot(p(:,1),p(:,2),'b-','LineWidth',2);
hold on;
plot(Cx, Cy,'r.','MarkerSize',20);
程序结果: