MATLAB程序：在圆环内放置最大数量的正方形

{ "title": "MATLAB程序：在圆环内放置最大数量的正方形", "description": "本程序使用MATLAB计算并绘制出在一个外圆半径为350米、内圆半径为100米的圆环内，放置边长为13米的正方形，且正方形之间不能相互接触的最大数量，并输出每个正方形中心的坐标。", "keywords": "MATLAB, 圆环, 正方形, 坐标, 最大数量, 程序, 算法, 几何", "content": ""function max_squares = findMaxSquares()\n\n % 外圆半径和内圆半径\n R_outer = 350;\n R_inner = 100;\n\n % 正方形边长\n L_square = 13;\n\n % 圆环中心\n center = [0, 0];\n\n % 计算圆环的面积\n area_ring = pi * (R_outer^2 - R_inner^2);\n\n % 计算正方形的面积\n area_square = L_square^2;\n\n % 计算最多能放入的正方形个数\n max_squares = floor(area_ring / area_square);\n\n % 计算每个正方形中心的坐标\n theta = linspace(0, 2pi, max_squares+1);\n theta = theta(1:end-1);\n x = center(1) + (R_inner + L_square/2) * cos(theta);\n y = center(2) + (R_inner + L_square/2) * sin(theta);\n\n % 绘制圆环\n t = linspace(0, 2pi, 1000);\n x_outer = center(1) + R_outer * cos(t);\n y_outer = center(2) + R_outer * sin(t);\n x_inner = center(1) + R_inner * cos(t);\n y_inner = center(2) + R_inner * sin(t);\n figure;\n plot(x_outer, y_outer, 'b');\n hold on;\n plot(x_inner, y_inner, 'r');\n axis equal;\n\n % 绘制正方形\n for i = 1:max_squares\n rectangle('Position', [x(i)-L_square/2, y(i)-L_square/2, L_square, L_square], 'EdgeColor', 'k');\n end\nend"\n\n使用该函数 findMaxSquares 可以得到最多能放入的正方形个数，并绘制出圆环和正方形的图形。