平面与五角柱相交曲线求解与三维图绘制： 1、构建根据输入参数改变位置和角度的平面函数的MATLAB代码 2、构建求解判断五角柱面n边与平面相交曲线的函数 3、绘制其中5种平面与五角柱面相交的曲线

1、构建根据输入参数改变位置和角度的平面函数的MATLAB代码：

function [x,y,z] = plane_func(a, b, c, d, x_range, y_range)
% a,b,c,d为平面方程系数，x_range和y_range为平面在x和y轴上的范围
[x,y] = meshgrid(x_range, y_range);
z = (-a*x - b*y - d) / c;
surf(x, y, z);
axis equal;
rotate3d on;
end

2、构建求解判断五角柱面n边与平面相交曲线的函数：

function [x, y, z] = intersect_func(a, b, c, d, n)
% a,b,c,d为平面方程系数，n为五角柱的边数
theta = linspace(0, 2*pi*(n-1)/n, n);
x = cos(theta);
y = sin(theta);
z = linspace(-0.5, 0.5, n+1);
[X,Y,Z] = cylinder(z, n);
for i = 1:n
    p = [x(i), y(i), 0];
    v = [0, 0, 1];
    [intersect_point, ~, ~] = intersect_line_plane(p, v, [a,b,c,d]);
    x(i) = intersect_point(1);
    y(i) = intersect_point(2);
    z(i) = intersect_point(3);
end
plot3(x, y, z, 'LineWidth', 2);
hold on;
surf(X, Y, Z);
axis equal;
rotate3d on;
end

function [intersect_point, t, u] = intersect_line_plane(p, v, plane)
% p为直线上一点，v为直线方向向量，plane为平面方程系数
% t为直线参数，u为交点在平面上的坐标，intersect_point为交点
t = (-(plane(1)*p(1) + plane(2)*p(2) + plane(3)*p(3) + plane(4))) / (plane(1)*v(1) + plane(2)*v(2) + plane(3)*v(3));
u = [p(1) + t*v(1), p(2) + t*v(2), p(3) + t*v(3)];
intersect_point = u;
end

3、绘制其中5种平面与五角柱面相交的曲线：

% 绘制平面1
plane_func(1, 0, 1, -1, linspace(-1, 1, 20), linspace(-1, 1, 20));
intersect_func(1, 0, 1, -1, 5);
title('Intersection of Plane and Pentagonal Prism');

% 绘制平面2
figure;
plane_func(0, 1, 1, -1, linspace(-1, 1, 20), linspace(-1, 1, 20));
intersect_func(0, 1, 1, -1, 5);
title('Intersection of Plane and Pentagonal Prism');

% 绘制平面3
figure;
plane_func(1, 1, 1, -1, linspace(-1, 1, 20), linspace(-1, 1, 20));
intersect_func(1, 1, 1, -1, 5);
title('Intersection of Plane and Pentagonal Prism');

% 绘制平面4
figure;
plane_func(0, 0, 1, -1, linspace(-1, 1, 20), linspace(-1, 1, 20));
intersect_func(0, 0, 1, -1, 5);
title('Intersection of Plane and Pentagonal Prism');

% 绘制平面5
figure;
plane_func(1, 0, 0, -1, linspace(-1, 1, 20), linspace(-1, 1, 20));
intersect_func(1, 0, 0, -1, 5);
title('Intersection of Plane and Pentagonal Prism');