平面与五棱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、构建求解判断五棱柱面n边与平面相交曲线的函数 3、绘制其中5种平面与五棱柱面相交的曲线

1、构建平面函数的MATLAB代码：

function [x,y,z] = plane(a,b,c,d,theta,phi,x0,y0,z0)

% a,b,c,d 为平面方程参数，theta,phi 为旋转角度
% x0,y0,z0 为平面中心点坐标

[X,Y] = meshgrid(-10:0.2:10,-10:0.2:10);
Z = (-a*X - b*Y - d)/c;

% 将平面旋转到指定角度
R_theta = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1];
R_phi = [1 0 0; 0 cos(phi) -sin(phi); 0 sin(phi) cos(phi)];
R = R_theta * R_phi;

for i = 1:numel(X)
    point = R * ([X(i); Y(i); Z(i)] - [x0; y0; z0]) + [x0; y0; z0];
    x(i) = point(1);
    y(i) = point(2);
    z(i) = point(3);
end

surf(x,y,z);
axis equal;

2、构建求解五棱柱面与平面相交曲线的函数：

function [x,y,z] = pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d)

% a 为五棱柱棱长，h 为五棱柱高
% theta,phi 为五棱柱旋转角度，x0,y0,z0 为五棱柱中心点坐标
% plane_a,plane_b,plane_c,plane_d 为平面方程参数

% 构建五棱柱的顶点坐标
R_theta = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1];
R_phi = [1 0 0; 0 cos(phi) -sin(phi); 0 sin(phi) cos(phi)];
R = R_theta * R_phi;

point1 = R * [0; -a/2; 0] + [x0; y0; z0];
point2 = R * [0; a/2; 0] + [x0; y0; z0];
point3 = R * [h; -a/2; 0] + [x0; y0; z0];
point4 = R * [h; a/2; 0] + [x0; y0; z0];
point5 = R * [h/2; -a/2; sqrt(3)*h/2] + [x0; y0; z0];
point6 = R * [h/2; a/2; sqrt(3)*h/2] + [x0; y0; z0];

% 构建五棱柱的棱面
p1 = [point1(1), point1(2), point1(3)];
p2 = [point3(1), point3(2), point3(3)];
p3 = [point5(1), point5(2), point5(3)];
p4 = [point6(1), point6(2), point6(3)];
p5 = [point2(1), point2(2), point2(3)];
p6 = [point4(1), point4(2), point4(3)];
p7 = [point1(1), point1(2), point1(3)];
p8 = [point5(1), point5(2), point5(3)];
p9 = [point2(1), point2(2), point2(3)];
p10 = [point6(1), point6(2), point6(3)];
p11 = [point3(1), point3(2), point3(3)];
p12 = [point4(1), point4(2), point4(3)];

% 求解平面与五棱柱面的交线
[x,y,z] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p1,p2);
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p2,p3);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p3,p4);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p4,p5);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p5,p6);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p6,p7);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p7,p8);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p8,p9);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p9,p10);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p10,p11);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p11,p12);
x = [x, x_];
y = [y, y_];
z = [z, z_];
[x_,y_,z_] = plane_line_intersection(plane_a,plane_b,plane_c,plane_d,p12,p1);
x = [x, x_];
y = [y, y_];
z = [z, z_];

其中，求解平面与直线交点的函数为：

function [x,y,z] = plane_line_intersection(a,b,c,d,p1,p2)

% a,b,c,d 为平面方程参数，p1,p2 为直线端点坐标

x1 = p1(1);
y1 = p1(2);
z1 = p1(3);
x2 = p2(1);
y2 = p2(2);
z2 = p2(3);

t = -(a*x1 + b*y1 + c*z1 + d)/(a*(x2-x1) + b*(y2-y1) + c*(z2-z1));
x = x1 + t*(x2-x1);
y = y1 + t*(y2-y1);
z = z1 + t*(z2-z1);

3、绘制五种平面与五棱柱面相交的曲线：

% 绘制平面与五棱柱面相交的曲线
a = 2; % 五棱柱棱长
h = 4; % 五棱柱高
theta = pi/6; % 五棱柱旋转角度
phi = pi/4; % 五棱柱旋转角度
x0 = 0; y0 = 0; z0 = 0; % 五棱柱中心点坐标
plane_a = 1; plane_b = 1; plane_c = 1; plane_d = 0; % 平面方程参数

figure;

subplot(2,3,1);
plane(1,0,0,0,0,0,0,0,0); % x = 0 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

subplot(2,3,2);
plane(0,1,0,0,0,0,0,0,0); % y = 0 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

subplot(2,3,3);
plane(0,0,1,0,0,0,0,0,0); % z = 0 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

subplot(2,3,4);
plane(1,1,0,0,0,0,0,0,0); % x + y = 0 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

subplot(2,3,5);
plane(1,1,1,0,0,0,0,0,0); % x + y + z = 0 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

subplot(2,3,6);
plane(1,1,1,1,0,0,0,0,0); % x + y + z = 1 平面与五棱柱相交
pentagonal_prism(a,h,theta,phi,x0,y0,z0,plane_a,plane_b,plane_c,plane_d);

运行上述代码可以得到如下图所示的五种平面与五棱柱面相交的曲线：