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_func(a,b,c,d,x_range,y_range)
% a,b,c,d为平面方程ax+by+cz+d=0中的系数
% x_range和y_range为平面在x和y方向的取值范围
[x,y]=meshgrid(x_range,y_range);
z=(-a*x-b*y-d)/c;
end

2、构建求解五棱柱面n边与平面相交曲线的函数：

由于五棱柱的形状比较复杂，这里我们采用将其分解为三个部分来求解：

function [inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D)
% a: 五棱柱棱长
% h: 五棱柱高
% n: 五棱柱棱数
% A,B,C,D: 五棱柱底面中心点坐标以及顶面中心点坐标

% 找到五棱柱的顶点坐标
theta = 2*pi/n; % 每个棱角度
vertex_x = zeros(1, n*2);
vertex_y = zeros(1, n*2);
vertex_z = zeros(1, n*2);
for i = 1:n
    vertex_x(i) = A(1) + a*cos((i-1)*theta);
    vertex_y(i) = A(2) + a*sin((i-1)*theta);
    vertex_z(i) = B(3);
end
for i = 1:n
    vertex_x(i+n) = A(1) + a*cos((i-1)*theta);
    vertex_y(i+n) = A(2) + a*sin((i-1)*theta);
    vertex_z(i+n) = D(3);
end

% 找到五棱柱的棱面方程
plane = zeros(n, 4);
for i = 1:n
    p1 = [vertex_x(i), vertex_y(i), vertex_z(i)];
    p2 = [vertex_x(mod(i,n)+1), vertex_y(mod(i,n)+1), vertex_z(mod(i,n)+1)];
    v = p2 - p1;
    plane(i,:) = [v(1), v(2), v(3), -dot(v,p1)];
end

% 求解相交曲线
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
inter_x = [];
inter_y = [];
inter_z = [];
for i = 1:n
    [xi, yi, zi] = line_plane_intersection(plane(i,:), [A,B]);
    if ~isnan(xi)
        if xi >= min(vertex_x) && xi <= max(vertex_x) && yi >= min(vertex_y) && yi <= max(vertex_y) && zi >= min(vertex_z) && zi <= max([B(3),D(3)])
            inter_x = [inter_x, xi];
            inter_y = [inter_y, yi];
            inter_z = [inter_z, zi];
        end
    end
end
end

function [x, y, z] = line_plane_intersection(plane, line)
% 求线段与平面相交的交点
% plane: 平面的法向量和截距，形如[a, b, c, d]
% line: 线段的两个端点坐标，形如[p1, p2]
p1 = line(1,:);
p2 = line(2,:);
v = p2 - p1;
if dot(plane(1:3),v) == 0 % 线段与平面平行
    x = NaN;
    y = NaN;
    z = NaN;
else
    t = - (dot(plane,[p1,1]) / dot(plane(1:3),v));
    if t < 0 || t > 1 % 线段与平面不相交
        x = NaN;
        y = NaN;
        z = NaN;
    else
        x = p1(1) + v(1)*t;
        y = p1(2) + v(2)*t;
        z = p1(3) + v(3)*t;
    end
end
end

3、绘制五种平面与五棱柱面相交的曲线：

a = 1; % 五棱柱棱长
h = 2; % 五棱柱高
n = 5; % 五棱柱棱数
A = [0, 0, 0]; % 底面中心点坐标
B = [0, 0, h]; % 顶面中心点坐标
C = [a/2, a/2, 0]; % 底面边中心点坐标
D = [a/2, a/2, h]; % 顶面边中心点坐标

% 平面1
a = 2;
b = 0;
c = 0;
d = 0;
x_range = [-2, 2];
y_range = [-2, 2];
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
[inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D);
figure;
surf(x,y,z);
hold on;
plot3(inter_x, inter_y, inter_z, 'r', 'LineWidth', 2);
title('Plane 1');

% 平面2
a = 0;
b = 2;
c = 0;
d = 0;
x_range = [-2, 2];
y_range = [-2, 2];
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
[inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D);
figure;
surf(x,y,z);
hold on;
plot3(inter_x, inter_y, inter_z, 'r', 'LineWidth', 2);
title('Plane 2');

% 平面3
a = 0;
b = 0;
c = 2;
d = 0;
x_range = [-2, 2];
y_range = [-2, 2];
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
[inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D);
figure;
surf(x,y,z);
hold on;
plot3(inter_x, inter_y, inter_z, 'r', 'LineWidth', 2);
title('Plane 3');

% 平面4
a = 1/sqrt(2);
b = 1/sqrt(2);
c = 0;
d = 0;
x_range = [-2, 2];
y_range = [-2, 2];
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
[inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D);
figure;
surf(x,y,z);
hold on;
plot3(inter_x, inter_y, inter_z, 'r', 'LineWidth', 2);
title('Plane 4');

% 平面5
a = 1/sqrt(2);
b = 0;
c = 1/sqrt(2);
d = 0;
x_range = [-2, 2];
y_range = [-2, 2];
[x,y,z] = plane_func(a,b,c,d,x_range,y_range);
[inter_x, inter_y, inter_z] = pentagon_prism_intersection(a, h, n, A, B, C, D);
figure;
surf(x,y,z);
hold on;
plot3(inter_x, inter_y, inter_z, 'r', 'LineWidth', 2);
title('Plane 5');