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] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma)
% a,b,c,d: 平面方程系数
% x0,y0,z0: 平面上一点坐标
% alpha,beta,gamma: 平面旋转角度（单位为度）

% 平面旋转矩阵
Rx = [1, 0, 0; 0, cosd(alpha), -sind(alpha); 0, sind(alpha), cosd(alpha)];
Ry = [cosd(beta), 0, sind(beta); 0, 1, 0; -sind(beta), 0, cosd(beta)];
Rz = [cosd(gamma), -sind(gamma), 0; sind(gamma), cosd(gamma), 0; 0, 0, 1];
R = Rx * Ry * Rz;

% 平面上点的坐标
p = [x0; y0; z0];

% 平面法向量
n = [a; b; c];

% 平面方程
syms x y z
f = a*x + b*y + c*z + d;

% 计算平面上所有点的坐标
[X,Y] = meshgrid(-5:0.5:5);
Z = -(a*X + b*Y + d)/c;
P = [X(:), Y(:), Z(:)]';
P = R * P + p;
x = P(1,:);
y = P(2,:);
z = P(3,:);
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] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma)
% a: 五角柱底面半径
% h: 五角柱高度
% n: 五角柱边数
% x0,y0,z0: 五角柱中心点坐标
% alpha,beta,gamma: 五角柱旋转角度（单位为度）

% 五角柱旋转矩阵
Rx = [1, 0, 0; 0, cosd(alpha), -sind(alpha); 0, sind(alpha), cosd(alpha)];
Ry = [cosd(beta), 0, sind(beta); 0, 1, 0; -sind(beta), 0, cosd(beta)];
Rz = [cosd(gamma), -sind(gamma), 0; sind(gamma), cosd(gamma), 0; 0, 0, 1];
R = Rx * Ry * Rz;

% 五角柱侧面法向量
theta = linspace(0, 2*pi, n+1);
theta(end) = [];
theta = theta + pi/n;
nx = a*cos(theta);
ny = a*sin(theta);
nz = zeros(size(nx));
N = [nx; ny; nz];
N = R * N;

% 五角柱侧面上一点坐标
P = [a*cos(theta); a*sin(theta); linspace(0, h, n)] + repmat([x0; y0; z0], 1, n);

% 五角柱侧面方程
syms x y z
f = [];
for i = 1:n
    f = [f, dot([x;y;z]-P(:,i), N(:,i)) == 0];
end

% 计算相交曲线
[X,Y] = meshgrid(-5:0.5:5);
for i = 1:numel(X)
    Z = solve(f, z, 'Real', true, 'IgnoreAnalyticConstraints', true, 'ReturnConditions', false, 'MaxDegree', 3, 'Vars', [x,y]);
    if ~isempty(Z)
        Z = double(Z);
        P = R * [X(i); Y(i); Z] + repmat([x0; y0; z0], 1, size(Z,1));
        x(i,:) = P(1,:);
        y(i,:) = P(2,:);
        z(i,:) = P(3,:);
    end
end
end

3、绘制其中5种平面与五角柱面相交的曲线：

% 平面1：x-y平面
a = 0;
b = 0;
c = 1;
d = 0;
x0 = 0;
y0 = 0;
z0 = 0;
alpha = 0;
beta = 0;
gamma = 0;
[x1,y1,z1] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma);

% 平面2：y-z平面
a = 1;
b = 0;
c = 0;
d = 0;
x0 = 0;
y0 = 0;
z0 = 0;
alpha = 0;
beta = 0;
gamma = 0;
[x2,y2,z2] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma);

% 平面3：x-z平面
a = 0;
b = 1;
c = 0;
d = 0;
x0 = 0;
y0 = 0;
z0 = 0;
alpha = 0;
beta = 0;
gamma = 0;
[x3,y3,z3] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma);

% 平面4：过五角锥顶点且与底面垂直的平面
a = 0;
b = 0;
c = 1;
d = -sqrt(5)/5;
x0 = 0;
y0 = 0;
z0 = 1/3;
alpha = 0;
beta = 0;
gamma = 0;
[x4,y4,z4] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma);

% 平面5：过五角锥顶点且与底面呈45度角的平面
a = 1;
b = 1;
c = 0;
d = -sqrt(5)/5;
x0 = 0;
y0 = 0;
z0 = 1/3;
alpha = 0;
beta = 0;
gamma = 0;
[x5,y5,z5] = planeEquation(a,b,c,d,x0,y0,z0,alpha,beta,gamma);

% 五角柱1：半径为1，高为2，边数为5，底面圆心在原点
a = 1;
h = 2;
n = 5;
x0 = 0;
y0 = 0;
z0 = 0;
alpha = 0;
beta = 0;
gamma = 0;
[x6,y6,z6] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma);

% 五角柱2：半径为1，高为2，边数为5，底面圆心在(-2,2,1)处，绕z轴旋转45度，绕y轴旋转30度
a = 1;
h = 2;
n = 5;
x0 = -2;
y0 = 2;
z0 = 1;
alpha = 0;
beta = 30;
gamma = 45;
[x7,y7,z7] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma);

% 五角柱3：半径为2，高为1，边数为5，底面圆心在(3,-3,2)处，绕y轴旋转60度，绕x轴旋转30度
a = 2;
h = 1;
n = 5;
x0 = 3;
y0 = -3;
z0 = 2;
alpha = 30;
beta = 60;
gamma = 0;
[x8,y8,z8] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma);

% 五角柱4：半径为1.5，高为3，边数为5，底面圆心在(1,-1,-1)处，绕x轴旋转60度，绕z轴旋转45度
a = 1.5;
h = 3;
n = 5;
x0 = 1;
y0 = -1;
z0 = -1;
alpha = 60;
beta = 0;
gamma = 45;
[x9,y9,z9] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma);

% 五角柱5：半径为1.5，高为3，边数为5，底面圆心在(2,1,-2)处，绕y轴旋转30度，绕z轴旋转60度
a = 1.5;
h = 3;
n = 5;
x0 = 2;
y0 = 1;
z0 = -2;
alpha = 0;
beta = 30;
gamma = 60;
[x10,y10,z10] = pentagonalCylinder(a,h,n,x0,y0,z0,alpha,beta,gamma);

% 绘制图形
figure(1);
subplot(2,3,1);
surf(x1,y1,z1);
hold on;
surf(x6,y6,z6);
title('平面1与五角柱1相交');

subplot(2,3,2);
surf(x2,y2,z2);
hold on;
surf(x6,y6,z6);
title('平面2与五角柱1相交');

subplot(2,3,3);
surf(x3,y3,z3);
hold on;
surf(x6,y6,z6);
title('平面3与五角柱1相交');

subplot(2,3,4);
surf(x4,y4,z4);
hold on;
surf(x6,y6,z6);
title('平面4与五角柱1相交');

subplot(2,3,5);
surf(x5,y5,z5);
hold on;
surf(x6,y6,z6);
title('平面5与五角柱1相交');

figure(2);
subplot(2,3,1);
surf(x1,y1,z1);
hold on;
surf(x7,y7,z7);
title('平面1与五角柱2相交');

subplot(2,3,2);
surf(x2,y2,z2);
hold on;
surf(x7,y7,z7);
title('平面2与五角柱2相交');

subplot(2,3,3);
surf(x3,y3,z3);
hold on;
surf(x7,y7,z7);
title('平面3与五角柱2相交');

subplot(2,3,4);
surf(x4,y4,z4);
hold on;
surf(x7,y7,z7);
title('平面4与五角柱2相交');

subplot(2,3,5);
surf(x5,y5,z5);
hold on;
surf(x7,y7,z7);
title('平面5与五角柱2相交');

figure(3);
subplot(2,3,1);
surf(x1,y1,z1);
hold on;
surf(x8,y8,z8);
title('平面1与五角柱3相交');

subplot(2,3,2);
surf(x2,y2,z2);
hold on;
surf(x8,y8,z8);
title('平面2与五角柱3相交');

subplot(2,3,3);
surf(x3,y3,z3);
hold on;
surf(x8,y8,z8);
title('平面3与五角柱3相交');

subplot(2,3,4);
surf(x4,y4,z4);
hold on;
surf(x8,y8,z8);
title('平面4与五角柱3相交');

subplot(2,3,5);
surf(x5,y5,z5);
hold on;
surf(x8,y8,z8);
title('平面5与五角柱3相交');

figure(4);
subplot(2,3,1);
surf(x1,y1,z1);
hold on;
surf(x9,y9,z9);
title('平面1与五角柱4相交');

subplot(2,3,2);
surf(x2,y2,z2);
hold on;
surf(x9,y9,z9);
title('平面2与五角柱4相交');

subplot(2,3,3);
surf(x3,y3,z3);
hold on;
surf(x9,y9,z9);
title('平面3与五角柱4相交');

subplot(2,3,4);
surf(x4,y4,z4);
hold on;
surf(x9,y9,z9);
title('平面4与五角柱4相交');

subplot(2,3,5);
surf(x5,y5,z5);
hold on;
surf(x9,y9,z9);
title('平面5与五角柱4相交');

figure(5);
subplot(2,3,1);
surf(x1,y1,z1);
hold on;
surf(x10,y10,z10);
title('平面1与五角柱5相交');

subplot(2,3,2);
surf(x2,y2,z2);
hold on;
surf(x10,y10,z10);
title('平面2与五角柱5相交');

subplot(2,3,3);
surf(x3,y3,z3);
hold on;
surf(x10,y10,z10);
title('平面3与五角柱5相交');

subplot(2,3,4);
surf(x4,y4,z4);
hold on;
surf(x10,y10,z10);
title('平面4与五角柱5相交');

subplot(2,3,5);
surf(x5,y5,z5);
hold on;
surf(x10,y10,z10);
title('平面5与五角柱5相交');