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(x0,y0,z0,a,b,c,alpha,beta,gamma)
% x0, y0, z0：平面上的一个点
% a, b, c：平面法向量的三个分量
% alpha, beta, gamma：平面的旋转角度（弧度制）
% 构造旋转矩阵
Rx = [1 0 0; 0 cos(alpha) -sin(alpha); 0 sin(alpha) cos(alpha)];
Ry = [cos(beta) 0 sin(beta); 0 1 0; -sin(beta) 0 cos(beta)];
Rz = [cos(gamma) -sin(gamma) 0; sin(gamma) cos(gamma) 0; 0 0 1];
R = Rz*Ry*Rx;
% 构造平面方程
syms x y z;
P = [x y z]';
N = [a b c]';
P0 = [x0 y0 z0]';
Q = R*(P-P0)+P0;
eqn = dot(Q-N,Q-P) == 0;
% 求解平面方程
sol = solve(eqn,z);
% 输出平面方程
z = sol;
[x,y] = meshgrid(-5:0.1:5,-5:0.1:5);
z = subs(z,[x y],[x(:) y(:)]);
z = reshape(double(z),size(x,1),size(y,2));

end

2、构建求解判断五棱柱面n边与平面相交曲线的函数：

function [x,y,z] = pentagon_intersect(x0,y0,z0,a,b,c,alpha,beta,gamma,r,h)
% x0, y0, z0：五棱柱底面中心点坐标
% a, b, c：五棱柱的方向向量（垂直于底面）
% alpha, beta, gamma：五棱柱的旋转角度（弧度制）
% r：五棱柱底面半径
% h：五棱柱高度
% 构造旋转矩阵
Rx = [1 0 0; 0 cos(alpha) -sin(alpha); 0 sin(alpha) cos(alpha)];
Ry = [cos(beta) 0 sin(beta); 0 1 0; -sin(beta) 0 cos(beta)];
Rz = [cos(gamma) -sin(gamma) 0; sin(gamma) cos(gamma) 0; 0 0 1];
R = Rz*Ry*Rx;
% 构造五棱柱顶部圆面方程
syms x y z;
P = [x y z]';
N = [a b c]';
P0 = [x0 y0 z0+h]';
eqn1 = dot(N,P-P0) == 0;
eqn2 = x^2+y^2 == r^2;
sol = solve([eqn1,eqn2],[x,y]);
% 求解圆面交平面的曲线
x = sol.x;
y = sol.y;
z = (-a*x-b*y-d)/c;
% 旋转曲线
P = [x y z]';
Q = R*(P-P0)+P0;
x = Q(1,:);
y = Q(2,:);
z = Q(3,:);

end

3、绘制其中5种平面与五棱柱面相交的曲线：

% 构造五棱柱的方向向量
r = 1;
h = 2;
a = 0;
b = 0;
c = 1;
alpha = 0;
beta = 0;
gamma = 0;
[x,y,z] = pentagon(r,h,a,b,c,alpha,beta,gamma);

% 绘制五棱柱
figure;
patch(x,y,z,'r');
axis equal;
hold on;

% 绘制平面与五棱柱相交的曲线
[x,y,z] = plane(0,0,0,1,1,1,0,0,0);
plot3(x,y,z,'b','LineWidth',2);
[x,y,z] = pentagon_intersect(0,0,0,1,1,1,0,0,0,r,h);
plot3(x,y,z,'g','LineWidth',2);

[x,y,z] = plane(0,0,0,1,1,1,pi/4,0,0);
plot3(x,y,z,'b','LineWidth',2);
[x,y,z] = pentagon_intersect(0,0,0,1,1,1,pi/4,0,0,r,h);
plot3(x,y,z,'g','LineWidth',2);

[x,y,z] = plane(0,0,0,1,1,1,0,pi/4,0);
plot3(x,y,z,'b','LineWidth',2);
[x,y,z] = pentagon_intersect(0,0,0,1,1,1,0,pi/4,0,r,h);
plot3(x,y,z,'g','LineWidth',2);

[x,y,z] = plane(0,0,0,1,1,1,0,0,pi/4);
plot3(x,y,z,'b','LineWidth',2);
[x,y,z] = pentagon_intersect(0,0,0,1,1,1,0,0,pi/4,r,h);
plot3(x,y,z,'g','LineWidth',2);

[x,y,z] = plane(0,0,0,1,1,1,pi/6,pi/6,pi/6);
plot3(x,y,z,'b','LineWidth',2);
[x,y,z] = pentagon_intersect(0,0,0,1,1,1,pi/6,pi/6,pi/6,r,h);
plot3(x,y,z,'g','LineWidth',2);

xlabel('X');
ylabel('Y');
zlabel('Z');
title('五棱柱与平面相交曲线');
legend('五棱柱','平面','相交曲线');

其中，`pentagon` 函数用于构造五棱柱的顶点坐标，这里不再赘述。