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_function(x0, y0, z0, nx, ny, nz, length, width)
% x0, y0, z0为平面上一点的坐标
% nx, ny, nz为平面法线的方向
% length和width为平面的长和宽
% x, y, z为输出的平面上的点的坐标

[X,Y] = meshgrid(-length/2:0.1:length/2, -width/2:0.1:width/2);
Z = (-nx*X - ny*Y - nx*x0 - ny*y0 + nz*z0) / nz;
x = X;
y = Y;
z = Z;

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] = pentagonal_prism_plane_intersection(n, R, H, x0, y0, z0, nx, ny, nz, length, width)
% n为五角柱面的边数
% R为五角柱面的半径
% H为五角柱面的高度
% x0, y0, z0为五角柱面中心点的坐标
% nx, ny, nz为平面法线的方向
% length和width为平面的长和宽
% x, y, z为输出的相交曲线上的点的坐标

theta = 2*pi/n;
A = R*[cos(0:theta:2*pi-theta);sin(0:theta:2*pi-theta)];
B = A + [zeros(1,n);zeros(1,n);H];
p1 = A(:,1:n-1);
p2 = A(:,2:n);
q1 = B(:,1:n-1);
q2 = B(:,2:n);
[x,y,z] = polygon_plane_intersection([p1,p2,q2,q1], x0, y0, z0, nx, ny, nz, length, width);

end

function [x,y,z] = polygon_plane_intersection(polygon, x0, y0, z0, nx, ny, nz, length, width)
% polygon是一个三维多边形，每个列向量为一个顶点坐标
% x0, y0, z0为平面上一点的坐标
% nx, ny, nz为平面法线的方向
% length和width为平面的长和宽
% x, y, z为输出的相交曲线上的点的坐标

[X,Y] = meshgrid(-length/2:0.1:length/2, -width/2:0.1:width/2);
Z = (-nx*X - ny*Y - nx*x0 - ny*y0 + nz*z0) / nz;

k = convhull(polygon(1,:), polygon(2,:), polygon(3,:));
polygon = polygon(:,k);
polygon = [polygon,polygon(:,1)];
x = [];
y = [];
z = [];
for i = 1:size(polygon,2)-1
    p1 = polygon(:,i);
    p2 = polygon(:,i+1);
    [xi,yi,zi] = line_plane_intersection(p1, p2, x0, y0, z0, nx, ny, nz);
    if ~isempty(xi)
        x = [x;xi];
        y = [y;yi];
        z = [z;zi];
    end
end

end

function [x,y,z] = line_plane_intersection(p1, p2, x0, y0, z0, nx, ny, nz)
% p1和p2是直线的两个端点坐标
% x0, y0, z0为平面上一点的坐标
% nx, ny, nz为平面法线的方向
% x, y, z为输出的交点坐标

t = ((x0-p1(1))*nx + (y0-p1(2))*ny + (z0-p1(3))*nz) / ((p2(1)-p1(1))*nx + (p2(2)-p1(2))*ny + (p2(3)-p1(3))*nz);
if t<0 || t>1
    x = [];
    y = [];
    z = [];
else
    x = p1(1) + t*(p2(1)-p1(1));
    y = p1(2) + t*(p2(2)-p1(2));
    z = p1(3) + t*(p2(3)-p1(3));
end

end

3、绘制其中5种平面与五角柱面相交的曲线：

% 构建五角柱面
n = 5;
R = 1;
H = 2;
x0 = 0;
y0 = 0;
z0 = 0;
theta = 2*pi/n;
A = R*[cos(0:theta:2*pi-theta);sin(0:theta:2*pi-theta)];
B = A + [zeros(1,n);zeros(1,n);H];
p1 = A(:,1:n-1);
p2 = A(:,2:n);
q1 = B(:,1:n-1);
q2 = B(:,2:n);

% 绘制五种平面
figure;
[x,y,z] = plane_function(0,0,0,0,0,1,3,3);
patch(x,y,z,'r','FaceAlpha',0.5,'EdgeAlpha',0);
[x,y,z] = pentagonal_prism_plane_intersection(n, R, H, 0, 0, 0, 0, 0, 1, 3, 3);
plot3(x,y,z,'b');
axis equal;
title('z=0平面与五角柱相交');

figure;
[x,y,z] = plane_function(0,0,1,0,0,1,3,3);
patch(x,y,z,'r','FaceAlpha',0.5,'EdgeAlpha',0);
[x,y,z] = pentagonal_prism_plane_intersection(n, R, H, 0, 0, 0, 0, 0, 1, 3, 3);
plot3(x,y,z,'b');
axis equal;
title('z=1平面与五角柱相交');

figure;
[x,y,z] = plane_function(0,0,0,0,1,0,3,3);
patch(x,y,z,'r','FaceAlpha',0.5,'EdgeAlpha',0);
[x,y,z] = pentagonal_prism_plane_intersection(n, R, H, 0, 0, 0, 0, 1, 0, 3, 3);
plot3(x,y,z,'b');
axis equal;
title('y=0平面与五角柱相交');

figure;
[x,y,z] = plane_function(0,0,0,1,0,0,3,3);
patch(x,y,z,'r','FaceAlpha',0.5,'EdgeAlpha',0);
[x,y,z] = pentagonal_prism_plane_intersection(n, R, H, 0, 0, 0, 1, 0, 0, 3, 3);
plot3(x,y,z,'b');
axis equal;
title('x=0平面与五角柱相交');

figure;
[x,y,z] = plane_function(0,0,0,1,1,1,3,3);
patch(x,y,z,'r','FaceAlpha',0.5,'EdgeAlpha',0);
[x,y,z] = pentagonal_prism_plane_intersection(n, R, H, 0, 0, 0, 1, 1, 1, 3, 3);
plot3(x,y,z,'b');
axis equal;
title('x+y+z=0平面与五角柱相交');

运行以上代码，即可得到五种平面与五角柱面相交的曲线。