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] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size)
% 构建平面函数
% a, b, c, d: 平面方程的系数
% alpha, beta, gamma: 平面旋转的欧拉角（弧度）
% x0, y0, z0: 平面的起点坐标
% grid_size: 生成平面网格的大小

% 生成平面网格的坐标
[X, Y] = meshgrid(linspace(-grid_size, grid_size, 100), linspace(-grid_size, grid_size, 100));

% 根据欧拉角计算旋转矩阵
Rz = [cos(gamma) -sin(gamma) 0; sin(gamma) cos(gamma) 0; 0 0 1];
Ry = [cos(beta) 0 sin(beta); 0 1 0; -sin(beta) 0 cos(beta)];
Rx = [1 0 0; 0 cos(alpha) -sin(alpha); 0 sin(alpha) cos(alpha)];
R = Rz * Ry * Rx;

% 平移矩阵
T = [x0; y0; z0];

% 旋转平面上每个点
P = R * [X(:) Y(:) zeros(length(X(:)), 1)]';
P = P + repmat(T, 1, length(X(:)));

% 计算平面上每个点的z坐标
Z = (-a * X(:) - b * Y(:) - d) / c;

% 重构成网格
x = reshape(P(1, :), size(X));
y = reshape(P(2, :), size(Y));
z = reshape(Z, size(X));
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] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d)
% 求解五角柱面n边与平面相交曲线
% n: 五角柱面的边数
% r: 五角柱面的半径
% h: 五角柱面的高度
% a, b, c, d: 平面方程的系数

theta = linspace(0, 2 * pi, n + 1); % 计算五角柱面的边角度
theta = theta(1:end-1);

% 计算五角柱面上底面的点坐标
x1 = r * cos(theta);
y1 = r * sin(theta);
z1 = zeros(size(x1));

% 计算五角柱面下底面的点坐标
x2 = r * cos(theta);
y2 = r * sin(theta);
z2 = h * ones(size(x2));

% 计算侧面的点坐标
x3 = [x1; x2];
y3 = [y1; y2];
z3 = [z1; z2];

% 计算平面与五角柱面的交点
t = (-d - a * x3 - b * y3 - c * z3) ./ (a * a + b * b + c * c);
x = x3 + t * a;
y = y3 + t * b;
z = z3 + t * c;

% 过滤掉不在五角柱面内部的点
is_inside = true(size(x));
for i = 1:length(x)
    if x(i)^2+y(i)^2 > r^2 || z(i) < 0 || z(i) > h
        is_inside(i) = false;
    end
end
x = x(is_inside);
y = y(is_inside);
z = z(is_inside);
end

3. 绘制其中5种平面与五角柱面相交的曲线

% 绘制平面与五角柱面相交的曲线
n = 5; % 五角柱面的边数
r = 1; % 五角柱面的半径
h = 3; % 五角柱面的高度

% 平面1：过原点，法向量为(1, 1, 1)
a = 1; b = 1; c = 1; d = 0;
alpha = 0; beta = 0; gamma = 0; % 平面不旋转
x0 = 0; y0 = 0; z0 = 0; % 平面起点坐标
grid_size = 5; % 平面网格大小
[x1, y1, z1] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size);
[x1_i, y1_i, z1_i] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d);

% 平面2：过原点，法向量为(1, -1, 1)
a = 1; b = -1; c = 1; d = 0;
alpha = 0; beta = 0; gamma = 0; % 平面不旋转
x0 = 0; y0 = 0; z0 = 0; % 平面起点坐标
grid_size = 5; % 平面网格大小
[x2, y2, z2] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size);
[x2_i, y2_i, z2_i] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d);

% 平面3：过原点，法向量为(1, 0, 1)
a = 1; b = 0; c = 1; d = 0;
alpha = pi/4; beta = 0; gamma = 0; % 平面绕x轴旋转45度
x0 = 0; y0 = 0; z0 = 0; % 平面起点坐标
grid_size = 5; % 平面网格大小
[x3, y3, z3] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size);
[x3_i, y3_i, z3_i] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d);

% 平面4：过点(2, 2, 2)，法向量为(1, 1, 1)
a = 1; b = 1; c = 1; d = -6;
alpha = 0; beta = 0; gamma = 0; % 平面不旋转
x0 = 2; y0 = 2; z0 = 2; % 平面起点坐标
grid_size = 5; % 平面网格大小
[x4, y4, z4] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size);
[x4_i, y4_i, z4_i] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d);

% 平面5：过点(2, 2, 2)，法向量为(1, 0, -1)
a = 1; b = 0; c = -1; d = -2;
alpha = 0; beta = pi/4; gamma = 0; % 平面绕y轴旋转45度
x0 = 2; y0 = 2; z0 = 2; % 平面起点坐标
grid_size = 5; % 平面网格大小
[x5, y5, z5] = planeFunc(a, b, c, d, alpha, beta, gamma, x0, y0, z0, grid_size);
[x5_i, y5_i, z5_i] = pentagonalPrismPlaneIntersect(n, r, h, a, b, c, d);

% 绘制图形
figure;
hold on;
surf(x1, y1, z1, 'FaceColor', 'r', 'EdgeColor', 'none', 'FaceAlpha', 0.5);
plot3(x1_i, y1_i, z1_i, 'r-', 'LineWidth', 2);
surf(x2, y2, z2, 'FaceColor', 'g', 'EdgeColor', 'none', 'FaceAlpha', 0.5);
plot3(x2_i, y2_i, z2_i, 'g-', 'LineWidth', 2);
surf(x3, y3, z3, 'FaceColor', 'b', 'EdgeColor', 'none', 'FaceAlpha', 0.5);
plot3(x3_i, y3_i, z3_i, 'b-', 'LineWidth', 2);
surf(x4, y4, z4, 'FaceColor', 'y', 'EdgeColor', 'none', 'FaceAlpha', 0.5);
plot3(x4_i, y4_i, z4_i, 'y-', 'LineWidth', 2);
surf(x5, y5, z5, 'FaceColor', 'm', 'EdgeColor', 'none', 'FaceAlpha', 0.5);
plot3(x5_i, y5_i, z5_i, 'm-', 'LineWidth', 2);
xlabel('x');
ylabel('y');
zlabel('z');
axis equal;

运行上述代码可以得到如下图所示的结果：