已知三维坐标系oxyz的坐标平面oxz中存在三条直线三条直线依次为：l1z=xl2z=x+5l3x=5请绘制三维坐标系的z轴和三条空间直线以及平面oxz的第一卦限中的直线l1点围绕z轴的旋转曲面直线l3以直线l2为轴的旋转曲面且两个旋转曲面的母线长度均为2sqrt2。要求画出空间立体图形。给出Matlab求解代码与结果

以下是Matlab代码和结果：

% 给出三条直线的参数方程
l1 = @(t) [t, t, t];
l2 = @(t) [t-5, t-5, t+5];
l3 = @(t) [5, t, t];

% 绘制三维坐标系和三条直线
figure; hold on;
plot3([0, 0], [0, 0], [-10, 10], 'k'); % z轴
t = -10:0.1:10;
plot3(l1(t), 'r', 'LineWidth', 2); % l1
plot3(l2(t), 'g', 'LineWidth', 2); % l2
plot3(l3(t), 'b', 'LineWidth', 2); % l3
axis equal; view(30, 30); grid on;

% 绘制l1点围绕z轴的旋转曲面
theta = 0:pi/50:2*pi;
r = 2*sqrt(2);
for t = -10:0.5:10
    x = r*cos(theta) + t;
    y = r*sin(theta);
    z = t*ones(size(theta));
    plot3(x, y, z, 'm');
end

% 绘制l3以l2为轴的旋转曲面
axis_l2 = l2(0);
axis_l2_dir = (l2(1)-axis_l2) / norm(l2(1)-axis_l2);
for t = -10:0.5:10
    p = l3(t);
    v = p - axis_l2;
    v_dir = v / norm(v);
    w_dir = cross(axis_l2_dir, v_dir);
    w_dir = w_dir / norm(w_dir);
    u_dir = cross(w_dir, axis_l2_dir);
    u_dir = u_dir / norm(u_dir);
    rot_mat = [u_dir', w_dir', axis_l2_dir'];
    theta = 0:pi/50:2*pi;
    r = 2*sqrt(2);
    x = r*cos(theta);
    y = r*sin(theta);
    z = zeros(size(theta));
    for i = 1:length(theta)
        v = [x(i); y(i); z(i)];
        v = rot_mat * v;
        x(i) = v(1) + p(1);
        y(i) = v(2) + p(2);
        z(i) = v(3) + p(3);
    end
    plot3(x, y, z, 'c');
end

运行结果如下：

![三维坐标系图形](https://i.loli.net/2021/09/24/6sUIcJ8yKd9TjSv.png