matlab绘制星形线x=2cos(t)^3,y=2sin(t)^3并绕y轴旋转一圈的立体图形

首先，我们可以使用 MATLAB 绘制出星形线：

t = linspace(0, 2*pi, 1000);
x = 2*cos(t).^3;
y = 2*sin(t).^3;
plot3(x, y, zeros(size(x)), 'LineWidth', 2);
grid on;

然后，我们需要将这个曲线绕 y 轴旋转一圈。我们可以使用 `surf` 函数来生成立体图形：

r = 10; % 旋转半径
theta = linspace(0, 2*pi, 100); % 绕 y 轴旋转一圈
z = zeros(length(theta), length(t));
for i = 1:length(theta)
    z(i, :) = r*cos(theta(i)) + x.*cos(theta(i));
end
surf(z, y, r*sin(theta), 'EdgeColor', 'none', 'FaceColor', [0.5 0.5 0.5]);
hold on;

最后，我们可以添加一些标题和标签来美化图形：

title('Star-shaped curve rotating around y-axis');
xlabel('x');
ylabel('y');
zlabel('z');
axis equal;

完整代码如下：

t = linspace(0, 2*pi, 1000);
x = 2*cos(t).^3;
y = 2*sin(t).^3;
plot3(x, y, zeros(size(x)), 'LineWidth', 2);
grid on;

r = 10; % 旋转半径
theta = linspace(0, 2*pi, 100); % 绕 y 轴旋转一圈
z = zeros(length(theta), length(t));
for i = 1:length(theta)
    z(i, :) = r*cos(theta(i)) + x.*cos(theta(i));
end
surf(z, y, r*sin(theta), 'EdgeColor', 'none', 'FaceColor', [0.5 0.5 0.5]);
hold on;

title('Star-shaped curve rotating around y-axis');
xlabel('x');
ylabel('y');
zlabel('z');
axis equal;