graph the parametric surfaces

How do create the graph for the parametric surfaces?

My codes as below but it can't run properly.

% Define the parametric surface function r(u,v)
r = @(u,v) [u.*v.^(-2); u.^(-2).*v; (u.^(-2) - v.^(-2))];
% Define the range of u and v
u = linspace(0.1, 2, 50);  % Adjust the range and number of points as needed
v = linspace(0.1, 2, 50);
% Create a grid of (u,v) values
[U, V] = meshgrid(u, v);
% Evaluate the parametric surface function at each point on the grid
x = r(U, V);
% Plot the surface
surf(X, Y, Z, 'EdgeColor', 'none');

Unrecognized function or variable 'X'.

xlabel('x');
ylabel('y');
zlabel('z');
title('Parametric Surface: r(u,v) = (u*v^(-2))*i + (u^(-2)*v)*j + ((u^(-2) - v^(-2)))*k');

[Chuguang Pan]

You should use three different surface function , , . Instead of using just one function to repensent three components of vector fields.

Answer 1

[Hassaan]

% Define the parametric surface function r(u,v)
r = @(u,v) [u.*v, u.*v.^(-2); u.*v.^(-2), u.^(-2) - v.^(-2)];

% Define the range of u and v
u = linspace(0.1, 2, 50); % Adjust the range and number of points as needed
v = linspace(0.1, 2, 50);

% Create a grid of (u,v) values
[U, V] = meshgrid(u, v);

% Evaluate the parametric surface function at each point on the grid
% r is a function that returns a 2x2 matrix, but for plotting surfaces we need to evaluate three functions r_x, r_y, r_z for X, Y, Z coordinates.
R = r(U, V);

% Extract individual components for X, Y, Z coordinates
X = U .* V;           % r_x component: u*v
Y = U .* V.^(-2);     % r_y component: u*v^(-2)
Z = U.^(-2) - V.^(-2);% r_z component: u^(-2) - v^(-2)

% Plot the surface
surf(X, Y, Z, 'EdgeColor', 'none');

% Labeling the axes
xlabel('x');
ylabel('y');
zlabel('z');
title('Parametric Surface: r(u,v) = (uv)i + (u*v^(-2))j + (u^(-2) - v^(-2))k');

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