graph the parametric surfaces

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Lee
Lee 2024-3-20
回答： Hassaan 2024-3-20
Ran in:
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');
  1 个评论
Chuguang Pan
Chuguang Pan 2024-3-20
You should use three different surface function , , . Instead of using just one function to repensent three components of vector fields.

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回答（1 个）

Hassaan
Hassaan 2024-3-20
% 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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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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