how can i convert 2d plot in to 3d surface ??

I have this small code that plots ogive shape nose in 2d.

I want to develop 3d surface from this code !!! please help and guide....

I am using surf command and tried to turn vector in to matrix....

L = 500;
R = 79;
n= 0.4;
x = 0:0.01:50;
y= R*(x/L).^n;
z= 1.*(x/L).^n;
plot(x,y,'r','linewidth',2)
hold on
plot(x,-y,'r','linewidth',2)
xlabel('Length')
ylabel('Radius')
title('Nose Profile')
axis('equal');

[Walter Roberson]

For the third dimension, do you want change over L, or R, or n ?

[John D'Errico]

My wild guess is you want to find the rotational surface, inplied by a rotation around the axis of symmetry. At least that stems from your comment about a nose profile.

But there are multiple other ways you could create a surface from that curve. You could extend it along the third dimension, creating a surface of infinite extent in z. You could rotate it around some other axis, or around any general line.

[Dr Sohaib Khan]

hi walter.... for third dimension i dont want to change L R and n

[VBBV]

@Dr Sohaib Khan, As @Walter Roberson & @John D'Errico mentioned you could create multple surfaces depending on the which dimension is taken to rotate the 2D line plot. Since you dont want to change L, R, & n, you can use commands like surf or mesh as shown below

L = 500;
R = 79;
n= 0.4;
x = 0:0.01:50;
y = R*(x/L).^n;
z = 1.*(x/L).^n;
[X, Th] = meshgrid(linspace(1,50,100),linspace(0,2*pi,100));
Y = (R*(X/L).^n).*cos(Th);
Z = (1.*(X/L).^n).*sin(Th);
subplot(211)
plot(x,y,'r','linewidth',2)
hold on
plot(x,-y,'r','linewidth',2)
xlabel('Length')
ylabel('Radius')
title('Nose Profile')
axis([-10 50 -40 40]);
subplot(212)
s=surf(X,Y,Z);shading interp;view([30 15])

[Dr Sohaib Khan]

Thankyou soooo much VBBV !!!! :) :) :)

Answer 1

[Rohit Kulkarni]

Hi Sohaib,

In my understanding you want to develop a 3D surface from your 2D ogive shape nose profile, in order to do this we use the surf command. Here we create a meshgrid that represents domain for your surface and then compute the corresponding z-values using your ogive formula.

Here is the code:

L = 500;
R = 79;
n= 0.4;
x = 0:0.01:50;
y= R*(x/L).^n;
z= 1.*(x/L).^n;
plot(x,y,'r','linewidth',2)
hold on
plot(x,-y,'r','linewidth',2)
xlabel('Length')
ylabel('Radius')
title('Nose Profile')
axis('equal');
L = 500;
R = 79;
n = 0.4;
x = linspace(0, 50, 500); % Define x over the desired range with more points for smoothness
theta = linspace(0, 2*pi, 500); % Define theta for a full circle (360 degrees)

[X, Theta] = meshgrid(x, theta); % Create a meshgrid for X and Theta

% Calculate the radius (y) for each x using the ogive formula
Y = R * (X/L).^n;

% Convert polar coordinates (r, theta) to Cartesian coordinates (Y, Z) for plotting
Y = Y .* cos(Theta); % Y component
Z = Y .* sin(Theta); % Z component, using the same radius to maintain the profile shape

% Plot the 3D surface
surf(X, Y, Z, 'EdgeColor', 'none') % Use 'none' to remove gridlines for a smoother appearance
xlabel('Length')
ylabel('Radius')
zlabel('Height')
title('3D Ogive Shape')
axis equal % Use 'axis equal' to maintain aspect ratio

Refer to the following links for the documentation of the functions used above:

Linspace: https://www.mathworks.com/help/matlab/ref/linspace.html

Meshgrid: https://www.mathworks.com/help/matlab/ref/meshgrid.html

Surf: https://www.mathworks.com/help/matlab/ref/surf.html

Hope this helps!

[Dr Sohaib Khan]

Thank you rohit !!!! much appreciated :) :) :) regards