Complex surface to plot

Hello! I need to make represent the protection surface of a lightning arrester. This means I have a vertical cube(very slim)...height = 7; sides= 0.5; I also have a radius of a circle of about 3.5; I have to intersect these and plot a surface that looks like a circus tent. It should look like the images below (a wizard's hat, if you want). Can anybody help me? Thanks a lot!

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Answer 1

[Star Strider]

I don’t have your function to plot, so I created one. The rest of the code is (I hope) relatively straightforward to understand. I leave it to you to insert the correct structure of the lightning arrestor structure, although you may not need it since the mesh plot will obscure it. Change it as necessary to create the result you want.

The Code —

f = @(b,r) b(1).*exp(-b(2).*r);                     % Function Of Radius Only

a = linspace(0, 2*pi, 50);                          % Angle
r = linspace(0, 100, 50);                           % Radius
b = [30  0.05];                                     % Parameter Vector
[A,R] = meshgrid(a, r);                             % Creat Mesh Matrices

fr = f(b,R);                                        % Evaluate Function Of ‘R’ Matrix
[xm,ym,zm] = pol2cart(A,R,fr);                      % Convert To Cartesian

figure(1)
mesh(xm, ym, zm)
grid on

The Plot —

[Cezar Axintescu]

Thanks a lot!!! I cannot express how grateful I am!

[Star Strider]

As always, my pleasure!

It will look more like your original plot if you add

axis equal

after the grid on call. (I just thought of that.)

[Cezar Axintescu]

Thanks! I have another questions though. How can I change the program in order to make the margins of the tent as being part of a circle? (i tried inserting the equation of a circle/sphere somewhere but it doesn't seem to work.)

[Star Strider]

My pleasure!

I’m not certain what you want.

See if this works:

The Code —

f = @(b,r) b(1).*exp(-b(2).*r);                     % Function Of Radius Only

a = linspace(0, 2*pi, 75);                          % Angle
r = linspace(0, 100, 75);                           % Radius
b = [30  0.05];                                     % Parameter Vector
[A,R] = meshgrid(a, r);                             % Creat Mesh Matrices

fr = f(b,R);                                        % Evaluate Function Of ‘R’ Matrix
[xm,ym,zm] = pol2cart(A,R,fr);                      % Convert To Cartesian

[Xs,Ys,Zs] = sphere;

figure(1)
mesh(xm, ym, zm, 'FaceColor','interp')
ax1 = gca;
hold on
surf(Xs*100, Ys*100, Zs*100, 'FaceAlpha', 0, 'EdgeAlpha',0.2, 'EdgeColor','k')
ax2 = gca;
hold off
grid on
axis equal
colormap(ax1, jet)
view([-40, 20])

The Plot —

[Cezar Axintescu]

f = @(b,r) b(1).*exp(-b(2).*r); This function I wanted to change it in order to create the "margins" of the tent as being part of a circle/sphere. So, the function needs to describe a circle. The problem is I don't what function. Thanks!

[Star Strider]

My pleasure.

I don’t understand what you want. Do you have an image of what you want that you could share?

[Cezar Axintescu]

I tried explaining in the picture below.

[Star Strider]

You need to provide the function you want to use. I know essentially nothing about the physics of lightning arrestors.

The best I can do is a version of the inverse-square law (that seems appropriate here):

f = @(c,r) c*(1./(1 + r/c).^2);                     % Function Of Radius Only

a = linspace(0, 2*pi, 50);                          % Angle
r = linspace(0, 100, 50);                           % Radius
c = 30;
[A,R] = meshgrid(a, r);                             % Creat Mesh Matrices

fr = f(c,R);                                        % Evaluate Function Of ‘R’ Matrix
[xm,ym,zm] = pol2cart(A,R,fr);                      % Convert To Cartesian

figure(1)
mesh(xm, ym, zm)
grid on
axis equal