How to plot the following surface

How to plot the following surface:

Which type of parametrization is required to plot it... please give me a code

Answer 1

[Matt J]

fsurf(@(x,y) sqrt(x.^2+y.^2)+1,  [-3 3 -3 3] )
zlim([1,3])

[Atom]

Would you please show the axes in such a way that the intersect at the vertex (0,0,1) of the inverted cone z-axis vertical along verted upward?

Answer 2

[Matt J]

fimplicit3(@(x,y,z) (z-1).^2-x.^2-y.^2,  [-3 3 -3 3 1 3] )

Answer 3

[Sam Chak]

Hi @Matt J,

Sometimes I have troubles visualizing the geometry. Can I plot like this? It should look like an inverted cone.

x = linspace(-sqrt(2), sqrt(2), 41);
y = x;
[X, Y] = meshgrid(x, y);
Z = sqrt(X.^2 + Y.^2) + 1;
surf(X, Y, Z)

[Atom]

x = linspace(-sqrt(2), sqrt(2), 41); what does it mean? how you have restricted z in [1,3]?

[Sam Chak]

Hi @Atomic

Because the inverted cone appear to be symmetrical, I assumed and solved this equation to find the value of x that gives :

to obtain .

After that, I generated a linearly spaced vector on the x-axis variable, or in simple terms, created 41 points between and.

x = linspace(-sqrt(2), sqrt(2), 41);

And I do the same for the y-axis variable.

x = y

[Atom]

Nice .. thanks a lot

[Sam Chak]

Don't mention it. Aha... now I remember. You are the one who asked how to draw a Cylindrical structure inside a Dome. It's a good learning experience.