Surf a function with different values

I'm trying to surf a function f that takes 2 values: 1 if (x,y) is in A and 2 if (x,y) is in B. How can I do that? I attach also a drawing for x,y.

Answer 1

[Torsten]

Define the function as

f = @(x,y) (y>=2*x) + 2*(y<2*x);

and make a surface plot.

[Alexandra Roxana]

But the function doesn't depend on x and y. It is a constant function. And I want to go further with more triangles dividing the domain. And to make it have a different value within each triangle.

[Torsten]

The function has exactly the values you want:

f = @(x,y) (y>=2*x) + 2*(y<2*x);
f(0,1)

ans = 1

f(1,0)

ans = 2

But I admit: Defining a function with prescribed values on each triangle of a triangulation will soon become a hard job. And I really don't understand what it should be good for ...

[Alexandra Roxana]

I want the value to be 1 in every x and y, not just x=0 and y=1.

[Alexandra Roxana]

I've been thinking of this problem for weeks and can't seem to come to some results.

[Alexandra Roxana]

Long story short: I want to calculate the pressure on each triangle from the red domain. The left-hand side of the formula is the pressure on each triangle; the right-hand side is the sum of values of each node from the triangle. The thing is the pressure is constant on each triangle and it has to look like that in the surf. Before it looked like a continuous function which isn't right. And I wanted at first to begin with a simple example.

[Torsten]

f = @(x,y) (y>=2*x) + 2*(y<2*x);
x = linspace(0,1,100);
y = linspace(0,2,100);
[X,Y] = ndgrid(x,y);
surf(X,Y,f(X,Y))
shading interp
colorbar

[Alexandra Roxana]

It looks really good but there's a slight problem: what can I modify so I can see only the two triangles in the figure? It must look like a jump from 1 to 2.

[Star Strider]

Use the view function.

[Torsten]

Or:

f = @(x,y) (y>=2*x) + 2*(y<2*x);
x = linspace(0,1,100);
y = linspace(0,2,100);
[X,Y] = ndgrid(x,y);
contourf(X,Y,f(X,Y))
colorbar

[Alexandra Roxana]

No, it has to look like the first one without the middle part, in 3D also.

[Alexandra Roxana]

Probably the function has to be modified, I momentarily don't see how.

[Alexandra Roxana]

The marked part must not appear

[Torsten]

You might want to play with this representation:

x1 = [0,0,1];
y1 = [0,2,2];
z1 = [1,1,1];
x2 = [0,1,1];
y2 = [0,0,2];
z2 = [2,2,2];
hold on
s1 = fill3(x1,y1,z1,'r');
s2 = fill3(x2,y2,z2,'b');
hold off
view(25,45)
zlim ([0 3])
rotate(s1,[0 0 1],180)
rotate(s2,[0 0 1],180)

[Alexandra Roxana]

Unfortunately that's not going to help me very much because I want to go further and do the same thing but with more triangles like in this case and in each triangle the function to have a different value:

[Torsten]

This should help:

https://scicomp.stackexchange.com/questions/26739/plot-2d-piecewise-constant-in-matlab-in-a-finite-elements-mesh

[Alexandra Roxana]

Thank you for all your help!

[Alexandra Roxana]

The method from the link seems to work; however I'm a bit confused with the values of n1, n2 and n3. I don't know what values I should put: if I put [1,1,1] the first coordinates are different, the rest is the same as should be. So I'm guessing the choice of n1, n2 and n3 is wrong.