How do I draw a specific type of 3d mesh for a implicit function?

Here is the implicit function:(x1, x2, x3 are all in range [0,1])

p = 1;
f = @(x1,x2,x3) x1.^p + x2.^p + x3.^p - 1; 

I want to draw this type of plot:

Here is what I get:

I want to get the same mesh as the first figure.

This is my way of generating the second figure:

p=1;
f = @(x1,x2,x3) x1.^p + x2.^p + x3.^p - 1; 
[x,y,z] = meshgrid(0:.05:1,0:.05:1,0:.05:1);     
v = f(x,y,z);
h = patch(isosurface(x,y,z,v,0)); 
isonormals(x,y,z,v,h)              
set(h,'FaceColor','none','EdgeColor','r');
xlabel('x');ylabel('y');zlabel('z'); 
alpha(1)   
grid on; 
view([1,1,1]); axis equal; 

When I use fimplicit3, I get the same result as the second figure:

p=1;
f = @(f1,f2,f3) f1.^p + f2.^p + f3.^p - 1;      
interval = [0 1 0 1 0 1];
fimplicit3(f,interval,'FaceColor','none','EdgeColor','r');

[madhan ravi]

https://www.mathworks.com/help/symbolic/fimplicit3.html?s_tid=doc_ta#bvcxpkx-23

[Linjun He]

I tried this.

But I still failed to get the kind of mesh in the first figure.

Answer 1

[KSSV]

Read about transfinite interpolation.

https://in.mathworks.com/matlabcentral/fileexchange/40681-transfinite-interpolation

https://in.mathworks.com/matlabcentral/fileexchange/44670-mesh-a-plate-with-hole

[Linjun He]

Sorry, I did not get your idea.

[KSSV]

YOu can define your sides of triangle and use TRansfinite interpolation.......refer the codes of the link.