3D plotting of a spherical gyroid with thickness

the equation below is the equation of a spherical gyroid.

sin x * cos y + sin y * cos z + sin z * cos x = 0

i want to write a code and save the file so i can export it and do a 3D printing.to obtain the different surface areas as shown below. i also want to model so i can obtain various specific surface areas as shown below

Answer 1

[darova]

Use isosurface

clc,clear
cla

R = 10;
[x,y,z] = meshgrid(-R:0.3:R);
v = sin(x).*cos(y) + sin(y).*cos(z) + sin(z).*cos(x);
ix = x.^2+y.^2+z.^2 > R^2;
v(ix) = nan;                                    % fill nan outside radius
p = isosurface(x,y,z,v,1);                      % change isovalue
patch(p,'facecolor','y','edgecolor','none')

camlight
material('metal')
axis vis3d

iso=-1 iso=0

[Bruno Luong]

After

p = isosurface(x,y,z,v,1)

the surface area is

V = p.vertices;
F = p.faces;
X = reshape(V(F,:),[size(F),3]);
C = cross(X(:,2,:)-X(:,1,:),X(:,3,:)-X(:,2,:),3);
Area = sum(sqrt(sum(C.^2,3)),1)/2

[Bruno Luong]

v has value in [-3/2,3/2]. So is the isovalue.

If you select larger absolute value of isovalue, you'll get thinner gyroid, and vice versa.

[Arthur Leonard]

Hello sir, how could I make the gyroid thick as it is on the pictures in the question?

Thanks for your help

[darova]

What about simply use isosurface twice?

p = isosurface(x,y,z,v,1);                      % change isovalue
p = isosurface(x,y,z,v,0.98);                      % change isovalue