Cylindrical ring of implicit surfaces

Question

Fabian Günther 2020-8-18

1
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https://ww2.mathworks.cn/matlabcentral/answers/581193-cylindrical-ring-of-implicit-surfaces

回答： Kamal Uddin Mohammad Miah 2021-9-1

Dear community,

currently I try to model a cylindrical ring of implicit surfaces. Basically I found a solution for this, but unfortunately there appears a problem at the transition areas: First, these are not completely smooth and second, there are surplus surfaces there because of the isocaps.

Up to now I have proceeded in such a way that I first create a unit cell and then multiply and transform it until the ring is closed.

Below is a picture of a stl-file of my previous result and the corresponding code.

Does anyone have an idea to solve my problems (especially when combining the individual surfaces, or a possibility for preparation) or an alternative suggestion for creating such a structure where the problem does not occur?

Thanks a lot already and best regards

clc
clear
close all
n=80;
t=pi/n;
x_max=1; 
y_max=1;
z_max=1;
r_max=4;
num=12;        
factor=6.4/num;         
xi = -x_max/2:t:x_max/2;
yi = -y_max/2:t:y_max/2;
zi = -z_max/2:t:z_max/2;
[x,y,z] = meshgrid(xi,yi,zi);
F=cos(2.*pi.*x)+cos(2.*pi.*y)+cos(2.*pi.*z);   
% First body
[fs,v]=isosurface(x,y,z,F,0);
v(:,2)=v(:,2)+r_max;
[~,rho] = cart2pol(v(:,1),v(:,2));
theta=v(:,1).*factor;
[v(:,1),v(:,2)] = pol2cart(theta,rho);
[fc,v2,c] = isocaps(x,y,z,F,0);
v2(:,2)=v2(:,2)+r_max;
[~,rho] = cart2pol(v2(:,1),v2(:,2));
theta=v2(:,1).*factor;
[v2(:,1),v2(:,2)] = pol2cart(theta,rho);
fn = [fs ; fc+length(v(:,1))];
vn = [v ; v2];
fges=fn;
vges=vn;
% Further bodies
for i=1:Zellanzahl-1
    phi=(i*2*pi)/(num);
    R=[cos(phi) -sin(phi) 0;sin(phi) cos(phi) 0;0 0 1];
    
    for j=1:length(vn(:,1))  
        viteration(j,:)=R*vn(j,:)';
    end
    fiteration = fn+i*max(max(fn));
    fges = [fges ; fiteration];
    vges = [vges ; viteration];
end
stlwrite('geometry.stl',fges,vges);