nxm-braid

// draw the n x m braid 
// see https://arbitrarilyclose.com/2017/10/21/knots-links-learning/

m=3;
step=1;
radius=0.15;
thickness=0.02;
$fn=20;
grid=false;


// computed
r=radius*sqrt(2);
ar = step*0.5*sqrt(2)-2*r/sqrt(2)+thickness/2;

function centre(i,j,step,r)=[i*step,j*step,0];
function left(i,j,step,r) = [i*step-r,j*step,0];
function right(i,j,step,r) = [i*step+r,j*step,0];
function top(i,j,step,r) = [i*step,j*step +r,0];
function bottom(i,j,step,r) = [i*step,j*step -r,0];

module arc(r,d,a) {
    difference() {
         circle(r,$fn=50);
         circle(r-d,$fn=50);
         rotate([0,0,45+a]) translate([0,r,0])square(2*r,center=true);
         rotate([0,0,135+a]) translate([0,r,0])square(2*r,center=true);
    }
}

module line (p1,p2,thickness) {
    hull() {
            translate (p1) circle(d=thickness);
            translate (p2) circle(d=thickness);
         }
 }
     
if (grid) 
color ("white")
{
for (i=[1:n]) 
    for  (j=[1:m]) 
        translate (centre(i,j,step,radius))
          circle(radius);

for (i=[1:n-1]) 
    for  (j=[1:m-1]) 
        translate (centre(i+0.5,j+0.5,step,radius))
             circle(radius);
}

// braid
{
//upper right
color("red"){
  for (i=[1:n]) {
     for  (j=[1:m-1]) 
         line (left(i,j,step,r),top(i+0.5,j+0.5,step,r),thickness);
     line(left(i,m,step,r),top(i,m,step,r),thickness);
}

for  (i=[1:n]) 
     line(bottom(i-0.5,m+0.5,step,r),right(i-0.5,m+0.5,step,r),thickness);


     
//lower right

for (i=[1:n-1]) 
    for  (j=[1:m-1]) 
         line (bottom(i+0.5,j+0.5,step,r),right(i+1,j+1,step,r),thickness);

for(i=[1:n]) 
     line(bottom(i,1,step,r),right(i,1,step,r),thickness);
    
for  (j=[2:m]) 
     line(right(1,j,step,r),bottom(0.5,j-0.5,step,r),thickness);

//lower left
for (i=[2:n]) 
    for  (j=[1:m-1]) 
         line (bottom(i,j,step,r),left(i-0.5,j+0.5,step,r),thickness);
 
for  (i=[2:n]) 
     line(bottom(i,m,step,r),left(i-0.5,m+0.5,step,r),thickness);
 
for  (j=[1:m])
    line(bottom(1,j,step,r),left(1,j,step,r),thickness);
 
for  (j=[1:m]) 
     line(right(0.5,j-0.5,step,r),top(0.5,j-0.5,step,r),thickness);
   
//upper left
for (i=[1:n-1]) {
    for  (j=[1:m-1])
         line(right(i+0.5,j+0.5,step,r),top(i,j+1,step,r),thickness);
    line (top(i,1,step,r),right(i+0.5,0.5,step,r),thickness);
}

for  (j=[1:m]) 
     line(right(n,j,step,r),top(n,j,step,r),thickness);
  
for  (j=[1:m]) 
    line (left(n+0.5,j+0.5,step,r),bottom(n+0.5,j+0.5,step,r),thickness);
 
for  (i=[1:n])
    line(top(i+0.5,0.5,step,r),left(i+0.5,0.5,step,r),thickness);
}
color("black") {
for(i=[1:n]) {
    translate(bottom(i,1,step,r)) arc(ar,thickness,270);
    translate(top(i,m,step,r)) arc(ar,thickness,90);
}
for(j=[1:m]) {
    translate(left(1,j,step,r)) arc(ar,thickness,180);
    translate(right(n,j,step,r)) arc(ar,thickness,0);
}
}
}