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Question. Why does the following code produce a line from vertex 0 to vertex 1 which does not perfectly coincide with the analogous line drawn earlier (by way of the foreach-loop)?

 begintikzpicture
 foreach n/a/r in 0/0/100,1/72/100,2/144/100,3/216/100,4/288/100
 node (vn) at (a:r pt) [];
 
 foreach n in 0,1,2,3,4
 pgfmathsetmacroauxoneMod(n,5);
 pgfmathsetmacroauxtwoMod(add(n,1),5);
 pgfmathsetmacroauxthreeMod(add(n,2),5); 
 draw[opacity=0.5] (vauxtwo)--(vauxone);
 draw[opacity=0.5] (vauxthree)--(vauxone); 
 
 draw[opacity=0.5] (v0)--(v1);
 endtikzpicture

The offending output is the following:

Remarks.

• My wish is to have the second line from 0 to 1 coincide perfect with the previously drawn one (and hence create a darker hue, because of the superposition of two opacity-0.5-lines).




• I fail to see any reason for the non-congruence of the two lines. (If one mentally substitues the variables auxone and auxtwo, then the two drawing-commands in question seem perfectly identical to me, hence can be expected to have exactly the same effect.)



• 
  

  I tried to exchange the line

  
  
  

  draw[opacity=0.5] (v0)--(v1);
  

  
  

with the line

 draw[opacity=0.5] (v0.center)--(v1.center);

producing a slighly different, yet still unexplained and undesirable, result, which I permit myself to also reproduce (in the hope that this might help someone understand the problem):

Because you were using pgfmathsetmacro, which adds .0 at the end of the numbers, which get interpreted as anchors (.0 is equivalent to .east in this case). If you use pgfmathtruncatemacro instead the lines match perfectly, as they should.

documentclass[tikz,border=3.14mm]standalone
begindocument
 begintikzpicture
 foreach n/a/r in 0/0/100,1/72/100,2/144/100,3/216/100,4/288/100
 node (vn) at (a:r pt) [];
 
 foreach n in 0,1,2,3,4
 pgfmathtruncatemacroauxoneMod(n,5);
 pgfmathtruncatemacroauxtwoMod(add(n,1),5);
 pgfmathtruncatemacroauxthreeMod(add(n,2),5);
 draw[opacity=0.5] (vauxtwo)--(vauxone);
 draw[opacity=0.5] (vauxthree)--(vauxone); 
 
 draw[opacity=0.5] (v0)--(v1);
 endtikzpicture
enddocument

If you want to close the gaps, you may want to use coordinates instead of nodes.

documentclass[tikz,border=3.14mm]standalone
begindocument
 begintikzpicture
 foreach n/a/r in 0/0/100,1/72/100,2/144/100,3/216/100,4/288/100
 coordinate (vn) at (a:r pt);
 
 foreach n in 0,1,2,3,4
 pgfmathtruncatemacroauxoneMod(n,5);
 pgfmathtruncatemacroauxtwoMod(add(n,1),5);
 pgfmathtruncatemacroauxthreeMod(add(n,2),5);
 draw[opacity=0.5] (vauxtwo)--(vauxone);
 draw[opacity=0.5] (vauxthree)--(vauxone); 
 
 draw[opacity=0.5] (v0)--(v1);
 endtikzpicture
enddocument