Graphics, Figures & Tables ⇒ PSTricks | Draw regular polygons on top of each other

[CrazyHorse]

I see. Thank you (once again) for the explanation.

I would very much appreciate it if your would help me one last time; with drawing a hepragon+tetradecagon. If I have misunderstood that

gcd(#vertices, 360) = 1 ==> no possible "shortcuts" in the code when defining the vertices P_0,...,P_{n-1}

then I do not need any further help in this thread.

P.S. I believe that I now understand the basics of RPN notation. (See the attached example (the comments are Danish).)

I learned in my youth the german dialect spoken in the northern part of Germany, the reason why I mostly can understand Danish ...

However, back to the RPN ...
Your code looks good. Only a minor remark:

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    \pnode(!0 0){H1}
    


writing is as

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    \pnode(0, 0){H1}
 


will speed up the TeX run.

Do you want to use this code as a base to draw a heptagon?

[svend_tveskaeg]

Thank you for the code optimization!

I learned in my youth the german dialect spoken in the northern part of Germany, the reason why I mostly can understand Danish ...

Aber doch! I lived only 30 km from the German border when I was a child so I am almost German.

Do you want to use this code as a base to draw a heptagon?

I am not sure exactly what code you are talking about. I would like to use

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\begin{figure}
\centering
% Length a.
\def\valA{1 }
% Length k.
\def\valK{\valA 3 sqrt 2 mul 3 sub mul }
 \psset{unit=5,offset=-12pt}
  \begin{pspicture}(\valA,\valA)
    \pstGeonode[CurveType=polygon,PointName=,PointSymbol=none]
      (0,0){P0}
      (\valA,0){P1}
      (!\valA dup add 30 cos mul 30 PtoC){P2}
      (!\valA 4 mul 60 cos mul 60 PtoC){P3}
      (!\valA dup add 30 cos mul 90 PtoC){P4}
      (\valA;120){P5}
    \multido{\iA=0+60,\iP=0+1}{6}{%
      \rput{\iA}(P\iP){%
        \pnode(!\valA \valK sub % a-k   = 2x
                 2 div          % a-k/2 =  x
                 0              % y value
              ){P\iP:1}
       \pnode(!\psGetNodeCenter{P\iP:1} \valA P\iP:1.x sub 0){P\iP:2} 
      } % end of \rput
    }   % end of \multido
    \pcline{|-|}(P3)(P4)     \ncput*{$a$}
    \pcline{|-|}(P2)(P2:1)   \ncput*{$x$}
    \pcline{|-|}(P2:1)(P2:2) \ncput*{$k$}
    \pcline{|-|}(P2:2)(P3)   \ncput*{$x$}
    \psset{linestyle=dashed}
    \multido{\iA=0+1,\iB=1+1}{5}{\psline(P\iA:2)(P\iB:1)}
    \psline(P5:2)(P0:1)
  \end{pspicture}
\end{figure}

as the code base.

The more generalized I can get the code, the better. In general, in an n-gon,

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\def\valK{\valA pi n div cos 1 pi n div cos add div mul }
(\valK = cos(pi/n)/(1+cos(pi/n))*\valA)

Furthermore, the labels on the sides should be placed at something like

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\pcline{|-|}(P[n/2])(P[n/2+1])       \ncput*{$a$}
\pcline{|-|}(P[n/2-1])(P[n/2-1]:1)   \ncput*{$x$}
\pcline{|-|}(P[n/2-1]:1)(P[n/2-1]:2) \ncput*{$k$}
\pcline{|-|}(P[n/2-1]:2)(P[n/2])     \ncput*{$x$}

for even n and

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\pcline{|-|}(P[(n+1)/2])(P[(n+3)/2])     \ncput*{$a$}
\pcline{|-|}(P[(n-1)/2])(P[(n-1)/2]:1)   \ncput*{$x$}
\pcline{|-|}(P[(n-1)/2]:1)(P[(n-1)/2]:2) \ncput*{$k$}
\pcline{|-|}(P[(n-1)/2]:2)(P[(n+1)/2])   \ncput*{$x$}

for odd n.

The rest of the generalizations should be rather obvious.

I hope it makes sense!

P.S. In my code example with RPN notation, the two lines

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\pnode(!1 \valueA \valueC sub){I1}
\pnode(!1 \valueA){I2}

should be

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\pnode(!\indent 1 mul 3 div \valueA \valueC sub){I1}
\pnode(!\indent 1 mul 3 div \valueA){I2}

Update:

The rest of the generalizations should be rather obvious.

By ``rather obvious'' I mean that it should be obvious what I want, not how to do it.

The `ultimate' code would be something where \def\valN{<number of vertices> } is given and then both the regular n-gon (with the regular 2n-gon on top) and the labels are printed automatically.

Update 2:
I have computed the coordinates for every vertex in an regular n-gon. (See the attached note.) I have no idea if it is of any help, but here you go.

Update 3:
The expressions for the vertices in Update 2 can (of course) be written somewhat simpler. (See the attached note.)

[svend_tveskaeg]

@Herbert: Are we done with this thread?

I am just asking because if we are, I will make it as solved.

Edit:
make --> mark

[CrazyHorse]

@Herbert: Are we done with this thread?

I am just asking because if we are, I will make it as solved.

yes, we can close it ...

[svend_tveskaeg]

Okay.

Thank you very much for helping me.