Irregular Polygon with Angle Labels

Question

I am looking to create the 15-sided irregular polygon figure below, without having to declare coordinates for each point.

15-sided Irregular Polygon with angles

Is there an easier way to do this? Tikz? PGF?

Perhaps this answer will get you started: Circular sequence diagram (tikz?). Just connect the endpoints, and don't draw the circle. — Peter Grill, May 23 '13 at 20:26
Starting point can be something like
\draw (90:3) \foreach \x in {0, 80, 185, 200, 270} { -- (90+\x:3) node [anchor=\x] {\x} } -- cycle; — Jori Mäntysalo, May 23 '13 at 20:43
How is this figure built? What do the angles mean? How long are the segments? I suggest TikZ’ turtle library (maybe with some adjustments). — Qrrbrbirlbel, May 23 '13 at 21:01
You guys work fast. The point of the picture is to demonstrate the "interior angle sum theorem." Here, a 15-sided polygon, has an angle sum of 2700 degrees. It seems @Jake 's answer will be the most appropriate. I will confirm shortly. — Calhistorian, May 23 '13 at 21:59
@Calhistorian According to the English Wikipedia pages about Polygons a 15-sided polygon has an angle sum of 180 (15 - 2) = 2340 degrees. Besides that, doesn’t have such a polygon more than one solution if all sides do not have the same length? — Qrrbrbirlbel, May 23 '13 at 22:28
@Qrrbrbirlbel: There are infinitely many polygons with the same interior angles if the side lengths aren't fixed, but the angle sum will always be the same (just like the sum of the interior angles of a triangle is always 180, but there are infinitely many different triangles). — Jake, May 23 '13 at 22:32
Whoops, yep your right. That's what I get for paying attention to other's annotations. — Calhistorian, May 23 '13 at 22:32

Jake · Accepted Answer · 2013-05-24T02:06:09.107

10

Here's a way to draw this polygon from a list of interior angles. The key points are the \pgfextra{...} command, which allows you to execute code without interrupting the path construction, and the \path commands with the name path keywords within the pgfinterruptboundingbox environment, which are used to find the final corner.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric, intersections}

\begin{document}
\begin{tikzpicture}
\def\totalangle{0}
\draw (0,0) -- (0:1cm) \foreach \angle in {152,165,167,160,160,150,150,150,170,145,170,155,170,155}{ 
    \pgfextra{  % Calculate the current direction
        \pgfmathparse{180-\angle+\totalangle}
        \xdef\totalangle{\pgfmathresult}
    }
 -- ++(\totalangle:1cm) node [pos=0, circle, anchor=(\totalangle+\angle/2+180), inner sep=0pt] {$\angle^\circ$}
} coordinate (final);

\pgfmathsetmacro\unknownangle{\totalangle-180}

% The final point is on the intersection between the extensions of the first and last segments.
% Interrupt the bounding box, so we can use long paths for finding the intersection.
\begin{pgfinterruptboundingbox}
    \path [name path global=horizontal] (-20cm,0pt) -- (20cm,0pt);
    \path [name path global=lastsegment] (final) -- +(\totalangle:30cm);
\end{pgfinterruptboundingbox}

\draw [name intersections={of=horizontal and lastsegment}]
    (final) -- (intersection-1)
    node [anchor=south west] {$x$}
    -- (0,0);
\end{tikzpicture}
\end{document}

edited May 24 '13 at 02:06

answered May 23 '13 at 21:32

Jake

232,450

If I don't desire to actually calculate the unknown angle (x), how much of the code is necessary? I don't have much experience with pgf. – Calhistorian May 23 '13 at 22:09
1

The calculation of the angle is only one line \pgfmathsetmacro\unknownangle{\totalangle-180}. The entire second half of the code (from \begin{pgfinterruptboundingbox}) is only necessary because we don't know the length of the individual segments, so if you would precalculate that, the code could be shortened. – Jake May 23 '13 at 22:13
Ok. One last thing to confirm answer. Is it possible to add the degree symbol also to all the angles? I imagine this isn't that simple to do. – Calhistorian May 23 '13 at 22:25
1

@Calhistorian: Sure, just replace node ... {\angle} node ... {$\angle^\circ$}. I've edited my answer. – Jake May 23 '13 at 22:30
Ok, I know I said I was finished, but I shrunk the image by half (by modifying the 2cm to 1cm) which subsequently made the angle labels to be too far from the edge. I messed with some things, but can't get the label closer to the edge. – Calhistorian May 23 '13 at 22:43
1

@Calhistorian: In that case, you need to decrease the inner sep of the label nodes (or set it to 0pt). I've edited my answer. – Jake May 24 '13 at 02:06

score 4 · Answer 2 · edited Jun 10 '20 at 12:32

Here is an adaptation of Circular sequence diagram (tikz?) which will adapt to any number of segments based on the number of labels provided.

enter image description here

Code:

\documentclass{article}
\usepackage{tikz}
\usepackage{xstring}
% https://tex.stackexchange.com/questions/21559/macro-to-access-a-specific-member-of-a-list/21560#21560
\newcommand*\GetListMember[2]{\StrBetween[#2,\number\numexpr#2+1]{,#1,},,\par}%
\newlength{\MidRadius}
\newcommand{\LastAngle}{}%
\newcommand*{\CircularSequence}[3]{%
    % #1 = outer circle radius
    % #2 = inner circle radius
    % #3 = seqeunce
    \StrCount{#3}{,}[\NumberOfElements]
    \pgfmathsetmacro{\AngleSep}{360/(\NumberOfElements+1)}
    \pgfmathsetlength{\MidRadius}{(#1+#2)/2}
    \foreach [count = \Count] \Angle in {0,\AngleSep,..., 360} {%
        \IfStrEq{\LastAngle}{}{}{%
            \draw [blue, ultra thick] (\LastAngle:#1) -- (\Angle:#1);
        }%
        \xdef\LastAngle{\Angle}% Save it so we can access it next iteration
        \pgfmathsetmacro{\MidPoint}{\Angle+\AngleSep/2}
        \node at (\MidPoint:\MidRadius) {\GetListMember{#3}{\Count}};
    }%
}%
\begin{document}
\begin{tikzpicture}
    \CircularSequence{4.0cm}{3.0cm}{170,155,170,165,$x$,163,155,167,170,160,140,150,172,170,145}
\end{tikzpicture}
\end{document}

I thought the OP wanted the irregular polygon with the corner angles given by the labels. — Jake, May 23 '13 at 20:38
@Jake: Good point, it is not really clear as the OP desires to not specify the points of each of the coordinates. Also, note that the labels are not in order, so even more confusing. — Peter Grill, May 23 '13 at 20:40

Irregular Polygon with Angle Labels

2 Answers2

Code: