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I wrote a code using tkz-euclide to randomly pick a point on a circle and work from there as you can see in my question How to control label positions in tikz-euclide. I have seen several questions already about randomizing the choosing of points in TikZ such as Tangents to a circle from a point outside of it (tikz) and Extract x, y coordinate of an arbitrary point in TikZ. And I could see that it is not that easy to do this. But how do we do it with just TikZ?

Edit I am sorry if my question is not that clear. What I am looking for is a solution that is written with the usual TikZ commands (in combination maybe with some TeX/LaTeX macros) that randomly chooses a point on the circle just like what \tkzGetRandPointOn does.

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hpesoj626
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    Could you explain for non-tkz users what \tkzGetRandPointOn does? Looking at Peter Grill's code, I would do something like \pgfmathsetmacro\ang{360*rnd} to get a random angle and then generate the coordinate from that using sin and cosine. Would that be enough, or do you need more? – Andrew Stacey Sep 11 '12 at 09:45
  • @GarbageCollector What random finite set? – Andrew Stacey Sep 11 '12 at 09:51
  • @AndrewStacey: The \tkzGetRandPointOn gets an arbitrary point of the target object. The code of Peter Grill was taken from my question in http://tex.stackexchange.com/questions/71072/how-to-control-label-positions-in-tikz-euclide where I commented on each line to explain the code (from what I understand from the manual anyway). – hpesoj626 Sep 11 '12 at 09:51
  • @hpesoj626 So to do \tkzGetRandPointOn for a circle, all you need to do is generate a random angle which \pgfmathsetmacro\ang{360*rnd} does. After that, it's just trigonometry. – Andrew Stacey Sep 11 '12 at 09:54
  • @GarbageCollector But only one of them is randomly chosen. The others are fixed. If you want to ensure that the random point is not near to the fixed points (so that the labels don't overlap) then that's easy enough: define an exclusion zone. – Andrew Stacey Sep 11 '12 at 09:57
  • @AndrewStacey, yes something like that. I will come back tomorrow. – hpesoj626 Sep 11 '12 at 09:58
  • @GarbageCollector, What I want is to choose only one arbitrary point of the circle and define any other point of the circle or object based on that first point. – hpesoj626 Sep 11 '12 at 10:00
  • let us continue this discussion in chat – hpesoj626 Sep 12 '12 at 01:52

2 Answers2

16

Here is a very simple answer.

enter image description here

\documentclass[margin=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \coordinate (center) at (1,2);
  \def\radius{2.5cm}
  % a circle
  \draw (center) circle[radius=\radius];

  % a random point of the circle
  \fill[red] (center) ++(rand*180:\radius) circle[radius=2pt];
\end{tikzpicture}
\end{document}

The same idea in more detail:

enter image description here

\documentclass[margin=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  % choose a seed for pseudo-random generator
  \pgfmathsetseed{\pdfuniformdeviate 10000000}

  % define a circle (center=O and \radius)
  \coordinate (O) at (1,2);
  \def\radius{2.5cm}

  % draw this circle and its center
  \draw (O) circle[radius=\radius];
  \fill (O) circle[radius=2pt] node[below left] {O};

  % define a random point (A) on this circle
  \pgfmathsetmacro{\angleA}{rand*180}
  \path (O) ++(\angleA:\radius) coordinate (A);

  % draw (A) with a label
  \fill[red] (A) circle[radius=2pt] ++(\angleA:1em) node {A};
\end{tikzpicture}
\end{document}

To generate a pseudo-random number between -180 and 180, you can use one of the following expressions:

  • rand*180 (my solution)
  • rdn*360-180 (derived from Andrew Stacey's comment)
  • random(-180,180) (an integer value only!)

The default seed of pseudo-random generator is \time × \year. Thus, it changes each minute. To choose a seed changing more frequently, use something like:

\pgfmathsetseed{\pdfuniformdeviate 10000000}
Paul Gaborit
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5

Note that it is not TikZ solution and there is no guarantee that there is no duplicated points.

Case 1 (three fixed, one randomed)

enter image description here

\documentclass[pstricks,border=15pt]{standalone}
\usepackage{pst-eucl}

\pstVerb
{
    /randval {rand 36000 mod 100 div} def % random number from 0.00 to 359.99
}

\begin{document}
\psLoop{30}{%
\begin{pspicture}[showgrid=false](-2,-2)(2,2)
    \pnode(0,0){O}
    \pstGeonode[CurveType=polygon,linejoin=2]
    (2,0){A}
    (2;30){B}
    (2;70){C}
    (!2 randval PtoC){D}
    \pstCircleOA{O}{A}
\end{pspicture}}

\end{document}

Case 2 (all randomed)

enter image description here

\documentclass[pstricks,border=15pt]{standalone}
\usepackage{pst-eucl}

\pstVerb
{
    /randval {rand 36000 mod 100 div} def % random number from 0.00 to 359.99
}

\begin{document}
\psLoop{30}{%
\begin{pspicture}[showgrid=false](-2,-2)(2,2)
    \pnode(0,0){O}
    \pstGeonode[CurveType=polygon,linejoin=2]
    (!2 randval PtoC){A}
    (!2 randval PtoC){B}
    (!2 randval PtoC){C}
    (!2 randval PtoC){D}
    \pstCircleOA{O}{A}
\end{pspicture}}

\end{document}
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  • (!2 rand 360 mod PtoC){D} do not need any additional definitions with \pstVerb –  Sep 11 '12 at 11:00
  • It looks simple enough in pstricks. I know that it is very powerful. I learned it first before I learned tikz but I can't say I understand it anymore. Looking back, I say that my reliance on tikz maybe mainly due to my heavy use of pdflatex. I have to revisit the manual. Thanks. – hpesoj626 Sep 12 '12 at 01:39