An Efficient Method for Drawing a Constellation of Glowing Stars

Question

As an application of the question posed in How to Give Stars a Glow Effect

Consider the code

\documentclass{book}
\textheight 8.5in \textwidth 5.75in 

\usepackage{tikz}
\usetikzlibrary{fadings, calc}
\tikzfading[name=dim fade, inner color=transparent!50, outer color=transparent!100]
\tikzfading[name=bright fade, right color=transparent!100, left color=transparent!100, middle color=transparent!0]

\newcommand{\glowstar}[2][.5]{\fill[white,path fading=dim fade](#2)circle[radius=#1*.4];
    \foreach \t in {0,60,120}{
    \fill[rotate around={\t:(#2)}, white,path fading=bright fade]($(#2)-(.9*#1,0)$)--($(#2)-(0,.02*#1)$)--($(#2)+(.9*#1,0)$)--($(#2)+(0,.02*#1)$)--cycle;
    \fill[rotate around={\t:(#2)}, white,path fading=bright fade]($(#2)-(.3*#1,0)$)--($(#2)-(0,.04*#1)$)--($(#2)+(.3*#1,0)$)--($(#2)+(0,.04*#1)$)--cycle;}
    \fill[white] (#2)circle[radius=#1*.075];
    }

\begin{document}
\begin{center}
\begin{tikzpicture}
\fill[blue!25!black] rectangle (16,12);
\glowstar[0.8]{8,10}
\glowstar[0.8]{4,6}
\glowstar[0.8]{12,6}
\end{tikzpicture}
\end{center}
\end{document}

which produces

The three stars displayed are all equidistant (4 units) from the Cartesian point (8,6). I would like, in this case, to plot a semicircle of glowing stars (perhaps of various sizes) every 15 degrees in the counterclockwise direction beginning with the Cartesian (12,6) and terminating at the Cartesian point (4,6).

I would, moreover, like to obviate the need for calculating the Cartesian coordinates of these points and then plotting them as I have for the (easier to calculate) three displayed stars.

It seems to me that something along the lines of polar coordinates would be more simple an painless; e.g., ---

QUESTION: How may I at the start, fix a point, say the Cartesian point (8,6) in the case of the MWE, and then plot the points (4,0), (4,15), (4,30), (4,45), ... , (4,150), (4,165), (4, 180), where the ordinate of such polar points is measured in degrees? Is this possible? Is there a better way?

I am looking for a general method whereby I may fix a point and then plot, say, a constellation of stars according to a method that does not painstakingly rely on specifying the associated Cartesian coordinates.

Thank you.

Answer 1

I made a small change to the macro, requiring the argument to have parentheses \glowstar[0.8]{(8,10)} instead of \glowstar[0.8]{8,10}. This is probably better since it allow you to use polar coordinates, e.g., \glowstar[0.8]{(60:5)}

Then you can use a foreach loop and the syntax ($(8,6)+(\k:2)$) to draw your stars. The calc package is already loaded which is required for this "adding coordinates" syntax. It's fine to mix rectangular and polar coordinates.

\documentclass{book}
\textheight 8.5in \textwidth 5.75in 

\usepackage{tikz}
\usetikzlibrary{fadings, calc}
\tikzfading[name=dim fade, inner color=transparent!50, outer color=transparent!100]
\tikzfading[name=bright fade, right color=transparent!100, left color=transparent!100, middle color=transparent!0]

\newcommand{\glowstar}[2][.5]{\fill[white,path fading=dim fade]#2circle[radius=#1*.4];
    \foreach \t in {0,60,120}{
    \fill[rotate around={\t:#2}, white,path fading=bright fade]($#2-(.9*#1,0)$)--($#2-(0,.02*#1)$)--($#2+(.9*#1,0)$)--($#2+(0,.02*#1)$)--cycle;
    \fill[rotate around={\t:#2}, white,path fading=bright fade]($#2-(.3*#1,0)$)--($#2-(0,.04*#1)$)--($#2+(.3*#1,0)$)--($#2+(0,.04*#1)$)--cycle;}
    \fill[white] #2circle[radius=#1*.075];
    }

\begin{document}

\begin{center}
\begin{tikzpicture}
\fill[blue!25!black] rectangle (16,12);
\foreach \k in {0,15,...,180}{
  \glowstar[0.8]{($(8,6)+(\k:2)$)}}
\end{tikzpicture}
\end{center}

\end{document}