Modifying a Spirograph code

Question

I used the following modified code from the answer to this question (which was modified to allow accepting several rotations) to draw the following patterns.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{verbatim}
\begin{document}
% ====================== begin spirosegment setting with nRotations ======================
\tikzset{pics/spirosegment/.style={code={
\tikzset{spirosegment/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spirosegment/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spirosegment/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
plot[variable=\t,domain=(\pv{xmin}-0.002:\pv{xmax}+0.002)*\pv{nRotations}, samples=\pv{samples}, smooth]
(
{(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
 {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})}
);
}},
spirosegment/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1, dx/.initial=0.01,samples/.initial=21,nRotations/.initial=1,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spirosegment/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spirosegment/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi}
% ====================== end spirosegment setting nRotations ======================
\begin{frame}[t]
\frametitle{1}
\begin{center}
\vskip -.6cm
\begin{tikzpicture}[line width=.2mm]
\path (0,0)  
foreach \X [count=\Y starting from 0] in {blue}
{pic[scale=0.5,draw=\X,ultra thick]{spirosegment={R=9.6,r=-3,p=2,nRotations=5,dx=0.001}}};
\end{tikzpicture} 
\end{center} 
\end{frame}
\begin{frame}[fragile,t]
\frametitle{2}
\begin{tikzpicture}[line width=.4mm]
\path (0,0)
pic[scale=0.3,draw=yellow]{spirosegment={dx=0.03}}
foreach \X [count=\Y starting from 0] in {blue,red,green,orange}
{pic[scale=0.3,draw=\X]{spirosegment={domain={-pi/12+\Y*pi/2}:{pi/12+\Y*pi/2}}}
};
\path[line cap=round] (6,0)  
foreach \ScaleN [evaluate=\ScaleN as \Scale using {pow(0.85,\ScaleN)/0.8}]
in {1}
{foreach \Z in {0,...,3}
{foreach \X [count=\Y starting from 0] in 
{yellow,orange,red,blue,purple,cyan,magenta,green!70!black}
{pic[scale=0.5,draw=\X,fill=\X!40,rotate=\Y*90/8+\Z*90,  scale=\Scale,line width=\Scale*2pt]{spirosegment={domain={-pi/11.4}:{pi/11.4}}}
}}};
\end{tikzpicture}
\end{frame}
\end{document}

I tried to use the code used in the second frame to segment the pattern in the first frame, to produce the following drawing, but I could not figure out how to calculate the needed formula to produce it, or to produce filled spikes.

Answer 1

I am sorry, this is again something that adds something to your existing code, and not just adjusting some pgf values. I added a closed option, which is initially false to be downwards compatible. I also added an nfill style that cycles through the colors defined in spiro colors.

\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{tikz}
\usepackage{verbatim}
\newif\ifspiroclosed
\begin{document}
% ====================== begin spirosegment setting with nRotations ======================
\tikzset{pics/spirosegment/.style={code={
\tikzset{spirosegment/.cd,#1}
\def\pv##1{\pgfkeysvalueof{/tikz/spirosegment/##1}} 
\pgfmathparse{(int(1/\pv{dx}+1)}
\tikzset{spirosegment/samples=\pgfmathresult}
\draw[trig format=rad,pic actions] 
plot[variable=\t,domain=(\pv{xmin}-0.002:\pv{xmax}+0.002)*\pv{nRotations}, samples=\pv{samples}, smooth]
(
{(\pv{R}+\pv{r})*cos(\t)+\pv{p}*cos((\pv{R}+\pv{r})*\t/\pv{r})},
 {(\pv{R}+\pv{r})*sin(\t)+\pv{p}*sin((\pv{R}+\pv{r})*\t/\pv{r})}
)
\ifspiroclosed
 -- ({(\pv{xmax}+\pv{xmin})/2}:\pv{rmin}) -- cycle
\fi;
}},
spirosegment/.cd,R/.initial=6,r/.initial=-1.5,p/.initial=1, dx/.initial=0.01,samples/.initial=21,nRotations/.initial=1,domain/.code args={#1:#2}{%
\pgfmathparse{#1}\tikzset{spirosegment/xmin/.expanded=\pgfmathresult}
\pgfmathparse{#2}\tikzset{spirosegment/xmax/.expanded=\pgfmathresult}},
xmin/.initial=0,xmax/.initial=2*pi,closed/.is if=spiroclosed,closed=false,
rmin/.initial=1}
% ====================== end spirosegment setting nRotations ======================
\tikzset{nfill/.code={%
\pgfmathtruncatemacro{\myind}{Mod(#1,dim({\pgfkeysvalueof{/tikz/spiro colors}}))}%
\pgfmathsetmacro{\mycolor}{{\pgfkeysvalueof{/tikz/spiro colors}}[\myind]}%
\tikzset{fill=\mycolor,fill opacity=0.5,draw=\mycolor}%
},spiro colors/.initial={"green","cyan","orange","gray!50"}}

\begin{frame}[fragile,t]
\frametitle{2}
\begin{tikzpicture}[line width=.4mm]
\path[blue] (0,0)
foreach \Y in {1,...,16}
{pic[scale=0.3,rotate=\Y*360/16]{spirosegment={%
    domain={-pi/7.5}:{pi/7.5},closed,rmin=3.75}}
};
\path[line cap=round,line width=.2mm] (6,0) 
foreach \Y in {1,...,16}
{pic[scale=0.3,rotate=\Y*360/16,nfill=\Y]{spirosegment={%
    domain={-pi/7.5}:{pi/7.5},closed,rmin=3.75}}
}; 
\end{tikzpicture}
\end{frame}
\end{document}

Answer 2

The wheelchart package, which I wrote, can be used.

The gap between the slices is obtained with the key gap.

The shape of the slices is determined by the keys slices inner arrow and slices outer arrow.

The colors are specified with a list using the key WClistcolors. These colors can be used with the macro \WClistcolors.

The number of slices is determined by the key total count.

\documentclass[border=6pt]{standalone}
\usepackage{wheelchart}
\begin{document}
\begin{tikzpicture}
\wheelchart[
  gap,
  radius={2.5}{2.5},
  slices inner arrow={1}{0},
  slices outer arrow={1.5}{0},
%  slices={(-0.5,0)--(0,{2.5*tan(360/32)})--(0.8,0)--(0,{-2.5*tan(360/32)})--cycle;},
  slices style={
    fill=\WClistcolors!10,%none
    draw=\WClistcolors,
    %rounded corners
  },
  start half,
  total count=16,
  WClistcolors={green,cyan,orange,gray}
]{}
\end{tikzpicture}
\end{document}