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treeSpace4-balancedTreeNeighbourhood.tex
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treeSpace4-balancedTreeNeighbourhood.tex
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\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{snakes}
\begin{document}
\tikzset{
pics/combLeft/.style args={#1/#2/#3/#4}{
code={
%\draw[black,fill=white] (0,0) circle (2.25);
\def\d{0.5}
\node at (0,1.5+\d) (root) {};
\node at (-1.5,-1.5+\d) (A) {#1};
\node at (-0.5,-1.5+\d) (B) {#2};
\node at (0.5,-1.5+\d) (C) {#3};
\node at (1.5,-1.5+\d) (D) {#4};
\draw (A.north) to coordinate[pos=0.333] (x) coordinate[pos=0.667] (y) (root.center);
\draw (root.center) to (D.north);
\draw (x) to (B.north);
\draw (y) to (C.north);
}}
}
\tikzset{
pics/combRight/.style args={#1/#2/#3/#4}{
code={
\node at (0,1.5) (root) {};
\node at (-1.5,-1.5) (A) {#1};
\node at (-0.5,-1.5) (B) {#2};
\node at (0.5,-1.5) (C) {#3};
\node at (1.5,-1.5) (D) {#4};
\draw (A.north) to (root.center);
\draw (root.center) to coordinate[pos=0.333] (x) coordinate[pos=0.667] (y) (D.north);
\draw (x) to (B.north);
\draw (y) to (C.north);
}}
}
\tikzset{
pics/balancedLeft/.style args={#1/#2/#3/#4}{
code={
%\draw[fill=orange!10] (0,0) circle (2.25);
\def\d{0.5}
\node at (0,1.5+\d) (root) {};
\node at (-1.5,-1.5+\d) (A) {#1};
\node at (-0.5,-1.5+\d) (B) {#2};
\node at (0.5,-1.5+\d) (C) {#3};
\node at (1.5,-1.5+\d) (D) {#4};
\draw (A.north) to coordinate[pos=0.333] (x) (root.center);
\draw (root.center) to coordinate[pos=0.333] (y) (D.north);
\draw (x) to (B.north);
\draw (y) to (C.north);
}
}}
\tikzset{
pics/balancedRight/.style args={#1/#2/#3/#4}{
code={
\node at (0,1.5) (root) {};
\node at (-1.5,-1.5) (A) {#1};
\node at (-0.5,-1.5) (B) {#2};
\node at (0.5,-1.5) (C) {#3};
\node at (1.5,-1.5) (D) {#4};
\draw (A.north) to coordinate[pos=0.667] (x) (root.center);
\draw (root.center) to coordinate[pos=0.667] (y) (D.north);
\draw (x) to (B.north);
\draw (y) to (C.north);
}
}}
\begin{tikzpicture}[thick]
\def\ir{7.5}
\def\r{15}
\coordinate (p0) at (\r/2,0);
%\draw[red] (p0) arc[start angle=0, end angle=60, radius=\r];
\path (p0) arc[start angle=0, end angle=15, radius=\r] node[inner sep=0] (p1) {};
\path (p0) arc[start angle=0, end angle=30, radius=\r] node[inner sep=0] (p2) {};
\path (p0) arc[start angle=0, end angle=45, radius=\r] node[inner sep=0] (p3) {};
\path (p0) arc[start angle=0, end angle=60, radius=\r] node[inner sep=0] (p4) {};
%\draw[red] [rotate=120] (p4) arc[start angle=0, end angle=60, radius=\r];
\path [rotate=120] (p4) arc[start angle=0, end angle=15, radius=\r] node[inner sep=0] (p5) {};
\path [rotate=120] (p4) arc[start angle=0, end angle=30, radius=\r] node[inner sep=0] (p6) {};
\path [rotate=120] (p4) arc[start angle=0, end angle=45, radius=\r] node[inner sep=0] (p7) {};
\path [rotate=120] (p4) arc[start angle=0, end angle=60, radius=\r] node[inner sep=0] (p8) {};
%\draw[red] [rotate=240] (p8) arc[start angle=0, end angle=60, radius=\r];
\path [rotate=240] (p8) arc[start angle=0, end angle=15, radius=\r] node[inner sep=0] (p9) {};
\path [rotate=240] (p8) arc[start angle=0, end angle=30, radius=\r] node[inner sep=0] (p10) {};
\path [rotate=240] (p8) arc[start angle=0, end angle=45, radius=\r] node[inner sep=0] (p11) {};
% fix this coordinate, the 3.75 is (\r-\ir)/2 and 2.24... is (r-ir*sqrt(3)/2)/2-(15*(1-sqrt(3)/2))
\coordinate (p12) at (\r/2-3.75,2.242786);
%\draw[gray] (p12) arc[start angle=0, end angle=60, radius=\ir];
%\path (p12) arc[start angle=0, end angle=30, radius=\ir] node[inner sep=0] (p13) {};
\path (p12) arc[start angle=0, end angle=60, radius=\ir] node[inner sep=0] (p14) {};
%\draw[gray] [rotate=120] (p14) arc[start angle=0, end angle=60, radius=\ir];
%\path [rotate=120] (p14) arc[start angle=0, end angle=30, radius=\ir] node[inner sep=0] (p15) {};
\path [rotate=120] (p14) arc[start angle=0, end angle=60, radius=\ir] node[inner sep=0] (p16) {};
%\draw[gray] [rotate=240] (p16) arc[start angle=0, end angle=60, radius=\ir];
%\path [rotate=240] (p16) arc[start angle=0, end angle=30, radius=\ir] node[inner sep=0] (p17) {};
%\draw[red] (p12.center) -- (p14.center) -- (p16.center) -- (p12.center);
\node (p13) at (barycentric cs:p12=0.5,p14=0.5) {};
\node (p15) at (barycentric cs:p14=0.5,p16=0.5) {};
\node (p17) at (barycentric cs:p16=0.5,p12=0.5) {};
\def\ns{2.25}
%\draw [fill=red, opacity=0.1] (p6.center) -- (p7.center) -- (p9.center) -- (p10.center) -- (p17.center) -- (p15.center) -- (p6.center);
%\draw [fill=blue, opacity=0.1] (p1.center) -- (p2.center) -- (p13.center) -- (p17.center) -- (p10.center) -- (p11.center) -- (p1.center);
%\draw [fill=green, opacity=0.1] (p2.center) -- (p3.center) -- (p5.center) -- (p6.center) -- (p15.center) -- (p13.center) -- (p2.center);
\node[fill=yellow!50,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bc1ad) at (p0) {};
\node[fill=orange!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bcda) at (p1) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bdca) at (p2) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (cdba) at (p3) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (cd1ab) at (p4) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (cdab) at (p5) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (adcb) at (p6) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (acdb) at (p7) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (ac1bd) at (p8) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (acbd) at (p9) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (abcd) at (p10) {};
\node[fill=orange!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bcad) at (p11) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bd1ac) at (p12) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (bdac) at (p13) {};
\node[fill=orange!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (ad1bc) at (p14) {};
\node[fill=red!25,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (adbc) at (p15) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (ab1cd) at (p16) {};
\node[fill=white,draw=gray,circle,inner sep=0pt,minimum size=\ns cm] (abdc) at (p17) {};
\pic[scale=0.5] at (p0) {balancedLeft=B/C/A/D};
\pic[scale=0.5] at (p1) {combLeft=B/C/D/A};
\pic[scale=0.5] at (p2) {combLeft=B/D/C/A};
\pic[scale=0.5] at (p3) {combLeft=C/D/B/A};
\pic[scale=0.5] at (p4) {balancedLeft=C/D/A/B};
\pic[scale=0.5] at (p5) {combLeft=C/D/A/B};
\pic[scale=0.5] at (p6) {combLeft=A/D/C/B};
\pic[scale=0.5] at (p7) {combLeft=A/C/D/B};
\pic[scale=0.5] at (p8) {balancedLeft=A/C/B/D};
\pic[scale=0.5] at (p9) {combLeft=A/C/B/D};
\pic[scale=0.5] at (p10) {combLeft=A/B/C/D};
\pic[scale=0.5] at (p11) {combLeft=B/C/A/D};
\pic[scale=0.5] at (p12) {balancedLeft=B/D/A/C};
\pic[scale=0.5] at (p13) {combLeft=B/D/A/C};
\pic[scale=0.5] at (p14) {balancedLeft=A/D/B/C};
\pic[scale=0.5] at (p15) {combLeft=A/D/B/C};
\pic[scale=0.5] at (p16) {balancedLeft=A/B/C/D};
\pic[scale=0.5] at (p17) {combLeft=A/B/D/C};
% RED EDGES
\draw[black] (adbc) to node[opacity=0.0,auto] {1} (abdc);
\draw[black,double] (abdc) to node[opacity=0.0,auto] {2} (abcd);
\draw[black] (abcd) to node[opacity=0.0,auto] {1} (acbd);
\draw[black,double] (acbd) to node[opacity=0.0,auto] {2} (acdb);
\draw[black] (acdb) to node[opacity=0.0,auto] {1} (adcb);
\draw[black,double] (adcb) to node[opacity=0.0,auto] {2} (adbc);
% GREEN EDGES
\draw[black] (adcb) to node[opacity=0.0,auto] {1} (cdab);
\draw[black,double] (cdab) to node[opacity=0.0,auto] {2} (cdba);
\draw[black] (cdba) to node[opacity=0.0,auto] {1} (bdca);
\draw[black,double] (bdca) to node[opacity=0.0,auto] {2} (bdac);
\draw[black] (bdac) to node[opacity=0.0,auto] {1} (adbc);
%BLUE EDGES
\draw[black] (bdca) to node[opacity=0.0,auto] {1} (bcda);
\draw[black,double] (bcda) to node[opacity=0.0,auto] {2} (bcad);
\draw[black] (bcad) to node[opacity=0.0,auto] {1} (abcd);
\draw[black] (bdac) to node[opacity=0.0,auto] {1} (abdc);
% ORANGE EDGES
\draw[black] (cdab) to [bend right=45] node[opacity=0.0,auto,swap] {1} (acdb);
\draw[black] (bcad) to [bend left=45] node[opacity=0.0,auto] {1} (acbd);
\draw[black] (cdba) to [bend left=45] node[opacity=0.0,auto] {1} (bcda);
\draw[double] (cdab) to node[opacity=0.0,auto] {2} (cd1ab) to node[opacity=0.0,auto] {2} (cdba);
\draw[double] (bcda) to node[opacity=0.0,auto] {2} (bc1ad) to node[opacity=0.0,auto] {2} (bcad);
\draw[double] (acbd) to node[opacity=0.0,auto] {2} (ac1bd) to node[opacity=0.0,auto] {2} (acdb);
\draw[double] (abcd) to node[opacity=0.0,auto] {2} (ab1cd) to node[opacity=0.0,auto] {2} (abdc);
\draw[double] (bdac) to node[opacity=0.0,auto] {2} (bd1ac) to node[opacity=0.0,auto] {2} (bdca);
\draw[double] (adbc) to node[opacity=0.0,auto] {2} (ad1bc) to node[opacity=0.0,auto] {2} (adcb);
\tikzset{decoration={snake,amplitude=.3mm,segment length=2mm,
post length=0mm,pre length=0mm}}
%% curved rank swapping lines
\draw[decorate,black] (ab1cd) to[in=250, out=102] (cd1ab);
\draw[decorate,black] (bd1ac) to[in=12,out=225] (ac1bd);
\draw[decorate,black] (ad1bc) to[in=133,out=345] (bc1ad);
\draw[blue] ;
\end{tikzpicture}
\end{document}