Figures zig-zag.
This commit is contained in:
Georges Dupéron
parent
a32ec00566
commit
5eb7f92f4d
416
rapport.tex
416
rapport.tex
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@ -984,46 +984,208 @@ Il ne serait pas du tout utile de commencer par tous les couples $(0,y_{i})$ te
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Une solution, pour tous les nombres naturels, serait de parcourir un graphe comme suit:
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\begin{figure}[h!]
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%% «Paramètres»
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\xdef\maxdots{23}
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\xdef\maxdotsX{5}
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\xdef\maxdotsY{5}
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\xdef\maxnums{20}
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\xdef\maxcoordsX{3}
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\xdef\maxcoordsY{3}
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%% ===== Code is below =====
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%% Macros crades
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\makeatletter
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\def\myadv#1#2{%
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\xdef\incr@backup{\the\@tempcnta}%
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\@tempcnta=#1{}%
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\advance\@tempcnta by #2{}%
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\xdef#1{\the\@tempcnta}%
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\@tempcnta=\incr@backup{}%
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}
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\def\incr#1{%
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\myadv#1{1}%
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}
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\def\decr#1{%
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\myadv#1{-1}%
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}
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\makeatother
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\centering
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\begin{tikzpicture}[
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dot/.style = {
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circle,
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fill=black,
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inner sep=0.5pt
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},
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arc/.style = {
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->,
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>=stealth
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}
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scale=1.4,
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dot/.style={
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circle,
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inner sep=0.7pt,
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fill=black
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},
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dotphantom/.style={
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circle,
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inner sep=3pt,
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fill=none,
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draw=none
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},
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numero/.style={rectangle, fill=white, inner sep=2pt, text=red!50!black},
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coord/.style={darkgray, scale=.8},
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%
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bigarrow/.style={
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->,
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thick,
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draw=green!50!black
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},
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constatation1/.style={
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circle,
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inner sep=1.5pt,
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outer sep=0.8pt,
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fill=white,
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text=red,
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anchor=south,
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rotate around={45:(0,0)}
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},
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constatation2/.style={
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text=green!50!black,
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node distance=0.6cm
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}
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]
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\foreach \xpos in {0, ..., 4} {
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\foreach \ypos in {0, ..., 4} {
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\node[dot] at (\xpos,-\ypos) {};
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% %% Digonale
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% \draw[bigarrow,red] (0,0) -- (.5*7.5,-.5*7.5);
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% Définitions pour le code ci-dessous.
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\xdef\i{0}
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\xdef\x{0}
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\xdef\y{0}
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\xdef\corner{3}
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\xdef\sidelen{0}
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\xdef\nextsidelen{1}
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\xdef\direction{3}
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\incr\maxnums
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\incr\maxcoordsX
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\incr\maxcoordsY
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\foreach \x in {0,...,\maxcoordsX} {
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\foreach \y in {1,...,\maxcoordsY} {
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\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{0}
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}
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}
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\draw[arc] (0,-0) -- (1,-0);
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\def\reallysmallcheat#1{%
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\ensuremath{\hphantom{\vphantom{X}}_{\hphantom{\vphantom{X}}_{#1}}}
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}
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\def\drawnode{%
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\node[dot] (dot-\x-\y) at (\x,-\y) {};
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\node[dotphantom] (phantom-\x-\y) at (\x,-\y) {};
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\ifnum\maxnums>\i
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% \ifnum\corner=0 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
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% \ifnum\corner=1 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
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% \ifnum\corner=2 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
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% \ifnum\corner=3 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
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% \ifnum\direction=0 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \else
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% \ifnum\direction=2 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \fi\fi\fi\fi\fi\fi
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\node[numero,anchor=north west] at (dot-\x-\y.south east) {\i};
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\fi
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\ifnum\maxcoordsX>\x
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\ifnum\maxcoordsY>\y
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% \ifnum\corner=0 \node[coord,anchor=south east] at (dot-\x-\y.north west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=1 \node[coord,anchor=north east] at (dot-\x-\y.south west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=2 \node[coord,anchor=north west] at (dot-\x-\y.south east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=3 \node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=0 \node[coord,anchor=east] at (dot-\x-\y.west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=1 \node[coord,anchor=north] at (dot-\x-\y.south) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=2 \node[coord,anchor=west] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=3 \node[coord,anchor=south] at (dot-\x-\y.north) {\reallysmallcheat{(\x, \y)}}; \fi\fi\fi\fi\fi\fi\fi\fi
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\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{1}
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\ifnum\y=0
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\node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
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\else
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\node[coord,anchor=west,xshift=0.2] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
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\fi
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\fi
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\fi
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}
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\def\drawlinknode{%
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\drawnode%
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\draw[->] (phantom-\oldx-\oldy) -- (phantom-\x-\y);%
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}
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\def\mystep{%
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\incr\i%
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\xdef\oldx{\x}%
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\xdef\oldy{\y}%
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}
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\def\changedir#1{%
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\xdef\direction{#1}%
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\xdef\corner{#1}%
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}
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\draw[arc] (1,-0) -- (0,-1);
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\draw[arc] (0,-1) -- (0,-2);
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\drawnode
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\mystep \incr\x
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\xdef\cornerc{0}
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\foreach \pos in {1,...,\maxdots} {
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% Detect when we are at the end of this edge.
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\ifnum\sidelen=0
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\ifnum\direction=0 \changedir{1} \incr\nextsidelen \xdef\sidelen{1} \else
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\ifnum\direction=1 \changedir{2} \xdef\sidelen{\nextsidelen} \else
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\ifnum\direction=2 \changedir{3} \incr\nextsidelen \xdef\sidelen{1} \else
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\ifnum\direction=3 \changedir{0} \xdef\sidelen{\nextsidelen} \fi\fi\fi\fi% Brin d'acier
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\fi
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% Draw node and link to previous, step counters
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\drawlinknode \mystep
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%% Se déplacer vers ↙↓↗→
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\ifnum\direction=0 \incr\y \decr\x \fi
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\ifnum\direction=1 \incr\y \fi
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\ifnum\direction=2 \decr\y \incr\x \fi
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\ifnum\direction=3 \incr\x \fi
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\decr\sidelen
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\xdef\corner{4}%% 4 == pas de coin-coin.
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}
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\draw[arc] (0,-2) -- (1,-1);
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\draw[arc] (1,-1) -- (2,-0);
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\draw[arc] (2,-0) -- (3,-0);
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\foreach \x in {0,...,\maxdotsX} {
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\foreach \y in {1,...,\maxdotsY} {
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\node[dot] (dot-\x-\y) at (\x,-\y) {};
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}
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}
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\decr\maxcoordsX
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\decr\maxcoordsY
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\foreach \x in {0,...,\maxcoordsX} {
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\foreach \y in {0,...,\maxcoordsY} {
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\node[dot,fill=none] (fakedot-\x-\y) at (\x,-\y) {};
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\expandafter\ifnum\csname dotxypresent-\x-\y\endcsname=0
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\ifnum\y=0
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\node[coord,anchor=south west] at (fakedot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
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\else
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\node[coord,anchor=west,xshift=0.2] at (fakedot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
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\fi
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\fi
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}
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}
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\draw[arc] (3,-0) -- (2,-1);
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\draw[arc] (2,-1) -- (1,-2);
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\draw[arc] (1,-2) -- (0,-3);
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\draw[arc] (0,-3) -- (0,-4);
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% \foreach \i in {1, ...,6}{
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% \node[constatation1] at (.5*\i,-.5*\i) {\i};
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% }
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% \node[constatation1] at (.5*7,-.5*7) {\vdots};
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\draw[arc] (0,-4) -- (1,-3);
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\draw[arc,dashed] (1,-3) -- (2,-2);
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% \node[coordinate] (fake0-0) at (0,0) {};
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% \node[coordinate] (fake1-0) at (1,0) {};
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% \node[coordinate] (fake3-0) at (3,0) {};
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% \node[coordinate] (fake5-0) at (5,0) {};
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% \node[coordinate] (fake0-2) at (0,-2) {};
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% \node[coordinate] (fake0-4) at (0,-4) {};
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% \node[coordinate] (fake0-6) at (0,-6) {};
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% \node[constatation2, above left of=fake0-0] {0};
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% \node[constatation2, above of=fake1-0] {1};
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% \node[constatation2, above of=fake3-0] {6};
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% \node[constatation2, above of=fake5-0] {15};
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% \node[constatation2, left of=fake0-2] {3};
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% \node[constatation2, left of=fake0-4] {10};
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% \node[constatation2, left of=fake0-6] {21};
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\end{tikzpicture}
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\caption{Codage d'un couple d'entiers naturels}% TODO : caption
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\caption{Codage d'un couple d'entiers relatifs}%% TODO : caption
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\label{fig:codage-zigzag}
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\end{figure}
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%% TODO: Il faudrait ajouter les coordonnées (0,0), (1,0), (0,1), et les codes correspondants au graphe ci-dessus, etc. VOIR LES DIAGRAMMES QUE J'AI DONNE A BERTRAND
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%% TODO : Réponse georges : c'est fait.
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Dans la figure \ref{fig:codage-zigzag}, on commence par le couple $(0,0)$, puis on procède aux couples $(1,0)$, $(0,1)$, $(0,2)$, $(1,1)$, $(2,0)$, $(3,0)$, $(2,1)$, $(1,2)$, $(0,3)$, $(0,4)$\ldots L'algorithme pour simplement parcourir les couples de cette façon consisterait tout d'abord de déclarer et d'intialiser trois variables globales~: le point de départ, \lstinline!*current*!, et les valeurs maximales courantes de $x$ et de $y$, c'est-à-dire \lstinline!*max-x*! et \lstinline!*max-y*!. En LISP, ceci pourrait être codé comme suit~:
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@ -1136,7 +1298,209 @@ Voici une trace de cette fonction en passant \lstinline!*current*! égal à \lst
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Donner les fonctions de codage et de décodage $f_1(z)\rightarrow x$ et $f_2(z)\rightarrow y$.
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\end{enonce}
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TODO: Même figure que la précédente, mais avec les 'constatations' ajoutées (je ferai un diagramme papier pour qu'on sache ce que je veux ici)
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\begin{figure}[h!]
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%% «Paramètres»
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\xdef\maxdots{23}
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\xdef\maxdotsX{5}
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\xdef\maxdotsY{5}
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\xdef\maxnums{20}
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\xdef\maxcoordsX{3}
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\xdef\maxcoordsY{3}
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%% ===== Code is below =====
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%% Macros crades
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\makeatletter
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\def\myadv#1#2{%
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\xdef\incr@backup{\the\@tempcnta}%
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\@tempcnta=#1{}%
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\advance\@tempcnta by #2{}%
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\xdef#1{\the\@tempcnta}%
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\@tempcnta=\incr@backup{}%
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}
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\def\incr#1{%
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\myadv#1{1}%
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}
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\def\decr#1{%
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\myadv#1{-1}%
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}
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\makeatother
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\centering
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\begin{tikzpicture}[
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scale=1.4,
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dot/.style={
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circle,
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inner sep=0.7pt,
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fill=black
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},
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dotphantom/.style={
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circle,
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inner sep=3pt,
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fill=none,
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draw=none
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},
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numero/.style={rectangle, fill=white, inner sep=2pt, text=red!50!black},
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coord/.style={darkgray, scale=.8},
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%
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bigarrow/.style={
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->,
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thick,
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draw=green!50!black
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},
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constatation1/.style={
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circle,
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inner sep=1.5pt,
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outer sep=0.8pt,
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fill=white,
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text=red,
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anchor=south,
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rotate around={45:(0,0)}
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},
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constatation2/.style={
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text=green!50!black,
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node distance=0.6cm
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}
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]
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%% Digonale
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\draw[bigarrow,red] (0,0) -- (.5*7.5,-.5*7.5);
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% Définitions pour le code ci-dessous.
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\xdef\i{0}
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\xdef\x{0}
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\xdef\y{0}
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\xdef\corner{3}
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\xdef\sidelen{0}
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\xdef\nextsidelen{1}
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\xdef\direction{3}
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\incr\maxnums
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\incr\maxcoordsX
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\incr\maxcoordsY
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\foreach \x in {0,...,\maxcoordsX} {
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\foreach \y in {1,...,\maxcoordsY} {
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\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{0}
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}
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}
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\def\reallysmallcheat#1{%
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\ensuremath{\hphantom{\vphantom{X}}_{\hphantom{\vphantom{X}}_{#1}}}
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}
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\def\drawnode{%
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\node[dot] (dot-\x-\y) at (\x,-\y) {};
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\node[dotphantom] (phantom-\x-\y) at (\x,-\y) {};
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\ifnum\maxnums>\i
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% \ifnum\corner=0 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
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% \ifnum\corner=1 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
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% \ifnum\corner=2 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
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% \ifnum\corner=3 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
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% \ifnum\direction=0 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \else
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% \ifnum\direction=2 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \fi\fi\fi\fi\fi\fi
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\node[numero,anchor=north west] at (dot-\x-\y.south east) {\i};
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\fi
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\ifnum\maxcoordsX>\x
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\ifnum\maxcoordsY>\y
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% \ifnum\corner=0 \node[coord,anchor=south east] at (dot-\x-\y.north west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=1 \node[coord,anchor=north east] at (dot-\x-\y.south west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=2 \node[coord,anchor=north west] at (dot-\x-\y.south east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\corner=3 \node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=0 \node[coord,anchor=east] at (dot-\x-\y.west) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=1 \node[coord,anchor=north] at (dot-\x-\y.south) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=2 \node[coord,anchor=west] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}}; \else
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% \ifnum\direction=3 \node[coord,anchor=south] at (dot-\x-\y.north) {\reallysmallcheat{(\x, \y)}}; \fi\fi\fi\fi\fi\fi\fi\fi
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\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{1}
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\ifnum\y=0
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\node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
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\else
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\node[coord,anchor=west,xshift=0.2] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
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\fi
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\fi
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\fi
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}
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\def\drawlinknode{%
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\drawnode%
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\draw[->] (phantom-\oldx-\oldy) -- (phantom-\x-\y);%
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}
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\def\mystep{%
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\incr\i%
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\xdef\oldx{\x}%
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\xdef\oldy{\y}%
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}
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\def\changedir#1{%
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\xdef\direction{#1}%
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\xdef\corner{#1}%
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}
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\drawnode
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\mystep \incr\x
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\xdef\cornerc{0}
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\foreach \pos in {1,...,\maxdots} {
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% Detect when we are at the end of this edge.
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\ifnum\sidelen=0
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\ifnum\direction=0 \changedir{1} \incr\nextsidelen \xdef\sidelen{1} \else
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\ifnum\direction=1 \changedir{2} \xdef\sidelen{\nextsidelen} \else
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\ifnum\direction=2 \changedir{3} \incr\nextsidelen \xdef\sidelen{1} \else
|
||||
\ifnum\direction=3 \changedir{0} \xdef\sidelen{\nextsidelen} \fi\fi\fi\fi% Brin d'acier
|
||||
|
||||
\fi
|
||||
% Draw node and link to previous, step counters
|
||||
\drawlinknode \mystep
|
||||
%% Se déplacer vers ↙↓↗→
|
||||
\ifnum\direction=0 \incr\y \decr\x \fi
|
||||
\ifnum\direction=1 \incr\y \fi
|
||||
\ifnum\direction=2 \decr\y \incr\x \fi
|
||||
\ifnum\direction=3 \incr\x \fi
|
||||
\decr\sidelen
|
||||
\xdef\corner{4}%% 4 == pas de coin-coin.
|
||||
}
|
||||
|
||||
\foreach \x in {0,...,\maxdotsX} {
|
||||
\foreach \y in {1,...,\maxdotsY} {
|
||||
\node[dot] (dot-\x-\y) at (\x,-\y) {};
|
||||
}
|
||||
}
|
||||
\decr\maxcoordsX
|
||||
\decr\maxcoordsY
|
||||
\foreach \x in {0,...,\maxcoordsX} {
|
||||
\foreach \y in {0,...,\maxcoordsY} {
|
||||
\node[dot,fill=none] (fakedot-\x-\y) at (\x,-\y) {};
|
||||
\expandafter\ifnum\csname dotxypresent-\x-\y\endcsname=0
|
||||
\ifnum\y=0
|
||||
\node[coord,anchor=south west] at (fakedot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
|
||||
\else
|
||||
\node[coord,anchor=west,xshift=0.2] at (fakedot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
|
||||
\fi
|
||||
\fi
|
||||
}
|
||||
}
|
||||
|
||||
\foreach \i in {1, ...,6}{
|
||||
\node[constatation1] at (.5*\i,-.5*\i) {\i};
|
||||
}
|
||||
\node[constatation1] at (.5*7,-.5*7) {\vdots};
|
||||
|
||||
\node[coordinate] (fake0-0) at (0,0) {};
|
||||
\node[constatation2, coordinate, above of=fake0-0] (fake0-0-bis) {};
|
||||
\node[coordinate] (fake1-0) at (1,0) {};
|
||||
\node[coordinate] (fake3-0) at (3,0) {};
|
||||
\node[coordinate] (fake5-0) at (5,0) {};
|
||||
\node[coordinate] (fake0-2) at (0,-2) {};
|
||||
\node[coordinate] (fake0-4) at (0,-4) {};
|
||||
\node[coordinate] (fake0-6) at (0,-6) {};
|
||||
\node[constatation2, left of=fake0-0-bis] {0};
|
||||
\node[constatation2, above of=fake1-0] {1};
|
||||
\node[constatation2, above of=fake3-0] {6};
|
||||
\node[constatation2, above of=fake5-0] {15};
|
||||
\node[constatation2, left of=fake0-2] {3};
|
||||
\node[constatation2, left of=fake0-4] {10};
|
||||
\node[constatation2, left of=fake0-6] {21};
|
||||
\end{tikzpicture}
|
||||
\caption{Codage d'un couple d'entiers relatifs}%% TODO : caption
|
||||
\label{fig:codage-nat-avec-constatation}
|
||||
\end{figure}
|
||||
%% TODO: Même figure que la précédente, mais avec les 'constatations' ajoutées (je ferai un diagramme papier pour qu'on sache ce que je veux ici)
|
||||
%% TODO : Réponse georges, c'est bon ?
|
||||
|
||||
En reprenant la figure ??? ci-dessus, on peut faire plusieurs constatations~:
|
||||
|
||||
|
|
|
|||
236
test.tex
236
test.tex
|
|
@ -50,9 +50,12 @@
|
|||
|
||||
\begin{figure}[h!]
|
||||
%% «Paramètres»
|
||||
\xdef\maxdots{81}
|
||||
\xdef\maxnums{56}
|
||||
\xdef\maxcoords{20}
|
||||
\xdef\maxdots{23}
|
||||
\xdef\maxdotsX{5}
|
||||
\xdef\maxdotsY{5}
|
||||
\xdef\maxnums{20}
|
||||
\xdef\maxcoordsX{3}
|
||||
\xdef\maxcoordsY{3}
|
||||
|
||||
%% ===== Code is below =====
|
||||
|
||||
|
|
@ -72,9 +75,9 @@
|
|||
\myadv#1{-1}%
|
||||
}
|
||||
\makeatother
|
||||
% \centering
|
||||
\hskip -21mm%% Hack-o-matic to get the picture more or less centered…
|
||||
\centering
|
||||
\begin{tikzpicture}[
|
||||
scale=1.4,
|
||||
dot/.style={
|
||||
circle,
|
||||
inner sep=0.7pt,
|
||||
|
|
@ -86,97 +89,82 @@
|
|||
fill=none,
|
||||
draw=none
|
||||
},
|
||||
numero/.style={circle, fill=white, inner sep=0.2pt, text=red, scale=.75},
|
||||
coord/.style={darkgray, scale=.6},
|
||||
numero/.style={rectangle, fill=white, inner sep=2pt, text=red!50!black},
|
||||
coord/.style={darkgray, scale=.8},
|
||||
%
|
||||
bigarrow/.style={
|
||||
->,
|
||||
thick,
|
||||
draw=green!50!black
|
||||
},
|
||||
constatation1/.style={
|
||||
circle,
|
||||
inner sep=1.5pt,
|
||||
outer sep=0.8pt,
|
||||
fill=white,
|
||||
text=red,
|
||||
anchor=south,
|
||||
rotate around={45:(0,0)}
|
||||
},
|
||||
constatation2/.style={
|
||||
text=green!50!black,
|
||||
node distance=0.6cm
|
||||
}
|
||||
]
|
||||
|
||||
% Diagonales
|
||||
\node[dotphantom] (pre-phantom-0-0) at (0,0) {};
|
||||
\node[dotphantom] (pre-phantom-1-0) at (1,0) {};
|
||||
% %% Digonale
|
||||
% \draw[bigarrow,red] (0,0) -- (.5*7.5,-.5*7.5);
|
||||
|
||||
% Top right
|
||||
\node[inner sep=0.1pt] (tr-start) at (4,4) {};
|
||||
\xdef\previous{tr-start}
|
||||
\foreach \pos/\content in {0/$1\times 2=2$,1/$3\times 4=12$,2/$5\times 6=30$,3/$7\times 8=56$,4/$\vphantom{X}\dots$}{
|
||||
\node[anchor=south] (tr-temp-\pos) at (intersection cs: first line={(\previous.north west)--(\previous.north east)}, second line={(0,0)--(6,6)}) {\phantom{\content}};
|
||||
\node[anchor=north west] (tr-\pos) at (intersection cs: first line={(tr-temp-\pos.north west)--(tr-temp-\pos.north east)}, second line={(0,0)--(6,6)}) {\content};
|
||||
\xdef\previous{tr-\pos}
|
||||
}
|
||||
\draw[bigarrow] (pre-phantom-0-0) -- (intersection cs: first line={(\previous.north west)--(\previous.south west)}, second line={(0,0)--(6,6)});
|
||||
|
||||
% Top left
|
||||
\node[inner sep=0.1pt] (tl-start) at (-4,4) {};
|
||||
\xdef\previous{tl-start}
|
||||
\foreach \pos/\content in {0/$0^2=0$,1/$2^2=4$,2/$6^2=36$,3/$8^2=64$,4/$\vphantom{X}\dots$}{
|
||||
\node[anchor=south] (tl-temp-\pos) at (intersection cs: first line={(\previous.north west)--(\previous.north east)}, second line={(0,0)--(-6,6)}) {\phantom{\content}};
|
||||
\node[anchor=north east] (tl-\pos) at (intersection cs: first line={(tl-temp-\pos.north west)--(tl-temp-\pos.north east)}, second line={(0,0)--(-6,6)}) {\content};
|
||||
\xdef\previous{tl-\pos}
|
||||
}
|
||||
\draw[bigarrow] (pre-phantom-0-0) -- (intersection cs: first line={(\previous.north east)--(\previous.south east)}, second line={(0,0)--(-6,6)});
|
||||
|
||||
% Bottom left
|
||||
\node[inner sep=0.1pt] (bl-start) at (-4,-4) {};
|
||||
\xdef\previous{bl-start}
|
||||
\foreach \pos/\content in {0/$0\times 1=0$,1/$2\times 3=6$,2/$4\times 5=20$,3/$6\times 7=42$,4/$\vphantom{X}\dots$}{
|
||||
\node[anchor=north] (bl-temp-\pos) at (intersection cs: first line={(\previous.south west)--(\previous.south east)}, second line={(0,0)--(-6,-6)}) {\phantom{\content}};
|
||||
\node[anchor=south east] (bl-\pos) at (intersection cs: first line={(bl-temp-\pos.south west)--(bl-temp-\pos.south east)}, second line={(0,0)--(-6,-6)}) {\content};
|
||||
\xdef\previous{bl-\pos}
|
||||
}
|
||||
\draw[bigarrow] (pre-phantom-0-0) -- (intersection cs: first line={(\previous.north east)--(\previous.south east)}, second line={(0,0)--(-6,-6)});
|
||||
|
||||
% Bottom right
|
||||
\node[inner sep=0.1pt] (br-start) at (5,-4) {};
|
||||
\xdef\previous{br-start}
|
||||
\foreach \pos/\content in {0/$1^2=1$,1/$3^2=9$,2/$5^2=25$,3/$7^2=49$,4/$\vphantom{X}\dots$}{
|
||||
\node[anchor=north] (br-temp-\pos) at (intersection cs: first line={(\previous.south west)--(\previous.south east)}, second line={(1,0)--(6,-5)}) {\phantom{\content}};
|
||||
\node[anchor=south west] (br-\pos) at (intersection cs: first line={(br-temp-\pos.south west)--(br-temp-\pos.south east)}, second line={(1,0)--(6,-5)}) {\content};
|
||||
\xdef\previous{br-\pos}
|
||||
}
|
||||
\draw[bigarrow] (pre-phantom-1-0) -- (intersection cs: first line={(\previous.north west)--(\previous.south west)}, second line={(1,0)--(6,-5)});
|
||||
% Fin diagonales
|
||||
|
||||
% Définitions pour le code ci-dessous.
|
||||
\xdef\i{0}
|
||||
\xdef\x{0}
|
||||
\xdef\y{0}
|
||||
\xdef\corner{4}
|
||||
\xdef\corner{3}
|
||||
\xdef\sidelen{0}
|
||||
\xdef\nextsidelen{1}
|
||||
\xdef\direction{3}
|
||||
\incr\maxnums
|
||||
\incr\maxcoords
|
||||
\incr\maxcoordsX
|
||||
\incr\maxcoordsY
|
||||
|
||||
\foreach \x in {0,...,\maxcoordsX} {
|
||||
\foreach \y in {1,...,\maxcoordsY} {
|
||||
\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{0}
|
||||
}
|
||||
}
|
||||
|
||||
\def\reallysmallcheat#1{%
|
||||
\ensuremath{\hphantom{\vphantom{X}}_{\hphantom{\vphantom{X}}_{#1}}}
|
||||
}
|
||||
\def\drawnode{%
|
||||
\node[dot] (dot-\x-\y) at (\x,\y) {};
|
||||
\node[dotphantom] (phantom-\x-\y) at (\x,\y) {};
|
||||
\node[dot] (dot-\x-\y) at (\x,-\y) {};
|
||||
\node[dotphantom] (phantom-\x-\y) at (\x,-\y) {};
|
||||
\ifnum\maxnums>\i
|
||||
\ifnum\corner=0 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \else
|
||||
\ifnum\corner=1 \node[numero,anchor=south west] at (dot-\x-\y.north east) {\i}; \else
|
||||
\ifnum\corner=2 \node[numero,anchor=south east] at (dot-\x-\y.north west) {\i}; \else
|
||||
\ifnum\corner=3 \node[numero,anchor=north east] at (dot-\x-\y.south west) {\i}; \else
|
||||
\ifnum\direction=0 \node[numero,anchor=west] at (dot-\x-\y.east) {\i}; \else
|
||||
\ifnum\direction=1 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
|
||||
\ifnum\direction=2 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
|
||||
\ifnum\direction=3 \node[numero,anchor=north] at (dot-\x-\y.south) {\i}; \fi\fi\fi\fi\fi\fi\fi\fi
|
||||
% \ifnum\corner=0 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
|
||||
% \ifnum\corner=1 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
|
||||
% \ifnum\corner=2 \node[numero,anchor=east] at (dot-\x-\y.west) {\i}; \else
|
||||
% \ifnum\corner=3 \node[numero,anchor=south] at (dot-\x-\y.north) {\i}; \else
|
||||
% \ifnum\direction=0 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \else
|
||||
% \ifnum\direction=2 \node[numero,anchor=north west] at (dot-\x-\y.south east) {\i}; \fi\fi\fi\fi\fi\fi
|
||||
\node[numero,anchor=north west] at (dot-\x-\y.south east) {\i};
|
||||
\fi
|
||||
\ifnum\maxcoordsX>\x
|
||||
\ifnum\maxcoordsY>\y
|
||||
% \ifnum\corner=0 \node[coord,anchor=south east] at (dot-\x-\y.north west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\corner=1 \node[coord,anchor=north east] at (dot-\x-\y.south west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\corner=2 \node[coord,anchor=north west] at (dot-\x-\y.south east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\corner=3 \node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\direction=0 \node[coord,anchor=east] at (dot-\x-\y.west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\direction=1 \node[coord,anchor=north] at (dot-\x-\y.south) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\direction=2 \node[coord,anchor=west] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
% \ifnum\direction=3 \node[coord,anchor=south] at (dot-\x-\y.north) {\reallysmallcheat{(\x, \y)}}; \fi\fi\fi\fi\fi\fi\fi\fi
|
||||
\expandafter\xdef\csname dotxypresent-\x-\y\endcsname{1}
|
||||
\ifnum\y=0
|
||||
\node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
|
||||
\else
|
||||
\node[coord,anchor=west,xshift=0.2] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
|
||||
\fi
|
||||
\fi
|
||||
\ifnum\maxcoords>\i
|
||||
\ifnum\corner=0 \node[coord,anchor=south east] at (dot-\x-\y.north west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\corner=1 \node[coord,anchor=north east] at (dot-\x-\y.south west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\corner=2 \node[coord,anchor=north west] at (dot-\x-\y.south east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\corner=3 \node[coord,anchor=south west] at (dot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\direction=0 \node[coord,anchor=east] at (dot-\x-\y.west) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\direction=1 \node[coord,anchor=north] at (dot-\x-\y.south) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\direction=2 \node[coord,anchor=west] at (dot-\x-\y.east) {\reallysmallcheat{(\x, \y)}}; \else
|
||||
\ifnum\direction=3 \node[coord,anchor=south] at (dot-\x-\y.north) {\reallysmallcheat{(\x, \y)}}; \fi\fi\fi\fi\fi\fi\fi\fi
|
||||
\fi
|
||||
}
|
||||
\def\drawlinknode{%
|
||||
|
|
@ -200,25 +188,105 @@
|
|||
\foreach \pos in {1,...,\maxdots} {
|
||||
% Detect when we are at the end of this edge.
|
||||
\ifnum\sidelen=0
|
||||
\ifnum\direction=0 \changedir{1} \incr\nextsidelen \else
|
||||
\ifnum\direction=1 \changedir{2} \else
|
||||
\ifnum\direction=2 \changedir{3} \incr\nextsidelen \else
|
||||
\ifnum\direction=3 \changedir{0} \fi\fi\fi\fi% Brin d'acier
|
||||
\xdef\sidelen{\nextsidelen}
|
||||
\ifnum\direction=0 \changedir{1} \incr\nextsidelen \xdef\sidelen{1} \else
|
||||
\ifnum\direction=1 \changedir{2} \xdef\sidelen{\nextsidelen} \else
|
||||
\ifnum\direction=2 \changedir{3} \incr\nextsidelen \xdef\sidelen{1} \else
|
||||
\ifnum\direction=3 \changedir{0} \xdef\sidelen{\nextsidelen} \fi\fi\fi\fi% Brin d'acier
|
||||
|
||||
\fi
|
||||
% Draw node and link to previous, step counters
|
||||
\drawlinknode \mystep
|
||||
%% Se déplacer vers ↑←↓→
|
||||
\ifnum\direction=0 \incr\y \fi
|
||||
\ifnum\direction=1 \decr\x \fi
|
||||
\ifnum\direction=2 \decr\y \fi
|
||||
\ifnum\direction=3 \incr\x \fi
|
||||
%% Se déplacer vers ↙↓↗→
|
||||
\ifnum\direction=0 \incr\y \decr\x \fi
|
||||
\ifnum\direction=1 \incr\y \fi
|
||||
\ifnum\direction=2 \decr\y \incr\x \fi
|
||||
\ifnum\direction=3 \incr\x \fi
|
||||
\decr\sidelen
|
||||
\xdef\corner{4}%% 4 == pas de coin-coin.
|
||||
}
|
||||
|
||||
\foreach \x in {0,...,\maxdotsX} {
|
||||
\foreach \y in {1,...,\maxdotsY} {
|
||||
\node[dot] (dot-\x-\y) at (\x,-\y) {};
|
||||
}
|
||||
}
|
||||
\decr\maxcoordsX
|
||||
\decr\maxcoordsY
|
||||
\foreach \x in {0,...,\maxcoordsX} {
|
||||
\foreach \y in {0,...,\maxcoordsY} {
|
||||
\node[dot,fill=none] (fakedot-\x-\y) at (\x,-\y) {};
|
||||
\expandafter\ifnum\csname dotxypresent-\x-\y\endcsname=0
|
||||
\ifnum\y=0
|
||||
\node[coord,anchor=south west] at (fakedot-\x-\y.north east) {\reallysmallcheat{(\x, \y)}};
|
||||
\else
|
||||
\node[coord,anchor=west,xshift=0.2] at (fakedot-\x-\y.east) {\reallysmallcheat{(\x, \y)}};
|
||||
\fi
|
||||
\fi
|
||||
}
|
||||
}
|
||||
|
||||
% \foreach \i in {1, ...,6}{
|
||||
% \node[constatation1] at (.5*\i,-.5*\i) {\i};
|
||||
% }
|
||||
% \node[constatation1] at (.5*7,-.5*7) {\vdots};
|
||||
|
||||
% \node[coordinate] (fake0-0) at (0,0) {};
|
||||
% \node[coordinate] (fake1-0) at (1,0) {};
|
||||
% \node[coordinate] (fake3-0) at (3,0) {};
|
||||
% \node[coordinate] (fake5-0) at (5,0) {};
|
||||
% \node[coordinate] (fake0-2) at (0,-2) {};
|
||||
% \node[coordinate] (fake0-4) at (0,-4) {};
|
||||
% \node[coordinate] (fake0-6) at (0,-6) {};
|
||||
% \node[constatation2, above left of=fake0-0] {0};
|
||||
% \node[constatation2, above of=fake1-0] {1};
|
||||
% \node[constatation2, above of=fake3-0] {6};
|
||||
% \node[constatation2, above of=fake5-0] {15};
|
||||
% \node[constatation2, left of=fake0-2] {3};
|
||||
% \node[constatation2, left of=fake0-4] {10};
|
||||
% \node[constatation2, left of=fake0-6] {21};
|
||||
\end{tikzpicture}
|
||||
\caption{Codage d'un couple d'entiers relatifs}
|
||||
\label{fig:codage-rel}
|
||||
\caption{Codage d'un couple d'entiers relatifs}%% TODO : caption
|
||||
\label{fig:codage-nat-sans-constatation}
|
||||
\end{figure}
|
||||
|
||||
% \begin{figure}[h!]
|
||||
% \centering
|
||||
% \begin{tikzpicture}[
|
||||
% dot/.style = {
|
||||
% circle,
|
||||
% fill=black,
|
||||
% inner sep=0.5pt
|
||||
% },
|
||||
% arc/.style = {
|
||||
% ->,
|
||||
% >=stealth
|
||||
% }
|
||||
% ]
|
||||
% \foreach \xpos in {0, ..., 4} {
|
||||
% \foreach \ypos in {0, ..., 4} {
|
||||
% \node[dot] at (\xpos,-\ypos) {};
|
||||
% }
|
||||
% }
|
||||
|
||||
% \draw[arc] (0,-0) -- (1,-0);
|
||||
|
||||
% \draw[arc] (1,-0) -- (0,-1);
|
||||
% \draw[arc] (0,-1) -- (0,-2);
|
||||
|
||||
% \draw[arc] (0,-2) -- (1,-1);
|
||||
% \draw[arc] (1,-1) -- (2,-0);
|
||||
% \draw[arc] (2,-0) -- (3,-0);
|
||||
|
||||
% \draw[arc] (3,-0) -- (2,-1);
|
||||
% \draw[arc] (2,-1) -- (1,-2);
|
||||
% \draw[arc] (1,-2) -- (0,-3);
|
||||
% \draw[arc] (0,-3) -- (0,-4);
|
||||
|
||||
% \draw[arc] (0,-4) -- (1,-3);
|
||||
% \draw[arc,dashed] (1,-3) -- (2,-2);
|
||||
% \end{tikzpicture}
|
||||
% \caption{Codage d'un couple d'entiers relatifs}
|
||||
% \label{fig:codage-rel}
|
||||
% \end{figure}
|
||||
|
||||
\end{document}
|
||||
Loading…
Reference in New Issue
Block a user