503 lines
14 KiB
Typst
503 lines
14 KiB
Typst
#import "@preview/polylux:0.4.0": *
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#import "@preview/cetz:0.5.0"
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#import "@preview/cetz-plot:0.1.3": plot
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#set math.mat(delim: "[")
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// Infos
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#let auteur = "Anthony PERRONI"
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#let numero = "49871"
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#let titre = "Codes LDPC"
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#let annee = "2025 - 2026"
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// Template
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#let myslide(partie, contenu) = slide[
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// Header
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#block(width: 100%, fill: black, inset: (top: 0.6cm, bottom: 0.6cm, left: 1.5cm, right: 1.5cm))[
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#set text(fill: white, size: 28pt, weight: "bold")
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#partie
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]
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// Contenu
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#pad(x: 1.5cm, top: 0.2cm)[
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#set text(size: 20pt)
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#contenu
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]
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// Footer
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#v(1fr)
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#context {
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// let cur = counter(page).get().first()
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// let tot = counter(page).final().first()
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let cur = counter("logical-slide").get().first()
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let tot = counter("logical-slide").final().first()
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if cur > 1 {
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block(width: 100%, fill: black, inset: (top: 0.2cm, bottom: 0.2cm, left: 1.5cm, right: 1.5cm))[
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#set text(fill: white, size: 12pt, weight: "bold")
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#grid(
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columns: (1.5fr, 2fr, 1fr, auto),
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align: (left, center, center, right),
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[#auteur n°#numero], [#titre], [#annee], [#(cur - 1) / #(tot - 1)],
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)
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]
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}
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}
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]
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// Plan
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#let design_plan(items) = {
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let r = 6pt
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let epaisseur = 2pt
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let hauteur_ligne = 2.5em
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let espace_vertical = 20pt
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pad(left: 1cm, top: 1cm)[
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#block[
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#place(dx: r, dy: hauteur_ligne / 2)[
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#line(
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length: (items.len() - 1) * (hauteur_ligne + espace_vertical),
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angle: 90deg,
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stroke: epaisseur + black,
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)
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]
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#grid(
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columns: (2 * r, auto),
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column-gutter: 20pt,
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row-gutter: espace_vertical,
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..items
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.map(item => (
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box(height: hauteur_ligne, align(center + horizon)[
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#circle(radius: r, fill: white, stroke: epaisseur + black)
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]),
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box(height: hauteur_ligne, align(left + horizon)[
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#text(weight: "bold", size: 1.1em)[#item]
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]),
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))
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.flatten()
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)
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]
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]
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}
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// Graphe de Tanner en filigrane
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#let graphe_tanner_fond(taille, spread) = {
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cetz.canvas(length: taille, {
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import cetz.draw: *
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let n_var = 18
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let n_chk = 9
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let var_y = 11
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let chk_y = -8
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// Calcul automatique pour que le graphe soit centré sur X=0
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let dist_v = (n_var - 1) * spread
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let v_start = -dist_v / 2
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let vpos = range(n_var).map(i => (v_start + i * spread, var_y))
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let spread_c = dist_v / (n_chk - 1)
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let c_start = -dist_v / 2
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let cpos = range(n_chk).map(i => (c_start + i * spread_c, chk_y))
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let edges = (
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(0, 0),
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(0, 4),
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(0, 8),
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(1, 1),
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(1, 5),
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(1, 0),
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(2, 2),
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(2, 6),
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(2, 1),
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(3, 3),
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(3, 7),
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(3, 2),
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(4, 4),
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(4, 8),
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(4, 3),
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(5, 5),
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(5, 0),
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(5, 4),
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(6, 6),
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(6, 1),
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(6, 5),
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(7, 7),
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(7, 2),
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(7, 6),
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(8, 8),
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(8, 3),
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(8, 7),
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(9, 0),
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(9, 3),
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(9, 6),
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(10, 1),
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(10, 4),
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(10, 7),
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(11, 2),
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(11, 5),
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(11, 8),
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(12, 0),
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(12, 5),
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(12, 7),
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(13, 1),
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(13, 3),
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(13, 8),
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(14, 2),
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(14, 4),
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(14, 6),
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(15, 0),
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(15, 4),
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(15, 7),
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(16, 1),
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(16, 5),
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(16, 8),
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(17, 2),
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(17, 3),
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(17, 6),
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)
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for e in edges {
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let vp = vpos.at(e.at(0))
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let cp = cpos.at(e.at(1))
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line((vp.at(0), vp.at(1)), (cp.at(0), cp.at(1)), stroke: 0.45pt + rgb("#e0e0e0"))
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}
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for p in vpos {
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circle((p.at(0), p.at(1)), radius: 0.25, fill: white, stroke: 0.8pt + rgb("#cccccc"))
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}
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for p in cpos {
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let (x, y) = p
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rect((x - 0.25, y - 0.25), (x + 0.25, y + 0.25), fill: white, stroke: 0.8pt + rgb("#cccccc"))
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}
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})
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}
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// Schema Shannon
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#let canal_shannon_intro() = {
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cetz.canvas({
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import cetz.draw: *
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// Styles
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let s = (stroke: 2pt + black)
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let s_fleche = (stroke: 2pt + black)
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let pointe_pleine = (end: "stealth", fill: black)
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let espacement = 5.5
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// Blocs
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content((0, 0), [Source], name: "src", frame: "rect", ..s, padding: .3)
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content((espacement, 0), [Emetteur], name: "em", frame: "rect", ..s, padding: .3)
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content((espacement * 2, 0), [Canal], name: "chan", frame: "rect", ..s, padding: .3)
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content((espacement * 3, 0), [Récepteur], name: "rec", frame: "rect", ..s, padding: .3)
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content((espacement * 4, 0), [Destinataire], name: "dest", frame: "rect", ..s, padding: .3)
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// Bruit
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content((rel: (0, 1.8), to: "chan"), [Bruit], name: "bruit", frame: "rect", ..s, padding: .3)
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// Codage / Décodage
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content((rel: (0, 1), to: "em"), [*Codage*])
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content((rel: (0, 1), to: "rec"), [*Décodage*])
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// Flèches (On utilise s_fleche et pointe_pleine)
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line("src.east", "em.west", mark: pointe_pleine, ..s_fleche)
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line("em.east", "chan.west", mark: pointe_pleine, ..s_fleche)
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line("chan.east", "rec.west", mark: pointe_pleine, ..s_fleche)
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line("rec.east", "dest.west", mark: pointe_pleine, ..s_fleche)
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line("bruit.south", "chan.north", mark: pointe_pleine, ..s_fleche)
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// Annotation
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let note-style = (size: 0.75em, style: "italic")
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content((espacement * 0.5, -0.5), text(..note-style)[Message])
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content((espacement * 1.5, -0.5), text(..note-style)[Signal])
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content((espacement * 2.5, -0.5), text(..note-style)[Signal])
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content((espacement * 3.5, -0.5), text(..note-style)[Message])
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})
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}
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#let plongement_schema() = {
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cetz.canvas(length: 1.5cm, {
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import cetz.draw: *
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// Styles
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let style-pointille = (stroke: (paint: black, thickness: 1.2pt, dash: "dashed"))
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let style-point = (fill: black, stroke: none)
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let rayon-point = 0.08
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let pointe-fleche = (end: "stealth", fill: black)
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let m = (
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p00: (-4, 0),
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p01: (-2, 0),
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p11: (-2, -2),
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p10: (-4, -2),
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)
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// Arêtes pointillés
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line(m.p00, m.p01, m.p11, m.p10, close: true, ..style-pointille)
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// Points sur les sommets
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circle(m.p00, radius: rayon-point, ..style-point)
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circle(m.p01, radius: rayon-point, ..style-point)
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circle(m.p11, radius: rayon-point, ..style-point)
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circle(m.p10, radius: rayon-point, ..style-point)
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// Étiquettes
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content(m.p00, [00], anchor: "south-east", padding: .2)
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content(m.p01, [01], anchor: "south-west", padding: .2)
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content(m.p11, [11], anchor: "north-west", padding: .2)
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content(m.p10, [10], anchor: "north-east", padding: .2)
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content((-3, -2.6), [$FF_2^2$])
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line((-1.2, -1), (1.2, -1), mark: pointe-fleche, stroke: 1.5pt + black)
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content((0, -0.6), [*Plongement*])
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// Sommets face arrière
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let cb = (p000: (2.5, 0), p001: (4.5, 0), p011: (4.5, -2), p010: (2.5, -2))
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// Sommets face avant (décalés)
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let cf = (p100: (3.5, 1), p101: (5.5, 1), p111: (5.5, -1), p110: (3.5, -1))
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// Arêtes pointillés du cube
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line(cb.p000, cb.p001, cb.p011, cb.p010, close: true, ..style-pointille) // Face arrière
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line(cf.p100, cf.p101, cf.p111, cf.p110, close: true, ..style-pointille) // Face avant
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line(cb.p000, cf.p100, ..style-pointille) // Liaisons
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line(cb.p001, cf.p101, ..style-pointille)
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line(cb.p011, cf.p111, ..style-pointille)
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line(cb.p010, cf.p110, ..style-pointille)
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// Points sur les sommets du cube
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circle(cb.p000, radius: rayon-point, ..style-point)
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circle(cb.p001, radius: rayon-point, ..style-point)
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circle(cb.p011, radius: rayon-point, ..style-point)
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circle(cb.p010, radius: rayon-point, ..style-point)
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circle(cf.p100, radius: rayon-point, ..style-point)
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circle(cf.p101, radius: rayon-point, ..style-point)
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circle(cf.p111, radius: rayon-point, ..style-point)
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circle(cf.p110, radius: rayon-point, ..style-point)
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// Étiquettes du cube
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content(cb.p000, [000], anchor: "south-east", padding: .2)
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// content(cb.p001, [001], anchor: "south-west", padding: .2)
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content((rel: (-0.85, 0.1), to: cb.p001), [001], anchor: "south-west", padding: .2)
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content(cb.p011, [011], anchor: "north-west", padding: .2)
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content(cb.p010, [010], anchor: "north-east", padding: .2)
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content(cf.p100, [100], anchor: "south-east", padding: .2)
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content(cf.p101, [101], anchor: "south-west", padding: .2)
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content(cf.p111, [111], anchor: "north-west", padding: .2)
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// content(cf.p110, [110], anchor: "north-east", padding: .2)
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content((rel: (0.85, -0.1), to: cf.p110), [110], anchor: "north-east", padding: .2)
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content((4, -2.6), [$FF_2^3$])
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})
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}
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#let definition(
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titre: "Définition",
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accent: black,
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titre_taille: 1.13em,
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corps_taille: 1.2em,
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contenu,
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) = {
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block(
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width: 100%,
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fill: rgb("#f8f9fa"),
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stroke: 0.5pt + gray.lighten(60%),
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radius: 8pt,
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clip: true,
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grid(
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columns: (5pt, 1fr),
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rows: auto,
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fill: (col, row) => if col == 0 { accent },
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[],
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block(
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width: 100%,
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inset: (x: 16pt, y: 15pt),
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{
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{
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set text(fill: accent, weight: 800, size: titre_taille, tracking: 0.5pt)
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show math.equation: set text(weight: 700, size: 1.05em)
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titre
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}
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v(18pt, weak: true)
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{
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set text(size: corps_taille)
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set par(leading: 0.7em, justify: false)
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contenu
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}
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},
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),
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),
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)
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}
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#let limite_shannon_graphique() = {
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let col-shannon = red.darken(10%)
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let col-code-long = blue.darken(20%)
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let col-code-short = gray.lighten(10%)
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set text(size: 11pt)
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move(dx: -5pt, dy: 0pt)[
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#cetz.canvas({
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import cetz.draw: *
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plot.plot(
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size: (23, 15),
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// 1. On grossit les labels d'axes (15pt)
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x-label: pad(bottom: 30pt)[#move(dy: 80pt)[#text(size: 18pt)[$E_b/N_0$ (dB)]]],
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y-label: move(dx: -20pt, dy: -10pt)[#text(size: 18pt)[Bit Error Rate (BER)]],
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x-min: 0,
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x-max: 10,
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y-min: -8.5,
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y-max: 0.2,
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x-tick-step: 1,
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y-tick-step: 2,
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// Axis
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x-format: x => move(dy: 14pt)[#text(size: 16pt)[#x]],
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y-format: y => move(dx: -5pt)[#text(size: 16pt)[$10^(#y)$]],
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x-grid: true,
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y-grid: true,
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// Légende positionnée en bas.
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legend: "north-east",
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legend-style: (
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stroke: 0.5pt + gray,
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fill: white,
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padding: 0.2,
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offset: (-161.4pt, -45.1pt),
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),
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{
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// 1. Limite de Shannon (Asymptote)
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plot.add(
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((1.5, -8.5), (1.5, 0.2)),
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style: (stroke: (paint: col-shannon, thickness: 2pt, dash: "dashed")),
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label: [Limite de Shannon],
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)
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// 2. Petit bloc linéaire (n ≈ 100) - Ultra-densifié (smooth)
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plot.add(
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(
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(0.0, 0.00),
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(0.2, -0.01),
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(0.4, -0.03),
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(0.6, -0.05),
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(0.8, -0.07),
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(1.0, -0.10),
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(1.2, -0.13),
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(1.4, -0.17),
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(1.6, -0.21),
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(1.8, -0.25),
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(2.0, -0.30),
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(2.2, -0.36),
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(2.4, -0.43),
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(2.6, -0.51),
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(2.8, -0.60),
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(3.0, -0.70),
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(3.2, -0.80),
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(3.4, -0.91),
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(3.6, -1.03),
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(3.8, -1.16),
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(4.0, -1.30),
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(4.2, -1.44),
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(4.4, -1.59),
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(4.6, -1.75),
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(4.8, -1.92),
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(5.0, -2.10),
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(5.2, -2.28),
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(5.4, -2.47),
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(5.6, -2.67),
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(5.8, -2.88),
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(6.0, -3.10),
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(6.2, -3.32),
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(6.4, -3.55),
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(6.6, -3.79),
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(6.8, -4.04),
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(7.0, -4.30),
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(7.2, -4.56),
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(7.4, -4.83),
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(7.6, -5.11),
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(7.8, -5.40),
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(8.0, -5.70),
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(8.2, -6.00),
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(8.4, -6.31),
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(8.6, -6.63),
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(8.8, -6.96),
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(9.0, -7.30),
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(9.2, -7.62),
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(9.4, -7.95),
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(9.6, -8.29),
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(9.8, -8.64),
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(10.0, -9.00),
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),
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style: (stroke: (paint: col-code-short, thickness: 1.5pt)),
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label: [Code court ($n approx 100$)],
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)
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// 3. Grand bloc linéaire (n = 64 800) - Ultra-densifié (smooth & waterfall net)
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plot.add(
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(
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(0.0, 0.0),
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(0.2, -0.005),
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(0.4, -0.01),
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(0.6, -0.02),
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(0.8, -0.035),
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(1.0, -0.05),
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(1.1, -0.07),
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(1.2, -0.10),
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(1.3, -0.14),
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(1.4, -0.20),
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(1.45, -0.28),
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(1.50, -0.40),
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(1.52, -0.45),
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(1.54, -0.52),
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(1.56, -0.60),
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(1.58, -0.69),
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(1.60, -0.80),
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(1.62, -0.92),
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(1.64, -1.05),
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(1.66, -1.19),
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(1.68, -1.34),
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(1.70, -1.50),
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(1.72, -1.69),
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(1.74, -1.89),
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