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cloud","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fcloud","0.snt-2nde\u002Fsd-donnees-structurees\u002F5.cloud",{"title":119,"path":120,"stem":121,"children":122},"Localisation, cartographie et mobilité","\u002Fsnt-2nde\u002Fse-localisation-cartographie","0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index",[123,124,128,132,136,140],{"title":119,"path":120,"stem":121},{"title":125,"path":126,"stem":127},"GPS et Galileo — se situer grâce aux satellites","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo","0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo",{"title":129,"path":130,"stem":131},"Décoder une trame NMEA","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea","0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea",{"title":133,"path":134,"stem":135},"Cartes numériques — GeoPortail et 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embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fihm-objet-connecte","0.snt-2nde\u002Fsf-info-embarquee\u002F3.ihm-objet-connecte",{"title":163,"path":164,"stem":165,"children":166},"Photographie numérique","\u002Fsnt-2nde\u002Fsg-photo-numerique","0.snt-2nde\u002Fsg-photo-numerique\u002F0.index",[167,168,172,176,180],{"title":163,"path":164,"stem":165},{"title":169,"path":170,"stem":171},"Photosites, pixels et résolution","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fpixels-resolution","0.snt-2nde\u002Fsg-photo-numerique\u002F1.pixels-resolution",{"title":173,"path":174,"stem":175},"Les algorithmes de l'appareil photo","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Falgorithmes-photo","0.snt-2nde\u002Fsg-photo-numerique\u002F2.algorithmes-photo",{"title":177,"path":178,"stem":179},"Les métadonnées EXIF","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fmetadonnees-exif","0.snt-2nde\u002Fsg-photo-numerique\u002F3.metadonnees-exif",{"title":181,"path":182,"stem":183},"Traiter une image en Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — Première","\u002Fnsi-1ere","1.nsi-1ere\u002F0.index",[229,230,234,256,282,304,328,354,380,410],{"title":225,"path":226,"stem":227},{"title":231,"path":232,"stem":233},"Relecture pédagogique — 8 chapitres NSI 1ère (PA → PH)","\u002Fnsi-1ere\u002Freview","1.nsi-1ere\u002FREVIEW",{"title":235,"path":236,"stem":237,"children":238},"Histoire de 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aujourd'hui)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Freseaux-et-web","1.nsi-1ere\u002Fpa-histoire-info\u002F4.reseaux-et-web",{"title":257,"path":258,"stem":259,"children":260},"Représentation des données — types et valeurs","\u002Fnsi-1ere\u002Fpb-types-valeurs","1.nsi-1ere\u002Fpb-types-valeurs\u002F0.index",[261,262,266,270,274,278],{"title":257,"path":258,"stem":259},{"title":263,"path":264,"stem":265},"Bases de numération et entiers positifs","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs",{"title":267,"path":268,"stem":269},"Entiers relatifs et complément à deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule 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filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une fonction","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification","1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification",{"title":403,"path":404,"stem":405},"Mise au point des programmes","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fmise-au-point","1.nsi-1ere\u002Fpg-langages-prog\u002F5.mise-au-point",{"title":407,"path":408,"stem":409},"Utilisation de bibliothèques","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fbibliotheques","1.nsi-1ere\u002Fpg-langages-prog\u002F6.bibliotheques",{"title":411,"path":412,"stem":413,"children":414},"Algorithmique","\u002Fnsi-1ere\u002Fph-algorithmique","1.nsi-1ere\u002Fph-algorithmique\u002F0.index",[415,416,420,424,428,432,436],{"title":411,"path":412,"stem":413},{"title":417,"path":418,"stem":419},"Parcours séquentiel d'un tableau","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fparcours-sequentiel","1.nsi-1ere\u002Fph-algorithmique\u002F1.parcours-sequentiel",{"title":421,"path":422,"stem":423},"Bases de la complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — Terminale","\u002Fnsi-tale","2.nsi-tale\u002F0.index",[445,446,450,476,498,536,560],{"title":441,"path":442,"stem":443},{"title":447,"path":448,"stem":449},"Review pédagogique — chapitres NSI Terminale (TA, TB, TC, TD, TE)","\u002Fnsi-tale\u002Freview","2.nsi-tale\u002FREVIEW",{"title":451,"path":452,"stem":453,"children":454},"Structures de données","\u002Fnsi-tale\u002Fta-structures-donnees","2.nsi-tale\u002Fta-structures-donnees\u002F0.index",[455,456,460,464,468,472],{"title":451,"path":452,"stem":453},{"title":457,"path":458,"stem":459},"Objet, classe, interface","\u002Fnsi-tale\u002Fta-structures-donnees\u002Finterface-implementation","2.nsi-tale\u002Fta-structures-donnees\u002F1.interface-implementation",{"title":461,"path":462,"stem":463},"Implémenter une structure — l'exemple de la file FIFO","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fimplementer-une-structure","2.nsi-tale\u002Fta-structures-donnees\u002F2.implementer-une-structure",{"title":465,"path":466,"stem":467},"Listes, piles, files, dictionnaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Flistes-piles-files-dict","2.nsi-tale\u002Fta-structures-donnees\u002F3.listes-piles-files-dict",{"title":469,"path":470,"stem":471},"Arbres binaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires","2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires",{"title":473,"path":474,"stem":475},"Graphes","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes","2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes",{"title":477,"path":478,"stem":479,"children":480},"Bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees","2.nsi-tale\u002Ftb-bases-de-donnees\u002F0.index",[481,482,486,490,494],{"title":477,"path":478,"stem":479},{"title":483,"path":484,"stem":485},"Le modèle relationnel","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fmodele-relationnel","2.nsi-tale\u002Ftb-bases-de-donnees\u002F1.modele-relationnel",{"title":487,"path":488,"stem":489},"Bases de données relationnelles et anomalies de schéma","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fbase-relationnelle","2.nsi-tale\u002Ftb-bases-de-donnees\u002F2.base-relationnelle",{"title":491,"path":492,"stem":493},"Le langage SQL","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsql","2.nsi-tale\u002Ftb-bases-de-donnees\u002F3.sql",{"title":495,"path":496,"stem":497},"Les systèmes de gestion de bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsgbd","2.nsi-tale\u002Ftb-bases-de-donnees\u002F4.sgbd",{"title":499,"path":500,"stem":501,"children":502},"Architectures matérielles, systèmes d'exploitation et réseaux","\u002Fnsi-tale\u002Ftc-archi-os-reseaux","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F0.index",[503,504,508,512,516,520,524,528,532],{"title":499,"path":500,"stem":501},{"title":505,"path":506,"stem":507},"Le système sur puce (SoC)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fsysteme-sur-puce","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F1.systeme-sur-puce",{"title":509,"path":510,"stem":511},"Processus et ordonnancement par l'OS","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprocessus-os","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F2.processus-os",{"title":513,"path":514,"stem":515},"L'interblocage (deadlock)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Finterblocage","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F3.interblocage",{"title":517,"path":518,"stem":519},"Principes du routage","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Froutage-principes","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F4.routage-principes",{"title":521,"path":522,"stem":523},"Protocoles de routage RIP et OSPF","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprotocoles-rip-ospf","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F5.protocoles-rip-ospf",{"title":525,"path":526,"stem":527},"Chiffrement symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-symetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F6.chiffrement-symetrique",{"title":529,"path":530,"stem":531},"Chiffrement asymétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique",{"title":533,"path":534,"stem":535},"HTTPS — l'échange de clé symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de Boyer-Moore","\u002Fnsi-tale\u002Fte-algorithmique\u002Frecherche-textuelle","2.nsi-tale\u002Fte-algorithmique\u002F5.recherche-textuelle",[586,1137,2603,3121,3891],{"id":587,"title":125,"bo":588,"body":590,"description":1122,"eval":1123,"extension":1124,"labo":1123,"meta":1125,"navigation":1126,"path":126,"quizzes":1127,"readingTime":1134,"seo":1135,"stem":127,"tp":1123,"__hash__":1136},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo.md",[589],"SE04",{"type":591,"value":592,"toc":1113},"minimark",[593,598,611,614,618,625,707,726,730,741,810,934,953,960,967,998,1002,1013,1039,1053,1057,1076,1099,1103],[594,595,597],"h2",{"id":596},"introduction","Introduction",[599,600,601,602,606,607,610],"p",{},"Quand vous ouvrez une application de cartographie sur votre téléphone, un petit\npoint bleu apparaît presque instantanément à votre position. Ce point ne vient\npas du téléphone lui-même : il est calculé à partir de signaux émis par des\n",[603,604,605],"strong",{},"satellites"," situés à plus de vingt mille kilomètres au-dessus de votre tête.\nComprendre ce calcul, c'est comprendre la ",[603,608,609],{},"géolocalisation par satellites"," —\nau cœur du GPS américain, du Galileo européen, et de la plupart des services\nde mobilité contemporains.",[612,613],"bo-ref",{"code":589},[594,615,617],{"id":616},"plusieurs-systèmes-un-même-principe","Plusieurs systèmes, un même principe",[599,619,620,621,624],{},"Le mot « GPS » est devenu un nom commun, mais il désigne précisément un\nsystème : le ",[603,622,623],{},"Global Positioning System",", mis en service par les États-Unis\nà la fin des années 1970 pour des besoins militaires, puis ouvert à un usage\ncivil. Aujourd'hui, plusieurs constellations cohabitent et un récepteur moderne\npeut combiner leurs signaux.",[626,627,628,647],"table",{},[629,630,631],"thead",{},[632,633,634,638,641,644],"tr",{},[635,636,637],"th",{},"Système",[635,639,640],{},"Pays \u002F Région",[635,642,643],{},"Mise en service",[635,645,646],{},"Nb satellites",[648,649,650,665,679,693],"tbody",{},[632,651,652,656,659,662],{},[653,654,655],"td",{},"GPS",[653,657,658],{},"États-Unis",[653,660,661],{},"1978 (civil dès 1983)",[653,663,664],{},"~31",[632,666,667,670,673,676],{},[653,668,669],{},"Galileo",[653,671,672],{},"Union européenne",[653,674,675],{},"opérationnel depuis 2016",[653,677,678],{},"~28",[632,680,681,684,687,690],{},[653,682,683],{},"GLONASS",[653,685,686],{},"Russie",[653,688,689],{},"1982",[653,691,692],{},"~24",[632,694,695,698,701,704],{},[653,696,697],{},"BeiDou",[653,699,700],{},"Chine",[653,702,703],{},"2018",[653,705,706],{},"~35",[708,709,710],"note",{},[599,711,712,713,716,717,721,722,725],{},"Le terme générique pour ces systèmes est ",[603,714,715],{},"GNSS"," (",[718,719,720],"em",{},"Global Navigation Satellite\nSystem","). Votre téléphone est un récepteur GNSS qui utilise le plus souvent GPS\n",[603,723,724],{},"et"," Galileo simultanément pour gagner en précision.",[594,727,729],{"id":728},"le-principe-la-trilatération","Le principe : la trilatération",[599,731,732,733,736,737,740],{},"Chaque satellite émet en continu un signal radio qui contient deux\ninformations essentielles : ",[603,734,735],{},"son identifiant",", et ",[603,738,739],{},"l'heure très précise","\nà laquelle le signal est parti. Votre récepteur capte ce signal, compare\nl'heure d'émission avec l'heure de réception, et en déduit le temps de trajet.",[599,742,743,744,805,806,809],{},"Comme les ondes radio se propagent à la vitesse de la lumière (environ\n",[745,746,749,779],"span",{"className":747},[748],"katex",[745,750,753],{"className":751},[752],"katex-mathml",[754,755,757],"math",{"xmlns":756},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[758,759,760,774],"semantics",{},[761,762,763,767,771],"mrow",{},[764,765,766],"mn",{},"300",[768,769,770],"mtext",{}," ",[764,772,773],{},"000",[775,776,778],"annotation",{"encoding":777},"application\u002Fx-tex","300\\,000",[745,780,784],{"className":781,"ariaHidden":783},[782],"katex-html","true",[745,785,788,793,797,802],{"className":786},[787],"base",[745,789],{"className":790,"style":792},[791],"strut","height:0.6444em;",[745,794,766],{"className":795},[796],"mord",[745,798],{"className":799,"style":801},[800],"mspace","margin-right:0.1667em;",[745,803,773],{"className":804},[796]," km\u002Fs), connaître la durée du trajet revient à connaître la\n",[603,807,808],{},"distance"," entre le satellite et vous.",[811,812,813],"tip",{},[599,814,815,816,933],{},"Si le signal a mis 70 millisecondes pour vous parvenir, le satellite est à\nenviron ",[745,817,819,854],{"className":818},[748],[745,820,822],{"className":821},[752],[754,823,824],{"xmlns":756},[758,825,826,851],{},[761,827,828,830,832,834,838,841,844,847,849],{},[764,829,766],{},[768,831,770],{},[764,833,773],{},[835,836,837],"mo",{},"×",[764,839,840],{},"0,070",[835,842,843],{},"=",[764,845,846],{},"21",[768,848,770],{},[764,850,773],{},[775,852,853],{"encoding":777},"300\\,000 \\times 0{,}070 = 21\\,000",[745,855,857,884,918],{"className":856,"ariaHidden":783},[782],[745,858,860,864,867,870,873,877,881],{"className":859},[787],[745,861],{"className":862,"style":863},[791],"height:0.7278em;vertical-align:-0.0833em;",[745,865,766],{"className":866},[796],[745,868],{"className":869,"style":801},[800],[745,871,773],{"className":872},[796],[745,874],{"className":875,"style":876},[800],"margin-right:0.2222em;",[745,878,837],{"className":879},[880],"mbin",[745,882],{"className":883,"style":876},[800],[745,885,887,891,895,903,907,911,915],{"className":886},[787],[745,888],{"className":889,"style":890},[791],"height:0.8389em;vertical-align:-0.1944em;",[745,892,894],{"className":893},[796],"0",[745,896,898],{"className":897},[796],[745,899,902],{"className":900},[901],"mpunct",",",[745,904,906],{"className":905},[796],"070",[745,908],{"className":909,"style":910},[800],"margin-right:0.2778em;",[745,912,843],{"className":913},[914],"mrel",[745,916],{"className":917,"style":910},[800],[745,919,921,924,927,930],{"className":920},[787],[745,922],{"className":923,"style":792},[791],[745,925,846],{"className":926},[796],[745,928],{"className":929,"style":801},[800],[745,931,773],{"className":932},[796]," kilomètres de vous. C'est cohérent\navec l'altitude des satellites GPS, qui orbitent à ~20 200 km.",[599,935,936,937,940,941,944,945,948,949,952],{},"Connaître la distance à ",[603,938,939],{},"un"," satellite ne suffit pas : vous savez que vous\nêtes quelque part sur une sphère de rayon donné autour de lui, ce qui fait\nbeaucoup d'endroits possibles. Avec ",[603,942,943],{},"deux"," satellites, vous êtes à l'intersection\nde deux sphères, soit un cercle. Avec ",[603,946,947],{},"trois"," satellites, ce cercle se réduit\nà deux points, dont l'un est généralement absurde (à l'intérieur de la Terre\nou très loin dans l'espace). Avec ",[603,950,951],{},"quatre"," satellites, on lève la dernière\nambiguïté et on corrige l'horloge du récepteur, qui n'est pas aussi précise\nque celles, atomiques, embarquées sur les satellites.",[954,955],"illustration",{"alt":956,"kind":957,"src":958,"svg":959},"Schéma de la trilatération avec trois satellites","schema","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Ftrilateration.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 480 320\" role=\"img\" aria-label=\"Trilatération : trois satellites au-dessus du sol, chacun entouré d'un cercle de distance. Les trois cercles se recoupent en un point unique au sol, légendé « votre position ».\">\n  \u003Ctitle>La trilatération à trois satellites\u003C\u002Ftitle>\n  \u003Cstyle>\n    .tl-text   { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 13px; font-weight: 500; }\n    .tl-sat    { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .tl-satlbl { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 11px; font-weight: 600; }\n    .tl-ring   { fill: none; stroke: var(--diagram-node-border); stroke-width: 1.5; opacity: 0.65; }\n    .tl-ground { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .tl-dist   { stroke: var(--diagram-line); stroke-width: 1; stroke-dasharray: 3 3; fill: none; }\n    .tl-point  { fill: var(--diagram-node-border); }\n    .tl-pos    { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 12.5px; font-weight: 600; }\n    .tl-leader { stroke: var(--diagram-border); stroke-width: 1.5; stroke-dasharray: 4 3; fill: none; }\n  \u003C\u002Fstyle>\n\n  \u003C!-- Point au sol : intersection commune des trois cercles -->\n  \u003C!-- position P = (240, 250) -->\n\n  \u003C!-- trois cercles de distance, centrés sur chaque satellite, passant par P -->\n  \u003C!-- sat A (120, 60) : r = dist(A,P) = sqrt(120^2 + 190^2) = 224.7 -->\n  \u003Ccircle class=\"tl-ring\" cx=\"120\" cy=\"60\" r=\"224.7\"\u002F>\n  \u003C!-- sat B (360, 70) : r = sqrt(120^2 + 180^2) = 216.3 -->\n  \u003Ccircle class=\"tl-ring\" cx=\"360\" cy=\"70\" r=\"216.3\"\u002F>\n  \u003C!-- sat C (245, 30) : r = sqrt(5^2 + 220^2) = 220.1 -->\n  \u003Ccircle class=\"tl-ring\" cx=\"245\" cy=\"30\" r=\"220.1\"\u002F>\n\n  \u003C!-- traits de distance satellite -> position -->\n  \u003Cline class=\"tl-dist\" x1=\"120\" y1=\"60\" x2=\"240\" y2=\"250\"\u002F>\n  \u003Cline class=\"tl-dist\" x1=\"360\" y1=\"70\" x2=\"240\" y2=\"250\"\u002F>\n  \u003Cline class=\"tl-dist\" x1=\"245\" y1=\"30\" x2=\"240\" y2=\"250\"\u002F>\n\n  \u003C!-- satellites -->\n  \u003Cg>\n    \u003Crect x=\"98\"  y=\"44\"  width=\"44\" height=\"28\" rx=\"5\" class=\"tl-sat\"\u002F>\u003Ctext x=\"120\" y=\"62\"  text-anchor=\"middle\" class=\"tl-satlbl\">S1\u003C\u002Ftext>\n    \u003Crect x=\"338\" y=\"54\"  width=\"44\" height=\"28\" rx=\"5\" class=\"tl-sat\"\u002F>\u003Ctext x=\"360\" y=\"72\"  text-anchor=\"middle\" class=\"tl-satlbl\">S2\u003C\u002Ftext>\n    \u003Crect x=\"223\" y=\"14\"  width=\"44\" height=\"28\" rx=\"5\" class=\"tl-sat\"\u002F>\u003Ctext x=\"245\" y=\"32\"  text-anchor=\"middle\" class=\"tl-satlbl\">S3\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- sol -->\n  \u003Cline class=\"tl-ground\" x1=\"20\" y1=\"290\" x2=\"460\" y2=\"290\"\u002F>\n\n  \u003C!-- point de position -->\n  \u003Ccircle class=\"tl-point\" cx=\"240\" cy=\"250\" r=\"5\"\u002F>\n\n  \u003C!-- légende votre position -->\n  \u003Cpath class=\"tl-leader\" d=\"M 240 250 C 300 250, 330 256, 348 268\"\u002F>\n  \u003Ctext x=\"352\" y=\"272\" class=\"tl-pos\">votre position\u003C\u002Ftext>\n\u003C\u002Fsvg>\n",[599,961,962,963,966],{},"Ce principe s'appelle la ",[603,964,965],{},"trilatération",". Une analogie aide à le saisir :\nimaginez qu'on vous dise « je suis à 100 km de Lyon ». Vous savez juste que\nvous êtes sur un cercle autour de Lyon. Ajoutez « et à 80 km de Grenoble »,\nvous obtenez au plus deux endroits possibles. Une troisième mesure depuis\nSaint-Étienne lève le doute.",[968,969,973,980],"self-eval-qcm",{"correct":970,"explanation":971,"slug":972},"2","Il faut 4 satellites : 3 pour la position dans l'espace, et un 4e pour synchroniser l'horloge du récepteur avec celles des satellites.","gps-galileo-c1",[974,975,977],"template",{"v-slot:question":976},"",[599,978,979],{},"Combien de satellites au minimum pour calculer une position 3D précise (latitude, longitude, altitude) ?",[974,981,982],{"v-slot:choices":976},[983,984,985,989,992,995],"ul",{},[986,987,988],"li",{},"2 satellites",[986,990,991],{},"3 satellites",[986,993,994],{},"4 satellites",[986,996,997],{},"5 satellites",[594,999,1001],{"id":1000},"la-précision-et-ses-limites","La précision et ses limites",[599,1003,1004,1005,1008,1009,1012],{},"En conditions idéales, le GPS civil annonce une précision d'environ ",[603,1006,1007],{},"5 à\n10 mètres",". Galileo, plus récent, descend en pratique à ",[603,1010,1011],{},"1 à 2 mètres"," pour\nle grand public. Plusieurs facteurs dégradent ce résultat :",[983,1014,1015,1021,1027,1033],{},[986,1016,1017,1020],{},[603,1018,1019],{},"L'atmosphère"," : la traversée de l'ionosphère ralentit légèrement le signal.",[986,1022,1023,1026],{},[603,1024,1025],{},"Le multitrajet"," : en ville, le signal rebondit sur les immeubles avant\nd'atteindre le récepteur, ce qui fausse le temps de trajet.",[986,1028,1029,1032],{},[603,1030,1031],{},"L'obstruction"," : en intérieur, en tunnel, en forêt dense, le signal\nn'arrive plus du tout ou très dégradé.",[986,1034,1035,1038],{},[603,1036,1037],{},"La géométrie"," : si tous les satellites visibles sont regroupés dans la\nmême portion de ciel, la trilatération est moins précise.",[1040,1041,1042],"warning",{},[599,1043,1044,1045,1048,1049,1052],{},"Le GPS ",[603,1046,1047],{},"ne fonctionne pas en intérieur"," sans aide. Quand votre téléphone\ntrouve quand même votre position dans un bâtiment, c'est qu'il utilise d'autres\nsources : Wi-Fi connus, antennes 4G\u002F5G, capteurs internes. On parle alors de\n",[603,1050,1051],{},"géolocalisation hybride",".",[594,1054,1056],{"id":1055},"sens-unique-et-passif","Sens unique et passif",[599,1058,1059,1060,1063,1064,1067,1068,1071,1072,1075],{},"Un point essentiel à retenir, et souvent mal compris : ",[603,1061,1062],{},"le récepteur ne\ncommunique pas avec les satellites",". Il se contente d'",[603,1065,1066],{},"écouter"," leurs\nsignaux. Les satellites ne savent pas qui les écoute, ni combien d'utilisateurs\nles utilisent simultanément. Cela a une conséquence directe sur la\nconfidentialité, que vous étudierez dans le dernier cours : ",[603,1069,1070],{},"le seul fait\nd'utiliser le GPS ne transmet aucune donnée",". Ce qui en transmet, c'est ce\nque ",[603,1073,1074],{},"vos applications"," font ensuite de votre position.",[968,1077,1081,1086],{"correct":1078,"explanation":1079,"slug":1080},"1","Le GPS est strictement passif côté récepteur. Les satellites diffusent en permanence, sans connaître leurs auditeurs.","gps-galileo-c2",[974,1082,1083],{"v-slot:question":976},[599,1084,1085],{},"Quand vous utilisez le GPS de votre téléphone, les satellites savent-ils que vous êtes là ?",[974,1087,1088],{"v-slot:choices":976},[983,1089,1090,1093,1096],{},[986,1091,1092],{},"Oui, ils enregistrent chaque récepteur connecté",[986,1094,1095],{},"Non, le récepteur ne fait qu écouter passivement",[986,1097,1098],{},"Seulement si vous activez le mode haute précision",[594,1100,1102],{"id":1101},"pour-aller-plus-loin","Pour aller plus loin",[599,1104,1105,1106,716,1109,1112],{},"Galileo offre un service complémentaire payant, ",[603,1107,1108],{},"HAS",[718,1110,1111],{},"High Accuracy\nService","), qui descend à quelques centimètres pour l'agriculture de précision\net la conduite autonome. Pour le grand public en revanche, le service de base\nreste libre et gratuit dans le monde entier — un trait commun à tous les GNSS.",{"title":976,"searchDepth":1114,"depth":1114,"links":1115},2,[1116,1117,1118,1119,1120,1121],{"id":596,"depth":1114,"text":597},{"id":616,"depth":1114,"text":617},{"id":728,"depth":1114,"text":729},{"id":1000,"depth":1114,"text":1001},{"id":1055,"depth":1114,"text":1056},{"id":1101,"depth":1114,"text":1102},"Le principe de la géolocalisation par satellites, expliqué intuitivement à partir de la trilatération.",null,"md",{},true,[1128,1132],{"slug":972,"kind":1129,"question":979,"choices":1130,"correct":970,"multi":1131,"explanation":971},"qcm",[988,991,994,997],false,{"slug":1080,"kind":1129,"question":1085,"choices":1133,"correct":1078,"multi":1131,"explanation":1079},[1092,1095,1098],1,{"title":125,"description":1122},"vJXSQURYvKFvO_ucvUFFuZPRy1YTrJHK1vRUZYQAurY",{"id":1138,"title":129,"bo":1139,"body":1141,"description":2594,"eval":1123,"extension":1124,"labo":1123,"meta":2595,"navigation":1126,"path":130,"quizzes":2596,"readingTime":1134,"seo":2601,"stem":131,"tp":1123,"__hash__":2602},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.md",[1140],"SE05",{"type":591,"value":1142,"toc":2584},[1143,1145,1155,1157,1161,1173,1176,1203,1208,1212,1224,1233,1240,1322,1329,1350,1354,1372,1688,1694,1880,1885,2061,2068,2077,2081,2088,2109,2243,2246,2327,2439,2461,2465,2483,2490,2494,2497,2560,2563,2572,2574,2580],[594,1144,597],{"id":596},[599,1146,1147,1148,1151,1152,1052],{},"Le récepteur GPS de votre téléphone ne se contente pas de calculer votre\nposition : il la ",[603,1149,1150],{},"publie"," ensuite à toutes les applications qui ont besoin de\nla connaître. Mais sous quelle forme ? Comment cette suite de mesures\nsatellites devient-elle « 48,8566° N, 2,3522° E » ? La réponse passe par un\nprotocole textuel des années 1980, étonnamment encore en service aujourd'hui :\nle ",[603,1153,1154],{},"NMEA 0183",[612,1156],{"code":1140},[594,1158,1160],{"id":1159},"un-standard-maritime-devenu-universel","Un standard maritime devenu universel",[599,1162,1163,1164,1167,1168,1172],{},"NMEA est l'acronyme de la ",[718,1165,1166],{},"National Marine Electronics Association",", qui a\ndéfini ce protocole pour faire dialoguer entre eux les équipements\nélectroniques des navires : sonde, gouvernail automatique, traceur de cartes,\nrécepteur GPS… La version ",[1169,1170,1171],"code",{},"0183"," désigne une norme publiée en 1983, encore\nlargement utilisée.",[599,1174,1175],{},"Ce qu'il faut en retenir pour SNT :",[983,1177,1178,1185,1196],{},[986,1179,1180,1181,1184],{},"Le NMEA 0183 est ",[603,1182,1183],{},"textuel"," — il transmet des chaînes de caractères ASCII,\nlisibles à l'œil nu.",[986,1186,1187,1188,1191,1192,1195],{},"Chaque message est une ",[603,1189,1190],{},"trame"," : une ligne autonome qui commence par ",[1169,1193,1194],{},"$","\net se termine par un saut de ligne.",[986,1197,1198,1199,1202],{},"Chaque trame contient des ",[603,1200,1201],{},"champs séparés par des virgules",", comme un\nfichier CSV.",[708,1204,1205],{},[599,1206,1207],{},"Bien que conçu pour la marine, le NMEA 0183 est devenu le langage commun de\nquasiment tous les récepteurs GNSS du monde. C'est ce que produisent les\nmodules GPS qu'on trouve dans les Arduino, les drones, les anciens GPS de\nvoiture, et même beaucoup de smartphones en interne.",[594,1209,1211],{"id":1210},"anatomie-dune-trame-gga","Anatomie d'une trame GGA",[599,1213,1214,1215,716,1220,1223],{},"La trame la plus courante est la trame ",[603,1216,1217],{},[1169,1218,1219],{},"$GPGGA",[718,1221,1222],{},"Global Positioning\nSystem Fix Data","). Elle donne la position calculée à un instant précis. Voici\nun exemple réel :",[1225,1226,1231],"pre",{"className":1227,"code":1229,"language":1230,"meta":976},[1228],"language-text","$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\n","text",[1169,1232,1229],{"__ignoreMap":976},[599,1234,1235,1236,1239],{},"À première vue, illisible. Mais l'œil s'y fait vite : il suffit de repérer\n",[603,1237,1238],{},"les champs principaux"," que vous avez besoin de savoir reconnaître.",[626,1241,1242,1255],{},[629,1243,1244],{},[632,1245,1246,1249,1252],{},[635,1247,1248],{},"Champ",[635,1250,1251],{},"Valeur",[635,1253,1254],{},"Signification",[648,1256,1257,1270,1283,1296,1309],{},[632,1258,1259,1262,1267],{},[653,1260,1261],{},"heure UTC",[653,1263,1264],{},[1169,1265,1266],{},"123519",[653,1268,1269],{},"12h 35min 19s",[632,1271,1272,1275,1280],{},[653,1273,1274],{},"latitude",[653,1276,1277],{},[1169,1278,1279],{},"4807.038",[653,1281,1282],{},"48° 07,038′",[632,1284,1285,1288,1293],{},[653,1286,1287],{},"hémisphère",[653,1289,1290],{},[1169,1291,1292],{},"N",[653,1294,1295],{},"Nord",[632,1297,1298,1301,1306],{},[653,1299,1300],{},"longitude",[653,1302,1303],{},[1169,1304,1305],{},"01131.000",[653,1307,1308],{},"011° 31,000′",[632,1310,1311,1314,1319],{},[653,1312,1313],{},"méridien",[653,1315,1316],{},[1169,1317,1318],{},"E",[653,1320,1321],{},"Est",[599,1323,1324,1325,1328],{},"C'est tout ce qu'il faut viser : être capable de pointer dans une trame\n",[603,1326,1327],{},"où sont"," la latitude, l'hémisphère, la longitude, le méridien et l'heure.\nLa trame contient d'autres informations techniques (qualité du fix, nombre\nde satellites, altitude, vérification…), regroupées dans la note ci-dessous\npour qui veut creuser.",[968,1330,1333,1338],{"correct":1078,"explanation":1331,"slug":1332},"Le champ heure se lit HHMMSS — 12h 35min 19s.","trame-nmea-c1",[974,1334,1335],{"v-slot:question":976},[599,1336,1337],{},"Dans la trame ci-dessus, à quelle heure UTC la position a-t-elle été mesurée ?",[974,1339,1340],{"v-slot:choices":976},[983,1341,1342,1345,1347],{},[986,1343,1344],{},"1h 23min 51s",[986,1346,1269],{},[986,1348,1349],{},"13h 25min 19s",[594,1351,1353],{"id":1352},"du-format-nmea-aux-degrés-décimaux","Du format NMEA aux degrés décimaux",[599,1355,1356,1357,1360,1361,716,1364,1367,1368,1371],{},"Les coordonnées NMEA ne sont ",[603,1358,1359],{},"pas"," en degrés décimaux : elles sont au format\n",[603,1362,1363],{},"degrés-minutes",[1169,1365,1366],{},"DDMM.MMMM"," pour la latitude, ",[1169,1369,1370],{},"DDDMM.MMMM"," pour la\nlongitude). Pour les convertir en degrés décimaux, qu'utilisent la plupart des\napplications de cartographie, on applique :",[745,1373,1376],{"className":1374},[1375],"katex-display",[745,1377,1379,1445],{"className":1378},[748],[745,1380,1382],{"className":1381},[752],[754,1383,1385],{"xmlns":756,"display":1384},"block",[758,1386,1387,1442],{},[761,1388,1389,1415,1417,1430,1433],{},[761,1390,1391,1394,1403,1406,1412],{},[768,1392,1393],{},"degr",[1395,1396,1397,1400],"mover",{"accent":783},[768,1398,1399],{},"e",[835,1401,1402],{},"ˊ",[768,1404,1405],{},"s d",[1395,1407,1408,1410],{"accent":783},[768,1409,1399],{},[835,1411,1402],{},[768,1413,1414],{},"cimaux",[835,1416,843],{},[761,1418,1419,1421,1427],{},[768,1420,1393],{},[1395,1422,1423,1425],{"accent":783},[768,1424,1399],{},[835,1426,1402],{},[768,1428,1429],{},"s entiers",[835,1431,1432],{},"+",[1434,1435,1436,1439],"mfrac",{},[768,1437,1438],{},"minutes",[764,1440,1441],{},"60",[775,1443,1444],{"encoding":777},"\\text{degrés décimaux} = \\text{degrés entiers} + \\frac{\\text{minutes}}{60}",[745,1446,1448,1548,1603],{"className":1447,"ariaHidden":783},[782],[745,1449,1451,1455,1539,1542,1545],{"className":1450},[787],[745,1452],{"className":1453,"style":1454},[791],"height:0.8889em;vertical-align:-0.1944em;",[745,1456,1458,1461,1502,1505,1536],{"className":1457},[796,1230],[745,1459,1393],{"className":1460},[796],[745,1462,1465],{"className":1463},[796,1464],"accent",[745,1466,1469],{"className":1467},[1468],"vlist-t",[745,1470,1473],{"className":1471},[1472],"vlist-r",[745,1474,1478,1489],{"className":1475,"style":1477},[1476],"vlist","height:0.6944em;",[745,1479,1481,1486],{"style":1480},"top:-3em;",[745,1482],{"className":1483,"style":1485},[1484],"pstrut","height:3em;",[745,1487,1399],{"className":1488},[796],[745,1490,1491,1494],{"style":1480},[745,1492],{"className":1493,"style":1485},[1484],[745,1495,1499],{"className":1496,"style":1498},[1497],"accent-body","left:-0.25em;",[745,1500,1402],{"className":1501},[796],[745,1503,1405],{"className":1504},[796],[745,1506,1508],{"className":1507},[796,1464],[745,1509,1511],{"className":1510},[1468],[745,1512,1514],{"className":1513},[1472],[745,1515,1517,1525],{"className":1516,"style":1477},[1476],[745,1518,1519,1522],{"style":1480},[745,1520],{"className":1521,"style":1485},[1484],[745,1523,1399],{"className":1524},[796],[745,1526,1527,1530],{"style":1480},[745,1528],{"className":1529,"style":1485},[1484],[745,1531,1533],{"className":1532,"style":1498},[1497],[745,1534,1402],{"className":1535},[796],[745,1537,1414],{"className":1538},[796],[745,1540],{"className":1541,"style":910},[800],[745,1543,843],{"className":1544},[914],[745,1546],{"className":1547,"style":910},[800],[745,1549,1551,1554,1594,1597,1600],{"className":1550},[787],[745,1552],{"className":1553,"style":1454},[791],[745,1555,1557,1560,1591],{"className":1556},[796,1230],[745,1558,1393],{"className":1559},[796],[745,1561,1563],{"className":1562},[796,1464],[745,1564,1566],{"className":1565},[1468],[745,1567,1569],{"className":1568},[1472],[745,1570,1572,1580],{"className":1571,"style":1477},[1476],[745,1573,1574,1577],{"style":1480},[745,1575],{"className":1576,"style":1485},[1484],[745,1578,1399],{"className":1579},[796],[745,1581,1582,1585],{"style":1480},[745,1583],{"className":1584,"style":1485},[1484],[745,1586,1588],{"className":1587,"style":1498},[1497],[745,1589,1402],{"className":1590},[796],[745,1592,1429],{"className":1593},[796],[745,1595],{"className":1596,"style":876},[800],[745,1598,1432],{"className":1599},[880],[745,1601],{"className":1602,"style":876},[800],[745,1604,1606,1610],{"className":1605},[787],[745,1607],{"className":1608,"style":1609},[791],"height:2.0309em;vertical-align:-0.686em;",[745,1611,1613,1618,1684],{"className":1612},[796],[745,1614],{"className":1615},[1616,1617],"mopen","nulldelimiter",[745,1619,1621],{"className":1620},[1434],[745,1622,1625,1675],{"className":1623},[1468,1624],"vlist-t2",[745,1626,1628,1670],{"className":1627},[1472],[745,1629,1632,1644,1655],{"className":1630,"style":1631},[1476],"height:1.3449em;",[745,1633,1635,1638],{"style":1634},"top:-2.314em;",[745,1636],{"className":1637,"style":1485},[1484],[745,1639,1641],{"className":1640},[796],[745,1642,1441],{"className":1643},[796],[745,1645,1647,1650],{"style":1646},"top:-3.23em;",[745,1648],{"className":1649,"style":1485},[1484],[745,1651],{"className":1652,"style":1654},[1653],"frac-line","border-bottom-width:0.04em;",[745,1656,1658,1661],{"style":1657},"top:-3.677em;",[745,1659],{"className":1660,"style":1485},[1484],[745,1662,1664],{"className":1663},[796],[745,1665,1667],{"className":1666},[796,1230],[745,1668,1438],{"className":1669},[796],[745,1671,1674],{"className":1672},[1673],"vlist-s","​",[745,1676,1678],{"className":1677},[1472],[745,1679,1682],{"className":1680,"style":1681},[1476],"height:0.686em;",[745,1683],{},[745,1685],{"className":1686},[1687,1617],"mclose",[599,1689,1690,1691,1693],{},"Reprenons la latitude ",[1169,1692,1279],{}," :",[983,1695,1696,1702,1708],{},[986,1697,1698,1699],{},"degrés entiers : ",[603,1700,1701],{},"48",[986,1703,1704,1705],{},"minutes : ",[603,1706,1707],{},"07,038",[986,1709,1710,1711],{},"conversion : ",[745,1712,1714,1750],{"className":1713},[748],[745,1715,1717],{"className":1716},[752],[754,1718,1719],{"xmlns":756},[758,1720,1721,1747],{},[761,1722,1723,1725,1727,1737,1739,1742],{},[764,1724,1701],{},[835,1726,1432],{},[1728,1729,1730],"mstyle",{"scriptlevel":894,"displaystyle":783},[1434,1731,1732,1735],{},[764,1733,1734],{},"7,038",[764,1736,1441],{},[835,1738,843],{},[764,1740,1741],{},"48,1173",[1743,1744,1746],"mi",{"mathvariant":1745},"normal","°",[775,1748,1749],{"encoding":777},"48 + \\dfrac{7{,}038}{60} = 48{,}1173°",[745,1751,1753,1771,1861],{"className":1752,"ariaHidden":783},[782],[745,1754,1756,1759,1762,1765,1768],{"className":1755},[787],[745,1757],{"className":1758,"style":863},[791],[745,1760,1701],{"className":1761},[796],[745,1763],{"className":1764,"style":876},[800],[745,1766,1432],{"className":1767},[880],[745,1769],{"className":1770,"style":876},[800],[745,1772,1774,1778,1852,1855,1858],{"className":1773},[787],[745,1775],{"className":1776,"style":1777},[791],"height:2.0074em;vertical-align:-0.686em;",[745,1779,1781,1784,1849],{"className":1780},[796],[745,1782],{"className":1783},[1616,1617],[745,1785,1787],{"className":1786},[1434],[745,1788,1790,1841],{"className":1789},[1468,1624],[745,1791,1793,1838],{"className":1792},[1472],[745,1794,1797,1808,1816],{"className":1795,"style":1796},[1476],"height:1.3214em;",[745,1798,1799,1802],{"style":1634},[745,1800],{"className":1801,"style":1485},[1484],[745,1803,1805],{"className":1804},[796],[745,1806,1441],{"className":1807},[796],[745,1809,1810,1813],{"style":1646},[745,1811],{"className":1812,"style":1485},[1484],[745,1814],{"className":1815,"style":1654},[1653],[745,1817,1818,1821],{"style":1657},[745,1819],{"className":1820,"style":1485},[1484],[745,1822,1824,1828,1834],{"className":1823},[796],[745,1825,1827],{"className":1826},[796],"7",[745,1829,1831],{"className":1830},[796],[745,1832,902],{"className":1833},[901],[745,1835,1837],{"className":1836},[796],"038",[745,1839,1674],{"className":1840},[1673],[745,1842,1844],{"className":1843},[1472],[745,1845,1847],{"className":1846,"style":1681},[1476],[745,1848],{},[745,1850],{"className":1851},[1687,1617],[745,1853],{"className":1854,"style":910},[800],[745,1856,843],{"className":1857},[914],[745,1859],{"className":1860,"style":910},[800],[745,1862,1864,1867,1870,1876],{"className":1863},[787],[745,1865],{"className":1866,"style":1454},[791],[745,1868,1701],{"className":1869},[796],[745,1871,1873],{"className":1872},[796],[745,1874,902],{"className":1875},[901],[745,1877,1879],{"className":1878},[796],"1173°",[599,1881,1882,1883,1693],{},"Et la longitude ",[1169,1884,1305],{},[983,1886,1887,1892,1897],{},[986,1888,1698,1889],{},[603,1890,1891],{},"011",[986,1893,1704,1894],{},[603,1895,1896],{},"31,000",[986,1898,1710,1899],{},[745,1900,1902,1934],{"className":1901},[748],[745,1903,1905],{"className":1904},[752],[754,1906,1907],{"xmlns":756},[758,1908,1909,1931],{},[761,1910,1911,1914,1916,1924,1926,1929],{},[764,1912,1913],{},"11",[835,1915,1432],{},[1728,1917,1918],{"scriptlevel":894,"displaystyle":783},[1434,1919,1920,1922],{},[764,1921,1896],{},[764,1923,1441],{},[835,1925,843],{},[764,1927,1928],{},"11,5167",[1743,1930,1746],{"mathvariant":1745},[775,1932,1933],{"encoding":777},"11 + \\dfrac{31{,}000}{60} = 11{,}5167°",[745,1935,1937,1955,2042],{"className":1936,"ariaHidden":783},[782],[745,1938,1940,1943,1946,1949,1952],{"className":1939},[787],[745,1941],{"className":1942,"style":863},[791],[745,1944,1913],{"className":1945},[796],[745,1947],{"className":1948,"style":876},[800],[745,1950,1432],{"className":1951},[880],[745,1953],{"className":1954,"style":876},[800],[745,1956,1958,1961,2033,2036,2039],{"className":1957},[787],[745,1959],{"className":1960,"style":1777},[791],[745,1962,1964,1967,2030],{"className":1963},[796],[745,1965],{"className":1966},[1616,1617],[745,1968,1970],{"className":1969},[1434],[745,1971,1973,2022],{"className":1972},[1468,1624],[745,1974,1976,2019],{"className":1975},[1472],[745,1977,1979,1990,1998],{"className":1978,"style":1796},[1476],[745,1980,1981,1984],{"style":1634},[745,1982],{"className":1983,"style":1485},[1484],[745,1985,1987],{"className":1986},[796],[745,1988,1441],{"className":1989},[796],[745,1991,1992,1995],{"style":1646},[745,1993],{"className":1994,"style":1485},[1484],[745,1996],{"className":1997,"style":1654},[1653],[745,1999,2000,2003],{"style":1657},[745,2001],{"className":2002,"style":1485},[1484],[745,2004,2006,2010,2016],{"className":2005},[796],[745,2007,2009],{"className":2008},[796],"31",[745,2011,2013],{"className":2012},[796],[745,2014,902],{"className":2015},[901],[745,2017,773],{"className":2018},[796],[745,2020,1674],{"className":2021},[1673],[745,2023,2025],{"className":2024},[1472],[745,2026,2028],{"className":2027,"style":1681},[1476],[745,2029],{},[745,2031],{"className":2032},[1687,1617],[745,2034],{"className":2035,"style":910},[800],[745,2037,843],{"className":2038},[914],[745,2040],{"className":2041,"style":910},[800],[745,2043,2045,2048,2051,2057],{"className":2044},[787],[745,2046],{"className":2047,"style":1454},[791],[745,2049,1913],{"className":2050},[796],[745,2052,2054],{"className":2053},[796],[745,2055,902],{"className":2056},[901],[745,2058,2060],{"className":2059},[796],"5167°",[599,2062,2063,2064,2067],{},"La position décodée est donc : ",[603,2065,2066],{},"48,1173° N, 11,5167° E"," — ce qui place le\nrécepteur quelque part à Munich, en Allemagne.",[811,2069,2070],{},[599,2071,2072,2073,2076],{},"Pour vérifier rapidement, copiez ",[1169,2074,2075],{},"48.1173, 11.5167"," dans la barre de\nrecherche d'une carte en ligne. Le point bleu apparaîtra au cœur de la\ncapitale bavaroise.",[594,2078,2080],{"id":2079},"décoder-à-la-main-ou-en-pseudo-code","Décoder, à la main ou en pseudo-code",[599,2082,2083,2084,2087],{},"Décoder une trame, ce n'est rien d'autre que ",[603,2085,2086],{},"découper la chaîne autour\ndes virgules"," puis lire les morceaux dans l'ordre. À la main, vous suivez la\nligne du regard et vous numérotez les champs. En pseudo-code Python, l'idée\ns'écrit ainsi :",[708,2089,2090],{},[599,2091,2092,2093,2096,2097,2100,2101,2104,2105,2108],{},"Le bloc ci-dessous est du ",[603,2094,2095],{},"pseudo-code Python"," : la fonction\n",[1169,2098,2099],{},"decouper_autour_des_virgules"," n'existe pas sous ce nom et n'est pas\nexécutable telle quelle. En vraie syntaxe, on appellerait la méthode\n",[1169,2102,2103],{},"split(\",\")"," sur la chaîne. Ce qui compte ici est la ",[603,2106,2107],{},"logique"," : « je\ndécoupe, puis je lis le bon champ ».",[1225,2110,2114],{"className":2111,"code":2112,"language":2113,"meta":976,"style":976},"language-python shiki shiki-themes github-light github-light github-dark","trame = \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n\nchamps = decouper_autour_des_virgules(trame)\n\nheure       = champs[1]   # \"123519\"\nlatitude    = champs[2]   # \"4807.038\"\nhemisphere  = champs[3]   # \"N\"\nlongitude   = champs[4]   # \"01131.000\"\nmeridien    = champs[5]   # \"E\"\n","python",[1169,2115,2116,2130,2135,2146,2151,2172,2189,2207,2225],{"__ignoreMap":976},[745,2117,2119,2123,2126],{"class":2118,"line":1134},"line",[745,2120,2122],{"class":2121},"sxrX7","trame ",[745,2124,843],{"class":2125},"s8jYJ",[745,2127,2129],{"class":2128},"sIIMD"," \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n",[745,2131,2132],{"class":2118,"line":1114},[745,2133,2134],{"emptyLinePlaceholder":1126},"\n",[745,2136,2138,2141,2143],{"class":2118,"line":2137},3,[745,2139,2140],{"class":2121},"champs ",[745,2142,843],{"class":2125},[745,2144,2145],{"class":2121}," decouper_autour_des_virgules(trame)\n",[745,2147,2149],{"class":2118,"line":2148},4,[745,2150,2134],{"emptyLinePlaceholder":1126},[745,2152,2154,2157,2159,2162,2165,2168],{"class":2118,"line":2153},5,[745,2155,2156],{"class":2121},"heure       ",[745,2158,843],{"class":2125},[745,2160,2161],{"class":2121}," champs[",[745,2163,1078],{"class":2164},"sBjJW",[745,2166,2167],{"class":2121},"]   ",[745,2169,2171],{"class":2170},"sCsY4","# \"123519\"\n",[745,2173,2175,2178,2180,2182,2184,2186],{"class":2118,"line":2174},6,[745,2176,2177],{"class":2121},"latitude    ",[745,2179,843],{"class":2125},[745,2181,2161],{"class":2121},[745,2183,970],{"class":2164},[745,2185,2167],{"class":2121},[745,2187,2188],{"class":2170},"# \"4807.038\"\n",[745,2190,2192,2195,2197,2199,2202,2204],{"class":2118,"line":2191},7,[745,2193,2194],{"class":2121},"hemisphere  ",[745,2196,843],{"class":2125},[745,2198,2161],{"class":2121},[745,2200,2201],{"class":2164},"3",[745,2203,2167],{"class":2121},[745,2205,2206],{"class":2170},"# \"N\"\n",[745,2208,2210,2213,2215,2217,2220,2222],{"class":2118,"line":2209},8,[745,2211,2212],{"class":2121},"longitude   ",[745,2214,843],{"class":2125},[745,2216,2161],{"class":2121},[745,2218,2219],{"class":2164},"4",[745,2221,2167],{"class":2121},[745,2223,2224],{"class":2170},"# \"01131.000\"\n",[745,2226,2228,2231,2233,2235,2238,2240],{"class":2118,"line":2227},9,[745,2229,2230],{"class":2121},"meridien    ",[745,2232,843],{"class":2125},[745,2234,2161],{"class":2121},[745,2236,2237],{"class":2164},"5",[745,2239,2167],{"class":2121},[745,2241,2242],{"class":2170},"# \"E\"\n",[599,2244,2245],{},"Pour la conversion en degrés décimaux, le travail se fait en français aussi\nbien qu'en code :",[2247,2248,2249],"blockquote",{},[599,2250,2251,2252,2255,2256,2259,2260,1052],{},"On prend les ",[603,2253,2254],{},"deux premiers caractères"," de la latitude pour les degrés,\npuis ",[603,2257,2258],{},"tout ce qui suit"," pour les minutes. On applique la formule\n",[745,2261,2263,2288],{"className":2262},[748],[745,2264,2266],{"className":2265},[752],[754,2267,2268],{"xmlns":756},[758,2269,2270,2285],{},[761,2271,2272,2275,2277,2280,2283],{},[1743,2273,2274],{},"D",[835,2276,1432],{},[1743,2278,2279],{},"M",[1743,2281,2282],{"mathvariant":1745},"\u002F",[764,2284,1441],{},[775,2286,2287],{"encoding":777},"D + M\u002F60",[745,2289,2291,2312],{"className":2290,"ariaHidden":783},[782],[745,2292,2294,2298,2303,2306,2309],{"className":2293},[787],[745,2295],{"className":2296,"style":2297},[791],"height:0.7667em;vertical-align:-0.0833em;",[745,2299,2274],{"className":2300,"style":2302},[796,2301],"mathnormal","margin-right:0.0278em;",[745,2304],{"className":2305,"style":876},[800],[745,2307,1432],{"className":2308},[880],[745,2310],{"className":2311,"style":876},[800],[745,2313,2315,2319,2323],{"className":2314},[787],[745,2316],{"className":2317,"style":2318},[791],"height:1em;vertical-align:-0.25em;",[745,2320,2279],{"className":2321,"style":2322},[796,2301],"margin-right:0.109em;",[745,2324,2326],{"className":2325},[796],"\u002F60",[599,2328,2329,2330,2332,2333,2335,2336,2339,2340,2438],{},"Sur ",[1169,2331,1279],{}," : les deux premiers caractères sont ",[1169,2334,1701],{},", le reste est\n",[1169,2337,2338],{},"07.038",". Donc ",[745,2341,2343,2371],{"className":2342},[748],[745,2344,2346],{"className":2345},[752],[754,2347,2348],{"xmlns":756},[758,2349,2350,2368],{},[761,2351,2352,2354,2356,2358,2360,2362,2364,2366],{},[764,2353,1701],{},[835,2355,1432],{},[764,2357,1734],{},[1743,2359,2282],{"mathvariant":1745},[764,2361,1441],{},[835,2363,843],{},[764,2365,1741],{},[1743,2367,1746],{"mathvariant":1745},[775,2369,2370],{"encoding":777},"48 + 7{,}038\u002F60 = 48{,}1173°",[745,2372,2374,2392,2420],{"className":2373,"ariaHidden":783},[782],[745,2375,2377,2380,2383,2386,2389],{"className":2376},[787],[745,2378],{"className":2379,"style":863},[791],[745,2381,1701],{"className":2382},[796],[745,2384],{"className":2385,"style":876},[800],[745,2387,1432],{"className":2388},[880],[745,2390],{"className":2391,"style":876},[800],[745,2393,2395,2398,2401,2407,2411,2414,2417],{"className":2394},[787],[745,2396],{"className":2397,"style":2318},[791],[745,2399,1827],{"className":2400},[796],[745,2402,2404],{"className":2403},[796],[745,2405,902],{"className":2406},[901],[745,2408,2410],{"className":2409},[796],"038\u002F60",[745,2412],{"className":2413,"style":910},[800],[745,2415,843],{"className":2416},[914],[745,2418],{"className":2419,"style":910},[800],[745,2421,2423,2426,2429,2435],{"className":2422},[787],[745,2424],{"className":2425,"style":1454},[791],[745,2427,1701],{"className":2428},[796],[745,2430,2432],{"className":2431},[796],[745,2433,902],{"className":2434},[901],[745,2436,1879],{"className":2437},[796],". Aucun outil informatique\nparticulier n'est requis pour faire ce calcul.",[968,2440,2443,2448],{"correct":1078,"explanation":2441,"slug":2442},"5030.000 = 50° + 30 minutes \u002F 60 = 50 + 0,5 = 50,5°.","trame-nmea-c2",[974,2444,2445],{"v-slot:question":976},[599,2446,2447],{},"Si une trame indique une latitude de '5030.000' Nord, à combien de degrés décimaux cela correspond-il ?",[974,2449,2450],{"v-slot:choices":976},[983,2451,2452,2455,2458],{},[986,2453,2454],{},"50°",[986,2456,2457],{},"50,5°",[986,2459,2460],{},"50,8333°",[594,2462,2464],{"id":2463},"le-checksum-gardien-de-lintégrité","Le checksum, gardien de l'intégrité",[599,2466,2467,2468,2471,2472,2475,2476,2478,2479,2482],{},"Vous avez peut-être remarqué le ",[1169,2469,2470],{},"*47"," à la fin de la trame. C'est un\n",[603,2473,2474],{},"checksum"," : un petit code de vérification qui permet au récepteur de\ndétecter une éventuelle corruption en transmission. Il est calculé par XOR de\ntous les caractères entre ",[1169,2477,1194],{}," et ",[1169,2480,2481],{},"*",", et écrit en hexadécimal.",[599,2484,2485,2486,2489],{},"En pratique, vous n'avez pas à le calculer à la main : les bibliothèques le\nfont pour vous. Mais sa présence rappelle un principe général de tout\nprotocole de communication numérique : ",[603,2487,2488],{},"on vérifie toujours qu'un message\nest arrivé intact"," avant de lui faire confiance.",[594,2491,2493],{"id":2492},"dautres-types-de-trames","D'autres types de trames",[599,2495,2496],{},"Le NMEA 0183 définit des dizaines de trames. Les plus courantes :",[626,2498,2499,2509],{},[629,2500,2501],{},[632,2502,2503,2506],{},[635,2504,2505],{},"Type",[635,2507,2508],{},"Rôle",[648,2510,2511,2520,2530,2540,2550],{},[632,2512,2513,2517],{},[653,2514,2515],{},[1169,2516,1219],{},[653,2518,2519],{},"Position complète avec altitude",[632,2521,2522,2527],{},[653,2523,2524],{},[1169,2525,2526],{},"$GPRMC",[653,2528,2529],{},"Position + vitesse + cap",[632,2531,2532,2537],{},[653,2533,2534],{},[1169,2535,2536],{},"$GPGSA",[653,2538,2539],{},"Satellites utilisés et qualité géométrique",[632,2541,2542,2547],{},[653,2543,2544],{},[1169,2545,2546],{},"$GPGSV",[653,2548,2549],{},"Satellites visibles dans le ciel",[632,2551,2552,2557],{},[653,2553,2554],{},[1169,2555,2556],{},"$GPVTG",[653,2558,2559],{},"Vitesse et direction de déplacement",[599,2561,2562],{},"Un récepteur typique envoie plusieurs de ces trames par seconde. C'est à\nl'application qui les reçoit de choisir lesquelles décoder selon ses besoins.",[1040,2564,2565],{},[599,2566,2567,2568,2571],{},"Le format NMEA est ancien et présente plusieurs limites : précision réduite\n(quelques chiffres après la virgule), pas de chiffrement, débit faible (4800\nbauds par défaut). Les équipements modernes utilisent souvent ",[603,2569,2570],{},"NMEA 2000","\n(binaire, plus rapide) ou des protocoles propriétaires, mais NMEA 0183 reste\nla lingua franca pour l'apprentissage et les modules grand public.",[594,2573,1102],{"id":1101},[599,2575,2576,2577,1052],{},"La quasi-totalité des modules GPS « hobby » (par exemple le NEO-6M de\nu-blox, vendu une dizaine d'euros) sortent du NMEA 0183 sur leur port série.\nBranché à un Arduino ou à un Raspberry Pi, ce module permet de bricoler un\ntraceur de position en quelques lignes de code — un excellent projet pour\nprolonger ce cours dans le chapitre sur l'",[603,2578,2579],{},"informatique embarquée",[2581,2582,2583],"style",{},"html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":976,"searchDepth":1114,"depth":1114,"links":2585},[2586,2587,2588,2589,2590,2591,2592,2593],{"id":596,"depth":1114,"text":597},{"id":1159,"depth":1114,"text":1160},{"id":1210,"depth":1114,"text":1211},{"id":1352,"depth":1114,"text":1353},{"id":2079,"depth":1114,"text":2080},{"id":2463,"depth":1114,"text":2464},{"id":2492,"depth":1114,"text":2493},{"id":1101,"depth":1114,"text":1102},"La forme numérique brute d'une position GPS, et comment en extraire latitude et longitude.",{},[2597,2599],{"slug":1332,"kind":1129,"question":1337,"choices":2598,"correct":1078,"multi":1131,"explanation":1331},[1344,1269,1349],{"slug":2442,"kind":1129,"question":2447,"choices":2600,"correct":1078,"multi":1131,"explanation":2441},[2454,2457,2460],{"title":129,"description":2594},"bSF797YpFBP9VhLXQPuqacsCbebPk4GrffRCxMkzxxY",{"id":2604,"title":133,"bo":2605,"body":2607,"description":3112,"eval":1123,"extension":1124,"labo":1123,"meta":3113,"navigation":1126,"path":134,"quizzes":3114,"readingTime":1134,"seo":3119,"stem":135,"tp":1123,"__hash__":3120},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques.md",[2606],"SE02",{"type":591,"value":2608,"toc":3103},[2609,2611,2634,2636,2640,2651,2656,2659,2714,2736,2740,2749,2752,2796,2805,2812,2816,2832,2915,2924,2928,2938,2970,2981,2987,2996,3018,3022,3025,3052,3084,3086],[594,2610,597],{"id":596},[599,2612,2613,2614,2617,2618,2621,2622,2625,2626,2629,2630,2633],{},"Une carte papier IGN au 1\u002F25 000 représente un compromis figé : un éditeur a\nchoisi ce qu'il voulait montrer (relief, sentiers, lignes électriques) et l'a\nimprimé une fois pour toutes. Une ",[603,2615,2616],{},"carte numérique"," rompt avec ce\ncompromis : elle est constituée de ",[603,2619,2620],{},"couches"," que vous pouvez activer ou\nmasquer à volonté, mises à jour en continu, et parfois ",[603,2623,2624],{},"enrichies par les\nutilisateurs eux-mêmes",". Ce cours vous présente les deux écosystèmes\nfrançais de référence : le ",[603,2627,2628],{},"GeoPortail"," institutionnel et ",[603,2631,2632],{},"OpenStreetMap","\ncontributif.",[612,2635],{"code":2606},[594,2637,2639],{"id":2638},"une-carte-numérique-cest-une-pile-de-couches","Une carte numérique, c'est une pile de couches",[599,2641,2642,2643,2646,2647,2650],{},"Sur le papier, tout est mélangé : routes, courbes de niveau, noms de\ncommunes, forêts… La force du numérique, c'est de pouvoir ",[603,2644,2645],{},"séparer les\ninformations"," en couches indépendantes. Une analogie utile : pensez aux\n",[603,2648,2649],{},"calques"," d'une application de dessin (Procreate, Photoshop, Krita) ou aux\nfiltres empilés d'un appareil photo numérique. Chaque calque porte une\ncatégorie de données ; vous choisissez lesquels empiler et afficher.",[954,2652],{"alt":2653,"kind":957,"src":2654,"svg":2655},"Empilement de couches d'une carte numérique","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fcalques-carte.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 480 300\" role=\"img\" aria-label=\"Pile de quatre calques semi-transparents en perspective qui se superposent pour former une carte : de bas en haut, fond satellite, relief, routes, puis étiquettes. Des flèches verticales indiquent la superposition.\">\n  \u003Ctitle>Empilement des calques d'une carte numérique\u003C\u002Ftitle>\n  \u003Cstyle>\n    .lc-layer { fill: var(--diagram-surface-alt); stroke: var(--diagram-node-border); stroke-width: 1.5; opacity: 0.85; }\n    .lc-label { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 13px; font-weight: 500; }\n    .lc-num   { fill: var(--diagram-line); font-family: 'JetBrains Mono', monospace; font-size: 10px; letter-spacing: 1px; }\n    .lc-arrow-line { stroke: var(--diagram-line); stroke-width: 1.5; fill: none; }\n    .lc-arrow-head { fill: var(--diagram-line); }\n    .lc-result { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 12.5px; font-weight: 600; }\n  \u003C\u002Fstyle>\n\n  \u003C!-- Quatre parallélogrammes empilés (perspective isométrique légère).\n       Forme de base : largeur 200, profondeur (décalage) 70.\n       Empilés du bas (y haut) vers le haut, espacés de 56 px verticalement. -->\n\n  \u003C!-- (1) satellite — le plus bas -->\n  \u003Cg>\n    \u003Cpath class=\"lc-layer\" d=\"M 60 248 L 260 248 L 330 206 L 130 206 Z\"\u002F>\n    \u003Ctext x=\"118\" y=\"232\" class=\"lc-num\">CALQUE 1\u003C\u002Ftext>\n    \u003Ctext x=\"118\" y=\"246\" class=\"lc-label\">satellite\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- (2) relief -->\n  \u003Cg>\n    \u003Cpath class=\"lc-layer\" d=\"M 60 192 L 260 192 L 330 150 L 130 150 Z\"\u002F>\n    \u003Ctext x=\"118\" y=\"176\" class=\"lc-num\">CALQUE 2\u003C\u002Ftext>\n    \u003Ctext x=\"118\" y=\"190\" class=\"lc-label\">relief\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- (3) routes -->\n  \u003Cg>\n    \u003Cpath class=\"lc-layer\" d=\"M 60 136 L 260 136 L 330 94 L 130 94 Z\"\u002F>\n    \u003Ctext x=\"118\" y=\"120\" class=\"lc-num\">CALQUE 3\u003C\u002Ftext>\n    \u003Ctext x=\"118\" y=\"134\" class=\"lc-label\">routes\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- (4) étiquettes — le plus haut -->\n  \u003Cg>\n    \u003Cpath class=\"lc-layer\" d=\"M 60 80 L 260 80 L 330 38 L 130 38 Z\"\u002F>\n    \u003Ctext x=\"118\" y=\"64\" class=\"lc-num\">CALQUE 4\u003C\u002Ftext>\n    \u003Ctext x=\"118\" y=\"78\" class=\"lc-label\">étiquettes\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- flèche de superposition (de bas en haut, à droite de la pile) -->\n  \u003Cpath class=\"lc-arrow-line\" d=\"M 388 250 L 388 60\"\u002F>\n  \u003Cpolygon class=\"lc-arrow-head\" points=\"388,46 382,60 394,60\"\u002F>\n  \u003Ctext x=\"410\" y=\"150\" class=\"lc-result\" transform=\"rotate(-90 410 150)\" text-anchor=\"middle\">superposition\u003C\u002Ftext>\n\u003C\u002Fsvg>\n",[599,2657,2658],{},"Une carte numérique combine généralement trois grandes familles de couches :",[626,2660,2661,2673],{},[629,2662,2663],{},[632,2664,2665,2668,2671],{},[635,2666,2667],{},"Famille",[635,2669,2670],{},"Exemples",[635,2672,2508],{},[648,2674,2675,2688,2701],{},[632,2676,2677,2682,2685],{},[653,2678,2679],{},[603,2680,2681],{},"Fond cartographique",[653,2683,2684],{},"photo aérienne, plan dessiné, relief ombré",[653,2686,2687],{},"base visuelle",[632,2689,2690,2695,2698],{},[653,2691,2692],{},[603,2693,2694],{},"Données vectorielles",[653,2696,2697],{},"routes, bâtiments, frontières, courbes de niveau",[653,2699,2700],{},"tracés géométriques précis",[632,2702,2703,2708,2711],{},[653,2704,2705],{},[603,2706,2707],{},"Étiquettes et symboles",[653,2709,2710],{},"noms de villes, panneaux, icônes de POI",[653,2712,2713],{},"informations textuelles",[968,2715,2718,2723],{"correct":1078,"explanation":2716,"slug":2717},"C'est la modularité qui fait la force du numérique : chacun compose la carte dont il a besoin (un randonneur n'utilise pas les mêmes couches qu'un cycliste urbain).","cartes-numeriques-c1",[974,2719,2720],{"v-slot:question":976},[599,2721,2722],{},"Pourquoi sépare-t-on les informations en couches plutôt que de tout dessiner ensemble ?",[974,2724,2725],{"v-slot:choices":976},[983,2726,2727,2730,2733],{},[986,2728,2729],{},"Pour économiser de la place de stockage",[986,2731,2732],{},"Pour que l utilisateur puisse activer ou masquer chaque type d information indépendamment",[986,2734,2735],{},"Parce que les ordinateurs ne savent pas dessiner sur un seul calque",[594,2737,2739],{"id":2738},"geoportail-la-carte-officielle-française","GeoPortail — la carte officielle française",[599,2741,2742,2743,716,2745,2748],{},"Le ",[603,2744,2628],{},[1169,2746,2747],{},"geoportail.gouv.fr",") est le portail cartographique de\nl'IGN (Institut National de l'Information Géographique et Forestière) et de\nplusieurs organismes publics. Il rassemble en un seul endroit des dizaines de\ncouches officielles, mises à jour par les administrations françaises.",[599,2750,2751],{},"Quelques couches accessibles depuis le sélecteur de gauche :",[983,2753,2754,2760,2766,2772,2778,2784,2790],{},[986,2755,2756,2759],{},[603,2757,2758],{},"Cartes IGN"," (la classique « carte de randonnée » au 1\u002F25 000).",[986,2761,2762,2765],{},[603,2763,2764],{},"Photographies aériennes"," récentes et historiques (jusqu'à 1950, parfois 1920).",[986,2767,2768,2771],{},[603,2769,2770],{},"Cadastre"," (limites de parcelles, numéros).",[986,2773,2774,2777],{},[603,2775,2776],{},"Plan IGN"," (plan dessiné moderne).",[986,2779,2780,2783],{},[603,2781,2782],{},"Réseaux"," électriques, routiers, ferroviaires.",[986,2785,2786,2789],{},[603,2787,2788],{},"Risques"," : inondations, mouvements de terrain, sismicité.",[986,2791,2792,2795],{},[603,2793,2794],{},"Environnement"," : zones protégées, parcs nationaux.",[811,2797,2798],{},[599,2799,2800,2801,2804],{},"GeoPortail est particulièrement précieux pour les ",[603,2802,2803],{},"données réglementaires\net patrimoniales"," : c'est la source officielle. Le cadastre, par exemple,\nn'a aucun équivalent contributif.",[599,2806,2807,2808,2811],{},"L'intérêt majeur pour SNT : GeoPortail laisse comparer une ",[603,2809,2810],{},"photo aérienne\nde 1950"," avec celle d'aujourd'hui, sur le même endroit. On voit alors\ndisparaître des champs sous des lotissements, ou apparaître des autoroutes au\nmilieu de bocages. Une démonstration parlante du croisement entre données\nnumériques et histoire des territoires.",[594,2813,2815],{"id":2814},"openstreetmap-la-carte-du-monde-par-tout-le-monde","OpenStreetMap — la carte du monde, par tout le monde",[599,2817,2818,716,2820,2823,2824,2827,2828,2831],{},[603,2819,2632],{},[1169,2821,2822],{},"openstreetmap.org",", souvent abrégé ",[603,2825,2826],{},"OSM",") suit une\nlogique radicalement différente : c'est ",[603,2829,2830],{},"Wikipédia, mais pour les cartes",".\nTout le monde peut éditer, ajouter ou corriger une donnée. Le résultat,\npatiemment construit depuis 2004, est aujourd'hui une cartographie mondiale\nlibre, utilisée par d'innombrables applications (Komoot, OsmAnd, Mapy.cz,\nMaps.me, Wikipedia, et même certains services Apple ou Facebook).",[626,2833,2834,2845],{},[629,2835,2836],{},[632,2837,2838,2841,2843],{},[635,2839,2840],{},"Propriété",[635,2842,2628],{},[635,2844,2632],{},[648,2846,2847,2858,2869,2880,2894,2904],{},[632,2848,2849,2852,2855],{},[653,2850,2851],{},"Auteur",[653,2853,2854],{},"IGN + administrations",[653,2856,2857],{},"n'importe quel internaute inscrit",[632,2859,2860,2863,2866],{},[653,2861,2862],{},"Couverture",[653,2864,2865],{},"France principalement",[653,2867,2868],{},"mondiale",[632,2870,2871,2874,2877],{},[653,2872,2873],{},"Mise à jour",[653,2875,2876],{},"cycles administratifs",[653,2878,2879],{},"en continu",[632,2881,2882,2885,2888],{},[653,2883,2884],{},"Licence",[653,2886,2887],{},"restrictions selon couche",[653,2889,2890,2893],{},[603,2891,2892],{},"libre"," (ODbL)",[632,2895,2896,2898,2901],{},[653,2897,2770],{},[653,2899,2900],{},"officiel",[653,2902,2903],{},"absent",[632,2905,2906,2909,2912],{},[653,2907,2908],{},"Sentiers de randonnée",[653,2910,2911],{},"parfois incomplets",[653,2913,2914],{},"très détaillés (effet contributeurs)",[708,2916,2917],{},[599,2918,2919,2920,2923],{},"La ",[603,2921,2922],{},"licence libre"," d'OSM (ODbL) garantit que les données peuvent être\nréutilisées, modifiées et redistribuées par n'importe qui — y compris à des\nfins commerciales — à la seule condition de citer la source. C'est cette\nliberté qui explique son adoption massive.",[594,2925,2927],{"id":2926},"contribuer-à-openstreetmap","Contribuer à OpenStreetMap",[599,2929,2930,2931,2933,2934,2937],{},"Modifier OSM est plus simple qu'on ne l'imagine. Sur ",[1169,2932,2822],{},",\ncliquez sur ",[603,2935,2936],{},"Modifier"," : un éditeur en ligne (iD) s'ouvre directement dans\nle navigateur, sans installation. Les actions typiques :",[2939,2940,2941,2947,2953,2959,2964],"ol",{},[986,2942,2943,2946],{},[603,2944,2945],{},"Tracer un bâtiment"," absent (en superposition sur la photo aérienne).",[986,2948,2949,2952],{},[603,2950,2951],{},"Renommer une rue"," mal orthographiée.",[986,2954,2955,2958],{},[603,2956,2957],{},"Ajouter un point d'intérêt"," (boulangerie, fontaine, abri-vélo).",[986,2960,2961,1052],{},[603,2962,2963],{},"Corriger un sens unique",[986,2965,2966,2969],{},[603,2967,2968],{},"Compléter les horaires"," d'un commerce.",[599,2971,2972,2973,2976,2977,2980],{},"Chaque objet OSM est défini par sa ",[603,2974,2975],{},"géométrie"," (point, ligne, polygone) et\npar des ",[603,2978,2979],{},"tags"," clé=valeur :",[1225,2982,2985],{"className":2983,"code":2984,"language":1230,"meta":976},[1228],"Objet : ligne\nGéométrie : suite de points GPS\nTags :\n  highway = residential\n  name = Rue Victor Hugo\n  maxspeed = 30\n  surface = asphalt\n",[1169,2986,2984],{"__ignoreMap":976},[1040,2988,2989],{},[599,2990,2991,2992,2995],{},"Contribuer à OSM engage : vos modifications sont ",[603,2993,2994],{},"publiques, signées de\nvotre pseudonyme, et permanentes",". On ne dessine pas une rue qui n'existe\npas, on ne supprime pas un bâtiment par jeu. Une page wiki de débutant\nencadre les bonnes pratiques.",[968,2997,3000,3005],{"correct":1078,"explanation":2998,"slug":2999},"OSM repose sur la confiance et le contrôle communautaire a posteriori — comme Wikipédia. Les erreurs sont corrigées par d'autres contributeurs.","cartes-numeriques-c2",[974,3001,3002],{"v-slot:question":976},[599,3003,3004],{},"Quelle affirmation sur OpenStreetMap est exacte ?",[974,3006,3007],{"v-slot:choices":976},[983,3008,3009,3012,3015],{},[986,3010,3011],{},"Seuls les géographes professionnels peuvent contribuer",[986,3013,3014],{},"N importe quel internaute inscrit peut éditer, et ses modifications sont publiques et permanentes",[986,3016,3017],{},"Les modifications doivent être validées par un comité avant publication",[594,3019,3021],{"id":3020},"quel-outil-pour-quel-besoin","Quel outil pour quel besoin ?",[599,3023,3024],{},"Les deux services sont complémentaires :",[3026,3027,3030],"card",{"icon":3028,"title":3029},"i-lucide-shield-check","Quand choisir GeoPortail",[983,3031,3032,3039,3046],{},[986,3033,3034,3035,3038],{},"Besoin de ",[603,3036,3037],{},"données officielles"," (cadastre, risques, urbanisme).",[986,3040,3041,3042,3045],{},"Comparaison ",[603,3043,3044],{},"historique"," (photos aériennes anciennes).",[986,3047,3048,3049,1052],{},"Travail scolaire ou administratif nécessitant une ",[603,3050,3051],{},"source institutionnelle",[3026,3053,3056],{"icon":3054,"title":3055},"i-lucide-users","Quand choisir OpenStreetMap",[983,3057,3058,3064,3070,3077],{},[986,3059,3034,3060,3063],{},[603,3061,3062],{},"détails locaux fins"," (commerces, sentiers, équipements urbains).",[986,3065,3066,3067,1052],{},"Couverture ",[603,3068,3069],{},"hors France",[986,3071,3072,3073,3076],{},"Usage dans une application qui doit ",[603,3074,3075],{},"réutiliser librement"," la donnée.",[986,3078,3079,3080,3083],{},"Envie de ",[603,3081,3082],{},"contribuer"," au commun numérique.",[594,3085,1102],{"id":1101},[599,3087,3088,3089,3092,3093,716,3096,3099,3100,1052],{},"Au-delà de l'affichage, une carte numérique permet des ",[603,3090,3091],{},"requêtes spatiales"," :\n« tous les arrêts de bus dans un rayon de 300 m », « toutes les écoles d'une\ncommune », « tous les chemins traversant une forêt ». L'outil ",[603,3094,3095],{},"Overpass\nTurbo",[1169,3097,3098],{},"overpass-turbo.eu",") permet d'interroger OpenStreetMap dans ce style,\navec des résultats parfois étonnants. Vous croiserez ces idées de requête sur\ndonnées structurées dans le chapitre sur ",[603,3101,3102],{},"les données et leur traitement",{"title":976,"searchDepth":1114,"depth":1114,"links":3104},[3105,3106,3107,3108,3109,3110,3111],{"id":596,"depth":1114,"text":597},{"id":2638,"depth":1114,"text":2639},{"id":2738,"depth":1114,"text":2739},{"id":2814,"depth":1114,"text":2815},{"id":2926,"depth":1114,"text":2927},{"id":3020,"depth":1114,"text":3021},{"id":1101,"depth":1114,"text":1102},"Comment une carte interactive se compose de couches, et ce que change l'idée d'une cartographie collaborative.",{},[3115,3117],{"slug":2717,"kind":1129,"question":2722,"choices":3116,"correct":1078,"multi":1131,"explanation":2716},[2729,2732,2735],{"slug":2999,"kind":1129,"question":3004,"choices":3118,"correct":1078,"multi":1131,"explanation":2998},[3011,3014,3017],{"title":133,"description":3112},"yDtNLcvYlIkyozv_h7_WQBEadFfLzG8-m9YCNG9QZNM",{"id":3122,"title":137,"bo":3123,"body":3125,"description":3880,"eval":1123,"extension":1124,"labo":1123,"meta":3881,"navigation":1126,"path":138,"quizzes":3882,"readingTime":1134,"seo":3889,"stem":139,"tp":1123,"__hash__":3890},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.md",[3124],"SE01",{"type":591,"value":3126,"toc":3870},[3127,3129,3135,3137,3141,3148,3166,3169,3190,3195,3206,3228,3232,3249,3310,3324,3343,3347,3470],[594,3128,597],{"id":596},[599,3130,3131,3132,1052],{},"Vous demandez à votre téléphone un itinéraire de chez vous au lycée. En une\nseconde, il vous propose un trajet, une durée estimée, parfois trois\nvariantes : le plus rapide, le plus court, le plus économe. Comment une\nmachine prend-elle cette décision ? La réponse mêle géographie numérique\n(cours précédent) et un objet mathématique fondamental en informatique : le\n",[603,3133,3134],{},"graphe",[612,3136],{"code":3124},[594,3138,3140],{"id":3139},"dun-plan-à-un-graphe","D'un plan à un graphe",[599,3142,3143,3144,3147],{},"Sur un plan de ville, vous voyez des rues, des intersections, des places, des\nronds-points. Un logiciel de calcul d'itinéraire, lui, ne « voit » rien de\ntout cela. Il manipule une ",[603,3145,3146],{},"représentation abstraite"," : le graphe.",[3026,3149,3152],{"icon":3150,"title":3151},"i-lucide-share-2","Le graphe en deux mots",[599,3153,3154,3155,3157,3158,3161,3162,3165],{},"Un ",[603,3156,3134],{}," est une collection de ",[603,3159,3160],{},"sommets"," (les points) reliés par des\n",[603,3163,3164],{},"arêtes"," (les liens). C'est tout. Ni plus, ni moins.",[599,3167,3168],{},"Pour transformer un plan en graphe :",[983,3170,3171,3181],{},[986,3172,3173,3174,3177,3178,1052],{},"Chaque ",[603,3175,3176],{},"intersection"," devient un ",[603,3179,3180],{},"sommet",[986,3182,3173,3183,3186,3187,1052],{},[603,3184,3185],{},"tronçon de rue"," entre deux intersections devient une ",[603,3188,3189],{},"arête",[954,3191],{"alt":3192,"kind":957,"src":3193,"svg":3194},"Passage d'un plan de quartier à un graphe","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fplan-vers-graphe.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 520 260\" role=\"img\" aria-label=\"Double représentation. À gauche, un plan de quartier : quatre intersections A, B, C, D reliées par des rues. Une flèche « modélisation » mène à droite, au graphe correspondant : quatre sommets A, B, C, D reliés par cinq arêtes.\">\n  \u003Ctitle>Du plan de quartier au graphe\u003C\u002Ftitle>\n  \u003Cstyle>\n    .pg-title  { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 13px; font-weight: 600; }\n    .pg-block  { fill: var(--diagram-surface-alt); stroke: var(--diagram-border); stroke-width: 1.5; }\n    .pg-street { stroke: var(--diagram-line); stroke-width: 7; stroke-linecap: round; }\n    .pg-inter  { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .pg-edge   { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .pg-node   { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .pg-vlbl   { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 12px; font-weight: 600; }\n    .pg-modlbl { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 12px; font-weight: 500; font-style: italic; }\n    .pg-arrow-line { stroke: var(--diagram-line); stroke-width: 1.5; fill: none; }\n    .pg-arrow-head { fill: var(--diagram-line); }\n  \u003C\u002Fstyle>\n\n  \u003C!-- ░░ GAUCHE : plan de quartier ░░ -->\n  \u003Ctext x=\"110\" y=\"26\" text-anchor=\"middle\" class=\"pg-title\">plan de quartier\u003C\u002Ftext>\n\n  \u003C!-- îlots (blocs de bâti) pour donner l'idée d'un plan -->\n  \u003Crect class=\"pg-block\" x=\"58\"  y=\"62\"  width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"118\" y=\"62\"  width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"58\"  y=\"154\" width=\"44\" height=\"44\" rx=\"3\"\u002F>\n  \u003Crect class=\"pg-block\" x=\"118\" y=\"154\" width=\"44\" height=\"44\" rx=\"3\"\u002F>\n\n  \u003C!-- rues (entre les îlots) — coords des intersections :\n       A(50,50) B(170,50) C(50,210) D(170,210) -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"50\"  x2=\"170\" y2=\"50\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"50\"  x2=\"50\"  y2=\"210\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"pg-street\" x1=\"170\" y1=\"50\"  x2=\"170\" y2=\"210\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"pg-street\" x1=\"50\"  y1=\"210\" x2=\"170\" y2=\"210\"\u002F>  \u003C!-- C-D -->\n  \u003Cline class=\"pg-street\" x1=\"170\" y1=\"50\"  x2=\"50\"  y2=\"210\"\u002F>  \u003C!-- B-C (diagonale) -->\n\n  \u003C!-- intersections -->\n  \u003Cg>\n    \u003Ccircle class=\"pg-inter\" cx=\"50\"  cy=\"50\"  r=\"11\"\u002F>\u003Ctext x=\"50\"  y=\"54\"  text-anchor=\"middle\" class=\"pg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"170\" cy=\"50\"  r=\"11\"\u002F>\u003Ctext x=\"170\" y=\"54\"  text-anchor=\"middle\" class=\"pg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"50\"  cy=\"210\" r=\"11\"\u002F>\u003Ctext x=\"50\"  y=\"214\" text-anchor=\"middle\" class=\"pg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-inter\" cx=\"170\" cy=\"210\" r=\"11\"\u002F>\u003Ctext x=\"170\" y=\"214\" text-anchor=\"middle\" class=\"pg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- ░░ FLÈCHE modélisation ░░ -->\n  \u003Cpath class=\"pg-arrow-line\" d=\"M 222 130 L 296 130\"\u002F>\n  \u003Cpolygon class=\"pg-arrow-head\" points=\"310,130 296,124 296,136\"\u002F>\n  \u003Ctext x=\"262\" y=\"120\" text-anchor=\"middle\" class=\"pg-modlbl\">modélisation\u003C\u002Ftext>\n\n  \u003C!-- ░░ DROITE : graphe ░░ -->\n  \u003Ctext x=\"410\" y=\"26\" text-anchor=\"middle\" class=\"pg-title\">graphe\u003C\u002Ftext>\n\n  \u003C!-- arêtes (5) — coords des sommets :\n       A(350,60) B(470,60) C(350,200) D(470,200) -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"60\"  x2=\"470\" y2=\"60\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"60\"  x2=\"350\" y2=\"200\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"pg-edge\" x1=\"470\" y1=\"60\"  x2=\"470\" y2=\"200\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"pg-edge\" x1=\"350\" y1=\"200\" x2=\"470\" y2=\"200\"\u002F>  \u003C!-- C-D -->\n  \u003Cline class=\"pg-edge\" x1=\"470\" y1=\"60\"  x2=\"350\" y2=\"200\"\u002F>  \u003C!-- B-C -->\n\n  \u003C!-- sommets -->\n  \u003Cg>\n    \u003Ccircle class=\"pg-node\" cx=\"350\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"350\" y=\"65\"  text-anchor=\"middle\" class=\"pg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"470\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"470\" y=\"65\"  text-anchor=\"middle\" class=\"pg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"350\" cy=\"200\" r=\"15\"\u002F>\u003Ctext x=\"350\" y=\"205\" text-anchor=\"middle\" class=\"pg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"pg-node\" cx=\"470\" cy=\"200\" r=\"15\"\u002F>\u003Ctext x=\"470\" y=\"205\" text-anchor=\"middle\" class=\"pg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[599,3196,3197,3198,3201,3202,3205],{},"Sur ce graphe, ",[603,3199,3200],{},"trouver un itinéraire"," entre deux points, c'est trouver une\n",[603,3203,3204],{},"suite d'arêtes"," qui mène du sommet de départ au sommet d'arrivée.",[968,3207,3210,3215],{"correct":1078,"explanation":3208,"slug":3209},"Un sommet = un point du réseau, en général une intersection. Les rues entre intersections deviennent des arêtes.","itineraires-graphes-c1",[974,3211,3212],{"v-slot:question":976},[599,3213,3214],{},"Sur un graphe représentant une ville, que représente un sommet ?",[974,3216,3217],{"v-slot:choices":976},[983,3218,3219,3222,3225],{},[986,3220,3221],{},"Un tronçon de rue",[986,3223,3224],{},"Une intersection ou un carrefour",[986,3226,3227],{},"Une voiture en mouvement",[594,3229,3231],{"id":3230},"pondérer-les-arêtes","Pondérer les arêtes",[599,3233,3234,3235,3238,3239,3242,3243,3246,3247,1052],{},"Toutes les rues ne se valent pas. 50 mètres dans une zone piétonne, ce n'est\npas la même chose que 50 mètres sur un boulevard à 50 km\u002Fh. Pour en tenir\ncompte, on ",[603,3236,3237],{},"étiquette chaque arête avec un poids"," : ce poids représente le\n",[603,3240,3241],{},"coût"," du tronçon — typiquement la ",[603,3244,3245],{},"durée"," ou la ",[603,3248,808],{},[626,3250,3251,3267],{},[629,3252,3253],{},[632,3254,3255,3258,3261,3264],{},[635,3256,3257],{},"Arête",[635,3259,3260],{},"Distance (m)",[635,3262,3263],{},"Vitesse (km\u002Fh)",[635,3265,3266],{},"Durée (s)",[648,3268,3269,3283,3297],{},[632,3270,3271,3274,3277,3280],{},[653,3272,3273],{},"A → B",[653,3275,3276],{},"400",[653,3278,3279],{},"50",[653,3281,3282],{},"29",[632,3284,3285,3288,3291,3294],{},[653,3286,3287],{},"B → C",[653,3289,3290],{},"150",[653,3292,3293],{},"30",[653,3295,3296],{},"18",[632,3298,3299,3302,3305,3307],{},[653,3300,3301],{},"A → C",[653,3303,3304],{},"600",[653,3306,3279],{},[653,3308,3309],{},"43",[599,3311,3312,3313,3316,3317,3320,3321,1052],{},"On obtient un ",[603,3314,3315],{},"graphe pondéré",". La question devient alors : « quelle est la\nsuite d'arêtes qui ",[603,3318,3319],{},"minimise la somme des poids"," entre le départ et\nl'arrivée ? » C'est ce qu'on appelle le ",[603,3322,3323],{},"plus court chemin",[708,3325,3326],{},[599,3327,3328,3329,3331,3332,3334,3335,3338,3339,3342],{},"Le poids n'est pas forcément une distance. Selon ce que l'utilisateur\nchoisit, on peut pondérer par : la ",[603,3330,3245],{}," (le plus rapide), la\n",[603,3333,808],{}," (le plus court), la ",[603,3336,3337],{},"consommation"," (le plus économe), le\n",[603,3340,3341],{},"dénivelé"," (le moins fatigant à vélo)... Le graphe sous-jacent ne change\npas — seule la valeur du poids change.",[594,3344,3346],{"id":3345},"lidée-du-plus-court-chemin","L'idée du plus court chemin",[599,3348,3349,3350,3380,3381,3380,3411,3380,3441,3469],{},"Imaginons le mini-graphe suivant — quatre points ",[745,3351,3353,3367],{"className":3352},[748],[745,3354,3356],{"className":3355},[752],[754,3357,3358],{"xmlns":756},[758,3359,3360,3365],{},[761,3361,3362],{},[1743,3363,3364],{},"A",[775,3366,3364],{"encoding":777},[745,3368,3370],{"className":3369,"ariaHidden":783},[782],[745,3371,3373,3377],{"className":3372},[787],[745,3374],{"className":3375,"style":3376},[791],"height:0.6833em;",[745,3378,3364],{"className":3379},[796,2301],", ",[745,3382,3384,3398],{"className":3383},[748],[745,3385,3387],{"className":3386},[752],[754,3388,3389],{"xmlns":756},[758,3390,3391,3396],{},[761,3392,3393],{},[1743,3394,3395],{},"B",[775,3397,3395],{"encoding":777},[745,3399,3401],{"className":3400,"ariaHidden":783},[782],[745,3402,3404,3407],{"className":3403},[787],[745,3405],{"className":3406,"style":3376},[791],[745,3408,3395],{"className":3409,"style":3410},[796,2301],"margin-right:0.0502em;",[745,3412,3414,3428],{"className":3413},[748],[745,3415,3417],{"className":3416},[752],[754,3418,3419],{"xmlns":756},[758,3420,3421,3426],{},[761,3422,3423],{},[1743,3424,3425],{},"C",[775,3427,3425],{"encoding":777},[745,3429,3431],{"className":3430,"ariaHidden":783},[782],[745,3432,3434,3437],{"className":3433},[787],[745,3435],{"className":3436,"style":3376},[791],[745,3438,3425],{"className":3439,"style":3440},[796,2301],"margin-right:0.0715em;",[745,3442,3444,3457],{"className":3443},[748],[745,3445,3447],{"className":3446},[752],[754,3448,3449],{"xmlns":756},[758,3450,3451,3455],{},[761,3452,3453],{},[1743,3454,2274],{},[775,3456,2274],{"encoding":777},[745,3458,3460],{"className":3459,"ariaHidden":783},[782],[745,3461,3463,3466],{"className":3462},[787],[745,3464],{"className":3465,"style":3376},[791],[745,3467,2274],{"className":3468,"style":2302},[796,2301]," avec\nleurs durées en minutes :",[954,3471,3475,3535,3567,3641,3663,3667,3674,3686,3693,3697,3700,3733,3736,3749,3753,3756,3839,3861,3863],{"alt":3472,"kind":957,"src":3473,"svg":3474},"Mini-graphe à quatre sommets A, B, C, D : A—B de coût 2, A—C de coût 3, B—D de coût 1, C—D de coût 4","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fmini-graphe-pondere.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 320 240\" role=\"img\" aria-label=\"Mini-graphe pondéré à quatre sommets A, B, C, D. A est relié à B par une arête de coût 2, A à C par une arête de coût 3, B à D par une arête de coût 1, et C à D par une arête de coût 4.\">\n  \u003Ctitle>Mini-graphe pondéré à quatre sommets\u003C\u002Ftitle>\n  \u003Cstyle>\n    .mg-edge { stroke: var(--diagram-line); stroke-width: 1.5; }\n    .mg-node { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .mg-vlbl { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 13px; font-weight: 600; }\n    .mg-wpill { fill: var(--diagram-surface); stroke: var(--diagram-border); stroke-width: 1; }\n    .mg-wlbl { fill: var(--diagram-text); font-family: 'JetBrains Mono', monospace; font-size: 12px; font-weight: 600; }\n  \u003C\u002Fstyle>\n\n  \u003C!-- arêtes — sommets : A(80,60) B(240,60) C(80,180) D(240,180) -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"60\"  x2=\"240\" y2=\"60\"\u002F>   \u003C!-- A-B -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"60\"  x2=\"80\"  y2=\"180\"\u002F>  \u003C!-- A-C -->\n  \u003Cline class=\"mg-edge\" x1=\"240\" y1=\"60\"  x2=\"240\" y2=\"180\"\u002F>  \u003C!-- B-D -->\n  \u003Cline class=\"mg-edge\" x1=\"80\"  y1=\"180\" x2=\"240\" y2=\"180\"\u002F>  \u003C!-- C-D -->\n\n  \u003C!-- poids (pastilles au milieu des arêtes) -->\n  \u003Cg>\n    \u003Crect class=\"mg-wpill\" x=\"149\" y=\"51\"  width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"160\" y=\"64\"  text-anchor=\"middle\" class=\"mg-wlbl\">2\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"69\"  y=\"111\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"80\"  y=\"124\" text-anchor=\"middle\" class=\"mg-wlbl\">3\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"229\" y=\"111\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"240\" y=\"124\" text-anchor=\"middle\" class=\"mg-wlbl\">1\u003C\u002Ftext>\n    \u003Crect class=\"mg-wpill\" x=\"149\" y=\"171\" width=\"22\" height=\"18\" rx=\"4\"\u002F>\u003Ctext x=\"160\" y=\"184\" text-anchor=\"middle\" class=\"mg-wlbl\">4\u003C\u002Ftext>\n  \u003C\u002Fg>\n\n  \u003C!-- sommets -->\n  \u003Cg>\n    \u003Ccircle class=\"mg-node\" cx=\"80\"  cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"80\"  y=\"65\"  text-anchor=\"middle\" class=\"mg-vlbl\">A\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"240\" cy=\"60\"  r=\"15\"\u002F>\u003Ctext x=\"240\" y=\"65\"  text-anchor=\"middle\" class=\"mg-vlbl\">B\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"80\"  cy=\"180\" r=\"15\"\u002F>\u003Ctext x=\"80\"  y=\"185\" text-anchor=\"middle\" class=\"mg-vlbl\">C\u003C\u002Ftext>\n    \u003Ccircle class=\"mg-node\" cx=\"240\" cy=\"180\" r=\"15\"\u002F>\u003Ctext x=\"240\" y=\"185\" text-anchor=\"middle\" class=\"mg-vlbl\">D\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[599,3476,3477,3478,3506,3507,1693],{},"Quatre arêtes au total : A — B de coût 2, A — C de coût 3, B — D de coût 1,\nC — D de coût 4. Plusieurs trajets relient ",[745,3479,3481,3494],{"className":3480},[748],[745,3482,3484],{"className":3483},[752],[754,3485,3486],{"xmlns":756},[758,3487,3488,3492],{},[761,3489,3490],{},[1743,3491,3364],{},[775,3493,3364],{"encoding":777},[745,3495,3497],{"className":3496,"ariaHidden":783},[782],[745,3498,3500,3503],{"className":3499},[787],[745,3501],{"className":3502,"style":3376},[791],[745,3504,3364],{"className":3505},[796,2301]," à ",[745,3508,3510,3523],{"className":3509},[748],[745,3511,3513],{"className":3512},[752],[754,3514,3515],{"xmlns":756},[758,3516,3517,3521],{},[761,3518,3519],{},[1743,3520,2274],{},[775,3522,2274],{"encoding":777},[745,3524,3526],{"className":3525,"ariaHidden":783},[782],[745,3527,3529,3532],{"className":3528},[787],[745,3530],{"className":3531,"style":3376},[791],[745,3533,2274],{"className":3534,"style":2302},[796,2301],[626,3536,3537,3547],{},[629,3538,3539],{},[632,3540,3541,3544],{},[635,3542,3543],{},"Trajet",[635,3545,3546],{},"Coût total",[648,3548,3549,3559],{},[632,3550,3551,3554],{},[653,3552,3553],{},"A → B → D",[653,3555,3556,3557],{},"2 + 1 = ",[603,3558,2201],{},[632,3560,3561,3564],{},[653,3562,3563],{},"A → C → D",[653,3565,3566],{},"3 + 4 = 7",[599,3568,3569,3570,3506,3598,3626,3627,3629,3630,3633,3634,3637,3638,1052],{},"Le plus court chemin de ",[745,3571,3573,3586],{"className":3572},[748],[745,3574,3576],{"className":3575},[752],[754,3577,3578],{"xmlns":756},[758,3579,3580,3584],{},[761,3581,3582],{},[1743,3583,3364],{},[775,3585,3364],{"encoding":777},[745,3587,3589],{"className":3588,"ariaHidden":783},[782],[745,3590,3592,3595],{"className":3591},[787],[745,3593],{"className":3594,"style":3376},[791],[745,3596,3364],{"className":3597},[796,2301],[745,3599,3601,3614],{"className":3600},[748],[745,3602,3604],{"className":3603},[752],[754,3605,3606],{"xmlns":756},[758,3607,3608,3612],{},[761,3609,3610],{},[1743,3611,2274],{},[775,3613,2274],{"encoding":777},[745,3615,3617],{"className":3616,"ariaHidden":783},[782],[745,3618,3620,3623],{"className":3619},[787],[745,3621],{"className":3622,"style":3376},[791],[745,3624,2274],{"className":3625,"style":2302},[796,2301]," est donc ",[603,3628,3553],{}," pour un coût total\nde ",[603,3631,3632],{},"3 minutes",". Sur un mini-graphe, on trouve cela à l'œil. Sur un graphe\nde plusieurs ",[603,3635,3636],{},"millions de sommets"," (une ville moyenne en compte autour de\n50 000 intersections, un pays plusieurs millions), il faut un ",[603,3639,3640],{},"algorithme",[968,3642,3645,3650],{"correct":1078,"explanation":3643,"slug":3644},"Le 'plus court' est en fait le 'moins coûteux' au sens du poids choisi — ici, la durée totale. Un chemin avec plus d'intersections mais des tronçons rapides peut être préférable.","itineraires-graphes-c2",[974,3646,3647],{"v-slot:question":976},[599,3648,3649],{},"Dans un graphe routier pondéré par la durée, le plus court chemin entre deux points est…",[974,3651,3652],{"v-slot:choices":976},[983,3653,3654,3657,3660],{},[986,3655,3656],{},"la suite d arêtes la plus directe à vol d oiseau",[986,3658,3659],{},"la suite d arêtes dont la somme des durées est minimale",[986,3661,3662],{},"la suite d arêtes contenant le moins d intersections",[594,3664,3666],{"id":3665},"lidée-dun-algorithme-de-plus-court-chemin","L'idée d'un algorithme de plus court chemin",[599,3668,3669,3670,3673],{},"Sans entrer dans le détail, l'idée intuitive est la suivante : on part du\nsommet de départ et on ",[603,3671,3672],{},"propage la distance minimale"," vers les voisins,\nvoisins des voisins, etc., en notant à chaque étape la meilleure manière\nconnue d'atteindre chaque sommet. À la fin, on connaît le plus court chemin\nvers tous les autres sommets — et donc en particulier vers l'arrivée.",[811,3675,3676],{},[599,3677,3678,3679,3682,3683,1052],{},"Cet algorithme s'appelle ",[603,3680,3681],{},"Dijkstra"," (du nom du Néerlandais Edsger Dijkstra\nqui l'a publié en 1959). C'est le moteur historique des calculateurs\nd'itinéraire. Vous\nen étudierez le fonctionnement précis en NSI Terminale, dans le chapitre sur\n",[603,3684,3685],{},"l'algorithmique sur les graphes",[599,3687,3688,3689,3692],{},"Aujourd'hui, les services comme Google Maps, Mapbox ou OpenRouteService\nutilisent des variantes plus rapides (A*, ",[603,3690,3691],{},"contraction hierarchies",", etc.),\nmais l'idée fondamentale reste la même : un graphe pondéré, et un calcul de\nplus court chemin.",[594,3694,3696],{"id":3695},"que-prend-en-compte-un-calculateur-moderne","Que prend en compte un calculateur moderne ?",[599,3698,3699],{},"Sur le papier, un graphe routier suffirait. En pratique, un calculateur\nd'itinéraire moderne enrichit le calcul avec :",[983,3701,3702,3709,3715,3721,3727],{},[986,3703,3704,3705,3708],{},"Les ",[603,3706,3707],{},"sens uniques"," (arêtes orientées, qu'on ne peut emprunter que dans un\nsens).",[986,3710,3704,3711,3714],{},[603,3712,3713],{},"interdictions de tourner"," (à une intersection, certains\nenchaînements sont interdits).",[986,3716,2742,3717,3720],{},[603,3718,3719],{},"mode de transport"," (à pied, à vélo, en voiture, en transports en\ncommun — chaque mode ignore certaines arêtes).",[986,3722,2742,3723,3726],{},[603,3724,3725],{},"trafic en temps réel"," (les poids changent selon l'heure et la\ncongestion mesurée).",[986,3728,3704,3729,3732],{},[603,3730,3731],{},"péages"," et tarifs.",[599,3734,3735],{},"Tout cela enrichit le graphe sans en changer la nature : c'est toujours des\nsommets, des arêtes, des poids.",[1040,3737,3738],{},[599,3739,3740,3741,3744,3745,3748],{},"Un calculateur d'itinéraire ne ",[603,3742,3743],{},"mesure rien"," par lui-même. Il calcule sur\nles ",[603,3746,3747],{},"données qu'on lui fournit",". Si la carte n'est pas à jour, un trajet\npeut vous emmener dans une rue désormais piétonne, ou ignorer un raccourci\nrécemment ouvert. La qualité du calcul dépend de la qualité du graphe.",[594,3750,3752],{"id":3751},"le-graphe-au-delà-des-routes","Le graphe au-delà des routes",[599,3754,3755],{},"Le graphe sert bien plus que les itinéraires routiers. Quelques exemples :",[626,3757,3758,3771],{},[629,3759,3760],{},[632,3761,3762,3765,3768],{},[635,3763,3764],{},"Domaine",[635,3766,3767],{},"Sommets",[635,3769,3770],{},"Arêtes",[648,3772,3773,3784,3795,3806,3817,3828],{},[632,3774,3775,3778,3781],{},[653,3776,3777],{},"Réseau social",[653,3779,3780],{},"profils",[653,3782,3783],{},"amitiés \u002F abonnements",[632,3785,3786,3789,3792],{},[653,3787,3788],{},"Web",[653,3790,3791],{},"pages",[653,3793,3794],{},"hyperliens",[632,3796,3797,3800,3803],{},[653,3798,3799],{},"Transport ferroviaire",[653,3801,3802],{},"gares",[653,3804,3805],{},"lignes",[632,3807,3808,3811,3814],{},[653,3809,3810],{},"Métro",[653,3812,3813],{},"stations",[653,3815,3816],{},"tronçons",[632,3818,3819,3822,3825],{},[653,3820,3821],{},"Internet (cours SA)",[653,3823,3824],{},"routeurs",[653,3826,3827],{},"liens physiques",[632,3829,3830,3833,3836],{},[653,3831,3832],{},"Recommandation Netflix",[653,3834,3835],{},"films",[653,3837,3838],{},"partagent des spectateurs",[968,3840,3843,3848],{"correct":1078,"explanation":3841,"slug":3842},"Une station = un sommet ; un tronçon entre deux stations consécutives = une arête. Une correspondance peut être modélisée comme une arête supplémentaire à l'intérieur d'une station.","itineraires-graphes-c3",[974,3844,3845],{"v-slot:question":976},[599,3846,3847],{},"Quand vous calculez un itinéraire en métro, que représente un sommet ?",[974,3849,3850],{"v-slot:choices":976},[983,3851,3852,3855,3858],{},[986,3853,3854],{},"Une rame de métro",[986,3856,3857],{},"Une station",[986,3859,3860],{},"Une correspondance entre deux lignes",[594,3862,1102],{"id":1101},[599,3864,3865,3866,3869],{},"L'algorithme de Dijkstra a une ",[603,3867,3868],{},"complexité polynomiale"," : il termine en un\ntemps raisonnable même sur des graphes de plusieurs millions de sommets. La\nrecherche d'un itinéraire entre Paris et Marseille tient en quelques\nmillisecondes sur un serveur. C'est une réussite mathématique parmi les plus\ndiscrètes — vous l'utilisez probablement plusieurs fois par semaine sans le\nsavoir.",{"title":976,"searchDepth":1114,"depth":1114,"links":3871},[3872,3873,3874,3875,3876,3877,3878,3879],{"id":596,"depth":1114,"text":597},{"id":3139,"depth":1114,"text":3140},{"id":3230,"depth":1114,"text":3231},{"id":3345,"depth":1114,"text":3346},{"id":3665,"depth":1114,"text":3666},{"id":3695,"depth":1114,"text":3696},{"id":3751,"depth":1114,"text":3752},{"id":1101,"depth":1114,"text":1102},"Du plan de ville au plus court chemin, comment un logiciel calcule l'itinéraire que vous suivez en voiture ou à pied.",{},[3883,3885,3887],{"slug":3209,"kind":1129,"question":3214,"choices":3884,"correct":1078,"multi":1131,"explanation":3208},[3221,3224,3227],{"slug":3644,"kind":1129,"question":3649,"choices":3886,"correct":1078,"multi":1131,"explanation":3643},[3656,3659,3662],{"slug":3842,"kind":1129,"question":3847,"choices":3888,"correct":1078,"multi":1131,"explanation":3841},[3854,3857,3860],{"title":137,"description":3880},"HWbayOZvGnO_l8nGxtUgq3Pcsof8UMkqKaGEQYWGwxo",{"id":3892,"title":141,"bo":3893,"body":3895,"description":4344,"eval":1123,"extension":1124,"labo":1123,"meta":4345,"navigation":1126,"path":142,"quizzes":4346,"readingTime":1134,"seo":4353,"stem":143,"tp":1123,"__hash__":4354},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position.md",[3894],"SE03",{"type":591,"value":3896,"toc":4334},[3897,3899,3910,3912,3916,3927,3932,3938,4014,4036,4040,4043,4058,4069,4076,4083,4096,4100,4103,4109,4116,4135,4139,4145,4182,4199,4203,4210,4242,4247,4251,4284,4306,4308,4311,4331],[594,3898,597],{"id":596},[599,3900,3901,3902,3905,3906,3909],{},"Vous l'avez vu dans le premier cours : utiliser le GPS, en soi, ",[603,3903,3904],{},"ne transmet\naucune donnée",". Le récepteur écoute des satellites en silence. Pourtant, vous\navez sans doute entendu parler de « publicités ciblées sur la base de votre\nlocalisation », de scandales liés à des « données de déplacement vendues à\ndes courtiers », ou de procès liés à un suivi non consenti. D'où viennent ces\ndonnées ? De vous, plus exactement de votre ",[603,3907,3908],{},"téléphone et de ses\napplications",". Ce cours vous propose de comprendre ce que ces dernières\ncollectent par défaut, et comment vous reprenez la main.",[612,3911],{"code":3894},[594,3913,3915],{"id":3914},"ce-que-partage-un-téléphone-vraiment","Ce que partage un téléphone, vraiment",[599,3917,3918,3919,3922,3923,3926],{},"Quand vous installez une application — un jeu, un réseau social, une appli\nmétéo — celle-ci demande souvent l'autorisation d'accéder à votre\n",[603,3920,3921],{},"position",". C'est cette autorisation, et ce qu'en fait l'application, qui\ncréent les flux de données. Le GPS n'est qu'un capteur, neutre. L'enjeu est\n",[603,3924,3925],{},"l'usage"," qu'on en fait.",[954,3928],{"alt":3929,"kind":957,"src":3930,"svg":3931},"Trois niveaux : satellite → téléphone → applications → Internet","\u002Fillustrations\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fetages-position.svg","\u003Csvg class=\"illustration-svg\" xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 460 360\" role=\"img\" aria-label=\"Trois étages empilés verticalement. En bas, des satellites émettent un signal capté par le téléphone. Au milieu, le téléphone calcule sa position. En haut, des applications reçoivent la position et l'envoient à leurs serveurs sur Internet. Des flèches verticales relient les étages.\">\n  \u003Ctitle>Du signal satellite à l'usage des applications\u003C\u002Ftitle>\n  \u003Cstyle>\n    .ep-stage  { fill: var(--diagram-surface); stroke: var(--diagram-border); stroke-width: 1.5; }\n    .ep-eyebrow{ fill: var(--diagram-line); font-family: 'JetBrains Mono', monospace; font-size: 9.5px; letter-spacing: 1.2px; }\n    .ep-node   { fill: var(--diagram-node-bg); stroke: var(--diagram-node-border); stroke-width: 1.5; }\n    .ep-label  { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 12px; font-weight: 500; }\n    .ep-strong { fill: var(--diagram-text); font-family: Geist, Inter, system-ui, sans-serif; font-size: 13px; font-weight: 600; }\n    .ep-arrow-line { stroke: var(--diagram-node-border); stroke-width: 2; fill: none; }\n    .ep-arrow-head { fill: var(--diagram-node-border); }\n    .ep-arrow-lbl  { fill: var(--diagram-line); font-family: Geist, Inter, system-ui, sans-serif; font-size: 11px; }\n  \u003C\u002Fstyle>\n\n  \u003C!-- ░░ ÉTAGE 3 (haut) : applications -> Internet ░░ -->\n  \u003Crect class=\"ep-stage\" x=\"30\" y=\"20\" width=\"400\" height=\"86\" rx=\"6\"\u002F>\n  \u003Ctext x=\"46\" y=\"38\" class=\"ep-eyebrow\">APPLICATIONS — USAGE\u003C\u002Ftext>\n  \u003Cg>\n    \u003Crect class=\"ep-node\" x=\"52\"  y=\"50\" width=\"74\" height=\"40\" rx=\"5\"\u002F>\u003Ctext x=\"89\"  y=\"74\" text-anchor=\"middle\" class=\"ep-label\">jeu\u003C\u002Ftext>\n    \u003Crect class=\"ep-node\" x=\"146\" y=\"50\" width=\"74\" height=\"40\" rx=\"5\"\u002F>\u003Ctext x=\"183\" y=\"74\" text-anchor=\"middle\" class=\"ep-label\">réseau\u003C\u002Ftext>\n    \u003Crect class=\"ep-node\" x=\"240\" y=\"50\" width=\"74\" height=\"40\" rx=\"5\"\u002F>\u003Ctext x=\"277\" y=\"74\" text-anchor=\"middle\" class=\"ep-label\">météo\u003C\u002Ftext>\n  \u003C\u002Fg>\n  \u003C!-- bras vers Internet -->\n  \u003Ctext x=\"396\" y=\"64\" text-anchor=\"middle\" class=\"ep-strong\">Internet\u003C\u002Ftext>\n  \u003Ctext x=\"396\" y=\"80\" text-anchor=\"middle\" class=\"ep-arrow-lbl\">(serveurs)\u003C\u002Ftext>\n  \u003Cpath class=\"ep-arrow-line\" d=\"M 318 70 L 358 70\"\u002F>\n  \u003Cpolygon class=\"ep-arrow-head\" points=\"364,70 354,65 354,75\"\u002F>\n\n  \u003C!-- flèche étage 2 -> étage 3 -->\n  \u003Cpath class=\"ep-arrow-line\" d=\"M 230 162 L 230 112\"\u002F>\n  \u003Cpolygon class=\"ep-arrow-head\" points=\"230,106 225,116 235,116\"\u002F>\n  \u003Ctext x=\"244\" y=\"138\" class=\"ep-arrow-lbl\">position partagée\u003C\u002Ftext>\n\n  \u003C!-- ░░ ÉTAGE 2 (milieu) : le téléphone calcule ░░ -->\n  \u003Crect class=\"ep-stage\" x=\"30\" y=\"168\" width=\"400\" height=\"64\" rx=\"6\"\u002F>\n  \u003Ctext x=\"46\" y=\"186\" class=\"ep-eyebrow\">TÉLÉPHONE — CALCUL\u003C\u002Ftext>\n  \u003Crect class=\"ep-node\" x=\"162\" y=\"194\" width=\"136\" height=\"30\" rx=\"5\"\u002F>\n  \u003Ctext x=\"230\" y=\"213\" text-anchor=\"middle\" class=\"ep-label\">calcule sa position\u003C\u002Ftext>\n\n  \u003C!-- flèche étage 1 -> étage 2 -->\n  \u003Cpath class=\"ep-arrow-line\" d=\"M 230 286 L 230 238\"\u002F>\n  \u003Cpolygon class=\"ep-arrow-head\" points=\"230,232 225,242 235,242\"\u002F>\n  \u003Ctext x=\"244\" y=\"264\" class=\"ep-arrow-lbl\">signal capté\u003C\u002Ftext>\n\n  \u003C!-- ░░ ÉTAGE 1 (bas) : satellites émettent ░░ -->\n  \u003Crect class=\"ep-stage\" x=\"30\" y=\"292\" width=\"400\" height=\"56\" rx=\"6\"\u002F>\n  \u003Ctext x=\"46\" y=\"310\" class=\"ep-eyebrow\">SATELLITES — ÉMISSION\u003C\u002Ftext>\n  \u003Cg>\n    \u003Crect class=\"ep-node\" x=\"150\" y=\"316\" width=\"50\" height=\"26\" rx=\"5\"\u002F>\u003Ctext x=\"175\" y=\"333\" text-anchor=\"middle\" class=\"ep-label\">S1\u003C\u002Ftext>\n    \u003Crect class=\"ep-node\" x=\"210\" y=\"316\" width=\"50\" height=\"26\" rx=\"5\"\u002F>\u003Ctext x=\"235\" y=\"333\" text-anchor=\"middle\" class=\"ep-label\">S2\u003C\u002Ftext>\n    \u003Crect class=\"ep-node\" x=\"270\" y=\"316\" width=\"50\" height=\"26\" rx=\"5\"\u002F>\u003Ctext x=\"295\" y=\"333\" text-anchor=\"middle\" class=\"ep-label\">S3\u003C\u002Ftext>\n  \u003C\u002Fg>\n\u003C\u002Fsvg>\n",[599,3933,3704,3934,3937],{},[603,3935,3936],{},"types de données de position"," qu'une application peut récolter :",[626,3939,3940,3956],{},[629,3941,3942],{},[632,3943,3944,3947,3950,3953],{},[635,3945,3946],{},"Donnée",[635,3948,3949],{},"Précision",[635,3951,3952],{},"Exemple d'usage légitime",[635,3954,3955],{},"Exemple d'abus",[648,3957,3958,3972,3986,4000],{},[632,3959,3960,3963,3966,3969],{},[653,3961,3962],{},"Position ponctuelle",[653,3964,3965],{},"quelques mètres",[653,3967,3968],{},"météo locale, carte",[653,3970,3971],{},"partage involontaire d'adresse personnelle",[632,3973,3974,3977,3980,3983],{},[653,3975,3976],{},"Trajectoire continue",[653,3978,3979],{},"parcours complet",[653,3981,3982],{},"suivi sportif, livraison",[653,3984,3985],{},"profilage des trajets quotidiens",[632,3987,3988,3991,3994,3997],{},[653,3989,3990],{},"Historique de lieux",[653,3992,3993],{},"jours\u002Fsemaines",[653,3995,3996],{},"rappel de souvenirs photo",[653,3998,3999],{},"inférence du domicile, du travail, des fréquentations",[632,4001,4002,4005,4008,4011],{},[653,4003,4004],{},"Présence en un lieu",[653,4006,4007],{},"binaire",[653,4009,4010],{},"pointage horaire",[653,4012,4013],{},"surveillance d'un employé",[968,4015,4018,4023],{"correct":1078,"explanation":4016,"slug":4017},"C'est l'usage qui est fait de la position calculée par votre téléphone qui pose question — pas la réception des signaux satellites.","confidentialite-position-c1",[974,4019,4020],{"v-slot:question":976},[599,4021,4022],{},"Pourquoi le GPS en lui-même ne pose-t-il pas de problème de confidentialité ?",[974,4024,4025],{"v-slot:choices":976},[983,4026,4027,4030,4033],{},[986,4028,4029],{},"Parce qu il est chiffré",[986,4031,4032],{},"Parce que le récepteur écoute passivement les satellites, sans rien transmettre",[986,4034,4035],{},"Parce que les satellites refusent les nouveaux récepteurs",[594,4037,4039],{"id":4038},"les-trois-modes-dautorisation","Les trois modes d'autorisation",[599,4041,4042],{},"Sur Android comme sur iOS, l'utilisateur peut accorder l'accès à la position\nselon trois grands modes :",[3026,4044,4047],{"icon":4045,"title":4046},"i-lucide-circle-dot","Autoriser toujours",[599,4048,4049,4050,4053,4054,4057],{},"L'application peut accéder à votre position ",[603,4051,4052],{},"même quand elle n'est pas\nutilisée",", en arrière-plan. C'est le mode le plus permissif. À réserver aux\napplications qui en ont ",[603,4055,4056],{},"strictement besoin en continu"," (navigation\nguidée, suivi de course en cours d'exercice).",[3026,4059,4062],{"icon":4060,"title":4061},"i-lucide-circle-half","Autoriser pendant l'utilisation",[599,4063,4064,4065,4068],{},"L'application n'a accès à la position que lorsque vous l'avez ",[603,4066,4067],{},"ouverte au\npremier plan",". Mode raisonnable pour la plupart des cas (carte, météo,\nappel d'un service).",[3026,4070,4073],{"icon":4071,"title":4072},"i-lucide-circle","Refuser",[599,4074,4075],{},"L'application ne reçoit aucune position. La plupart des applications\nfonctionnent très bien sans (même certaines applications de météo, qui\npeuvent demander votre ville manuellement).",[599,4077,4078,4079,4082],{},"Depuis quelques années, un quatrième niveau est apparu : l'",[603,4080,4081],{},"accès une fois","\n— l'application reçoit la position pour cette session, puis l'autorisation\nexpire. Excellent compromis : utile sans engagement durable.",[811,4084,4085],{},[599,4086,4087,4088,4091,4092,4095],{},"Sur iOS, vous voyez parfois une ",[603,4089,4090],{},"flèche bleue"," dans la barre d'état : elle\nsignale qu'une application ",[603,4093,4094],{},"vient d'accéder à votre position",". Sur Android,\nune icône similaire apparaît dans le bandeau de notifications. Y prêter\nattention vous donne en temps réel l'état réel du partage.",[594,4097,4099],{"id":4098},"où-trouver-ces-réglages","Où trouver ces réglages ?",[599,4101,4102],{},"Les chemins exacts changent au fil des versions, mais l'arborescence reste\nproche d'un système à l'autre :",[1225,4104,4107],{"className":4105,"code":4106,"language":1230,"meta":976},[1228],"iOS :\n  Réglages\n    → Confidentialité et sécurité\n      → Service de localisation\n        → liste de toutes les applications\n\nAndroid :\n  Paramètres\n    → Localisation\n      → Autorisations des applis\n        → liste de toutes les applications\n",[1169,4108,4106],{"__ignoreMap":976},[599,4110,4111,4112,4115],{},"Pour chaque application, vous voyez le mode actuel et pouvez le modifier.\n",[603,4113,4114],{},"Prenez 5 minutes une fois par an"," pour passer en revue la liste : vous\nserez probablement surpris du nombre d'applis qui ont obtenu un accès\n« toujours » sans que vous ne vous en souveniez.",[968,4117,4120,4125],{"correct":1078,"explanation":4118,"slug":4119},"Une alerte météo peut s'appuyer sur la ville saisie manuellement ou sur la dernière position connue. L'accès en arrière-plan en continu est presque toujours surdimensionné.","confidentialite-position-c2",[974,4121,4122],{"v-slot:question":976},[599,4123,4124],{},"Une application météo qui affiche la pluie de votre ville a-t-elle besoin de l accès en arrière-plan ?",[974,4126,4127],{"v-slot:choices":976},[983,4128,4129,4132],{},[986,4130,4131],{},"Oui, sinon elle ne pourrait pas vous alerter",[986,4133,4134],{},"Non, elle peut très bien fonctionner avec l accès pendant utilisation, voire un accès ponctuel",[594,4136,4138],{"id":4137},"les-données-auxiliaires-oubliées","Les données « auxiliaires » oubliées",[599,4140,4141,4142,1693],{},"Même si vous refusez l'accès à la position, votre téléphone laisse d'autres\ntraces qui permettent à un service tiers de ",[603,4143,4144],{},"reconstituer une localisation\napproximative",[983,4146,4147,4154,4160,4166,4176],{},[986,4148,4149,4150,4153],{},"L'",[603,4151,4152],{},"adresse IP"," de votre connexion (en général à l'échelle de la ville).",[986,4155,2742,4156,4159],{},[603,4157,4158],{},"réseau Wi-Fi"," que vous rejoignez (sa position est connue de bases\ncomme Apple, Google, Mozilla).",[986,4161,3704,4162,4165],{},[603,4163,4164],{},"antennes mobiles"," auxquelles votre téléphone se connecte.",[986,4167,3704,4168,4171,4172,4175],{},[603,4169,4170],{},"métadonnées EXIF"," des photos (latitude\u002Flongitude embarquées dans le\nfichier, sauf si désactivées — vous étudierez cela dans le chapitre ",[603,4173,4174],{},"SG —\nphotographie numérique",").",[986,4177,3704,4178,4181],{},[603,4179,4180],{},"adresses postales"," que vous saisissez dans les formulaires.",[1040,4183,4184],{},[599,4185,4186,4187,4190,4191,4194,4195,4198],{},"Refuser le GPS ne suffit pas à devenir invisible : la ",[603,4188,4189],{},"convergence"," de\nplusieurs signaux faibles donne souvent une position aussi précise que le\nGPS lui-même. C'est tout l'enjeu de la ",[603,4192,4193],{},"privacy by design"," — concevoir des\nservices qui demandent ",[603,4196,4197],{},"le minimum"," de données.",[594,4200,4202],{"id":4201},"géolocalisation-et-droits","Géolocalisation et droits",[599,4204,4205,4206,4209],{},"En France et dans l'Union européenne, le ",[603,4207,4208],{},"RGPD"," (Règlement Général sur la\nProtection des Données, 2018) encadre strictement la collecte de données\npersonnelles, dont la position. Quelques principes à retenir :",[983,4211,4212,4222,4229,4235],{},[986,4213,4214,4215,4218,4219,1052],{},"Une application doit ",[603,4216,4217],{},"demander explicitement"," l'autorisation, avec une\n",[603,4220,4221],{},"finalité claire",[986,4223,4224,4225,4228],{},"Vous avez le droit de ",[603,4226,4227],{},"consulter, modifier et supprimer"," les données\nvous concernant.",[986,4230,4224,4231,4234],{},[603,4232,4233],{},"retirer votre consentement"," à tout moment.",[986,4236,4237,4238,4241],{},"Une donnée de position est une ",[603,4239,4240],{},"donnée à caractère personnel"," dès lors\nqu'elle peut être rattachée à une personne.",[708,4243,4244],{},[599,4245,4246],{},"La CNIL (Commission Nationale de l'Informatique et des Libertés) reçoit et\ninstruit les plaintes en France. En 2023, elle a sanctionné plusieurs\nacteurs majeurs pour des manquements à la confidentialité des données de\nlocalisation. Ce n'est pas un sujet abstrait : c'est un terrain juridique\nactif.",[594,4248,4250],{"id":4249},"bonnes-pratiques-en-quatre-points","Bonnes pratiques en quatre points",[3026,4252,4254],{"icon":3028,"title":4253},"Hygiène numérique de localisation",[2939,4255,4256,4262,4272,4278],{},[986,4257,4258,4261],{},[603,4259,4260],{},"Passer en revue la liste"," des applications ayant accès à votre\nposition une fois par an.",[986,4263,4264,4267,4268,4271],{},[603,4265,4266],{},"Préférer « pendant l'utilisation »"," ou ",[603,4269,4270],{},"« une seule fois »"," au\n« toujours ».",[986,4273,4274,4277],{},[603,4275,4276],{},"Désactiver les métadonnées EXIF"," dans les paramètres de la caméra si\nvous partagez beaucoup de photos publiquement.",[986,4279,4280,4283],{},[603,4281,4282],{},"Refuser le suivi publicitaire"," (option système, sur iOS depuis 2021,\nsur Android depuis 2024) — cela limite l'usage commercial de votre\nhistorique de déplacement.",[968,4285,4288,4293],{"correct":1078,"explanation":4286,"slug":4287},"Le mode 'pendant l'utilisation' ou 'une fois' donne un excellent compromis. Désactiver totalement le GPS gêne les usages légitimes ; changer d'IP est marginal face aux autres signaux.","confidentialite-position-c3",[974,4289,4290],{"v-slot:question":976},[599,4291,4292],{},"Quelle pratique réduit le mieux le risque d un partage involontaire de position ?",[974,4294,4295],{"v-slot:choices":976},[983,4296,4297,4300,4303],{},[986,4298,4299],{},"Désactiver totalement le GPS du téléphone",[986,4301,4302],{},"Refuser le mode ’toujours’ aux applications qui n en ont pas besoin",[986,4304,4305],{},"Changer d adresse IP en permanence",[594,4307,1102],{"id":1101},[599,4309,4310],{},"Quelques affaires marquantes à connaître :",[983,4312,4313,4319,4325],{},[986,4314,4315,4318],{},[603,4316,4317],{},"Strava heatmap"," (2018) : la carte mondiale des trajets de coureurs a\nrévélé l'emplacement de bases militaires secrètes.",[986,4320,4321,4324],{},[603,4322,4323],{},"Données Cuebiq, X-Mode et autres courtiers"," : revente à grande échelle\nde données de position aux annonceurs et, parfois, aux services\ngouvernementaux.",[986,4326,4327,4330],{},[603,4328,4329],{},"TikTok, Meta, Google"," : multiples sanctions CNIL et RGPD pour collecte\nexcessive ou consentement insuffisamment éclairé.",[599,4332,4333],{},"Ces affaires ne sont pas anecdotiques : elles cadrent désormais la manière\ndont les régulateurs européens encadrent les services numériques.",{"title":976,"searchDepth":1114,"depth":1114,"links":4335},[4336,4337,4338,4339,4340,4341,4342,4343],{"id":596,"depth":1114,"text":597},{"id":3914,"depth":1114,"text":3915},{"id":4038,"depth":1114,"text":4039},{"id":4098,"depth":1114,"text":4099},{"id":4137,"depth":1114,"text":4138},{"id":4201,"depth":1114,"text":4202},{"id":4249,"depth":1114,"text":4250},{"id":1101,"depth":1114,"text":1102},"Ce que votre téléphone partage de votre position, comment le constater, et comment reprendre la main sur ces réglages.",{},[4347,4349,4351],{"slug":4017,"kind":1129,"question":4022,"choices":4348,"correct":1078,"multi":1131,"explanation":4016},[4029,4032,4035],{"slug":4119,"kind":1129,"question":4124,"choices":4350,"correct":1078,"multi":1131,"explanation":4118},[4131,4134],{"slug":4287,"kind":1129,"question":4292,"choices":4352,"correct":1078,"multi":1131,"explanation":4286},[4299,4302,4305],{"title":141,"description":4344},"J5CXWCULSGSoq3WoFbGXFASuDU3ZDfJxwFP_YgbiGpk",{"id":4356,"title":119,"bo":1123,"body":4357,"description":4453,"eval":1123,"extension":1124,"labo":1123,"meta":4454,"navigation":1126,"path":120,"quizzes":4456,"readingTime":1134,"seo":4457,"stem":121,"tp":1123,"__hash__":4458},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index.md",{"type":591,"value":4358,"toc":4448},[4359,4363,4366,4389,4393,4414,4418],[594,4360,4362],{"id":4361},"au-programme","Au programme",[599,4364,4365],{},"En une vingtaine d'années, la localisation est devenue un service banal du\nquotidien : un appui sur une icône suffit à connaître sa position au mètre près\net à recevoir un itinéraire instantané. Derrière ce geste anodin se cache une\nconstellation de satellites, des protocoles vieux de 40 ans, des cartes\ncollaboratives à l'échelle de la planète, et une trace numérique parfois plus\nbavarde qu'on ne le souhaiterait.",[599,4367,4368,4369,4372,4373,4376,4377,4380,4381,4384,4385,4388],{},"Ce chapitre vous propose de soulever le capot. Vous découvrirez d'abord\n",[603,4370,4371],{},"comment"," un récepteur GPS calcule sa position à partir de signaux venus de\nl'espace, puis ",[603,4374,4375],{},"sous quelle forme"," ces coordonnées arrivent dans un téléphone\nou un GPS de voiture. Vous étudierez ensuite les ",[603,4378,4379],{},"cartes numériques"," modernes,\nqu'elles soient institutionnelles (GeoPortail) ou citoyennes (OpenStreetMap),\net la mécanique des ",[603,4382,4383],{},"calculs d'itinéraires"," qui les transforment en\nassistants de voyage. Vous terminerez par un volet pratique et politique : la\n",[603,4386,4387],{},"confidentialité de votre position",", ce qu'un téléphone partage par défaut,\net comment reprendre la main.",[594,4390,4392],{"id":4391},"objectifs","Objectifs",[3026,4394,4397],{"icon":4395,"title":4396},"i-lucide-target","À la fin du chapitre, vous saurez",[983,4398,4399,4402,4405,4408,4411],{},[986,4400,4401],{},"Décrire le principe de la géolocalisation par satellites (GPS, Galileo) et la trilatération.",[986,4403,4404],{},"Décoder une trame NMEA pour extraire latitude et longitude.",[986,4406,4407],{},"Identifier les couches d'information d'une carte numérique (GeoPortail, OpenStreetMap) et contribuer.",[986,4409,4410],{},"Modéliser un itinéraire comme un problème sur un graphe pondéré.",[986,4412,4413],{},"Régler les paramètres de confidentialité d'un téléphone pour maîtriser le partage de position.",[594,4415,4417],{"id":4416},"plan","Plan",[2939,4419,4420,4426,4431,4437,4442],{},[986,4421,4422,4425],{},[603,4423,4424],{},"GPS et Galileo"," — comment les satellites permettent de se situer.",[986,4427,4428,4430],{},[603,4429,129],{}," — la forme numérique brute d'une position.",[986,4432,4433,4436],{},[603,4434,4435],{},"Cartes numériques"," — GeoPortail, OpenStreetMap, couches et contributions.",[986,4438,4439,4441],{},[603,4440,137],{}," — du plan au plus court chemin.",[986,4443,4444,4447],{},[603,4445,4446],{},"Confidentialité et données de position"," — réglages et enjeux.",{"title":976,"searchDepth":1114,"depth":1114,"links":4449},[4450,4451,4452],{"id":4361,"depth":1114,"text":4362},{"id":4391,"depth":1114,"text":4392},{"id":4416,"depth":1114,"text":4417},"Comment votre téléphone sait où vous êtes, comment une carte numérique vous y guide, et ce que vous laissez derrière vous en chemin.",{"icon":4455},"i-lucide-map-pin",[],{"title":119,"description":4453},"mQMbBOAPE8muOK36RnkC0CNNImjcrUjznr8UuiFp7G8",[4460,4631,5256,5441,5611,5794],{"id":4461,"title":4462,"bo":4463,"body":4464,"description":4624,"eval":1123,"extension":1124,"labo":1123,"meta":4625,"navigation":1131,"path":4626,"quizzes":4627,"readingTime":1134,"seo":4628,"stem":4629,"tp":1123,"__hash__":4630},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo.memo.md","GPS et Galileo — l'essentiel",[589],{"type":591,"value":4465,"toc":4617},[4466,4470,4479,4483,4547,4551,4597,4601,4612,4614],[594,4467,4469],{"id":4468},"en-une-phrase","En une phrase",[599,4471,4472,4473,4476,4477,1052],{},"Un récepteur GPS calcule sa position en ",[603,4474,4475],{},"mesurant le temps de trajet"," des signaux radio émis par plusieurs satellites — c'est la ",[603,4478,965],{},[594,4480,4482],{"id":4481},"à-mémoriser","À mémoriser",[983,4484,4485,4505,4514,4517,4525,4536],{},[986,4486,4487,716,4489,4492,4493,4495,4496,4498,4499,4501,4502,4504],{},[603,4488,715],{},[718,4490,4491],{},"Global Navigation Satellite System",") est le terme générique. Constellations principales : ",[603,4494,655],{}," (USA), ",[603,4497,669],{}," (UE), ",[603,4500,683],{}," (Russie), ",[603,4503,697],{}," (Chine).",[986,4506,4507,4508,4510,4511,1052],{},"Chaque satellite diffuse en continu : ",[603,4509,735],{}," + ",[603,4512,4513],{},"l'heure d'émission",[986,4515,4516],{},"Distance satellite-récepteur = vitesse de la lumière × durée du trajet.",[986,4518,4519,4521,4522,4524],{},[603,4520,991],{}," suffisent en théorie pour une position 2D ; ",[603,4523,994],{}," sont nécessaires en pratique (le 4ᵉ corrige l'horloge du récepteur).",[986,4526,4527,4528,4531,4532,4535],{},"Précision usuelle : ",[603,4529,4530],{},"5 à 10 m"," (GPS seul), ",[603,4533,4534],{},"1 à 2 m"," (GPS + Galileo).",[986,4537,4538,4539,4542,4543,4546],{},"Le récepteur ",[603,4540,4541],{},"n'émet rien"," : il est ",[603,4544,4545],{},"passif",". Les satellites ignorent qui les écoute.",[594,4548,4550],{"id":4549},"à-savoir-reconnaître","À savoir reconnaître",[626,4552,4553,4563],{},[629,4554,4555],{},[632,4556,4557,4560],{},[635,4558,4559],{},"Situation",[635,4561,4562],{},"Action \u002F Explication",[648,4564,4565,4573,4581],{},[632,4566,4567,4570],{},[653,4568,4569],{},"Le GPS ne fonctionne pas en intérieur",[653,4571,4572],{},"Signal trop atténué ; le téléphone utilise alors Wi-Fi + 4G\u002F5G (géolocalisation hybride).",[632,4574,4575,4578],{},[653,4576,4577],{},"Position imprécise en ville",[653,4579,4580],{},"Multitrajets dus aux immeubles : le signal rebondit avant d'atteindre le récepteur.",[632,4582,4583,4586],{},[653,4584,4585],{},"« Les satellites me suivent »",[653,4587,4588,4589,4592,4593,4596],{},"Faux. Le récepteur ",[603,4590,4591],{},"écoute"," sans rien envoyer. Le suivi vient des ",[603,4594,4595],{},"applications"," qui transmettent ensuite la position.",[594,4598,4600],{"id":4599},"pièges-courants","Pièges courants",[983,4602,4603,4606,4609],{},[986,4604,4605],{},"Confondre GPS (système américain) et GNSS (terme générique).",[986,4607,4608],{},"Croire que le récepteur dialogue avec les satellites — il ne fait qu'écouter.",[986,4610,4611],{},"Penser qu'on a besoin d'Internet pour se localiser : le calcul de position se fait hors-ligne, la connexion sert juste à charger la carte.",[594,4613,1102],{"id":1101},[599,4615,4616],{},"Galileo propose un service haute précision (HAS) à quelques centimètres pour l'agriculture, la conduite autonome, la topographie.",{"title":976,"searchDepth":1114,"depth":1114,"links":4618},[4619,4620,4621,4622,4623],{"id":4468,"depth":1114,"text":4469},{"id":4481,"depth":1114,"text":4482},{"id":4549,"depth":1114,"text":4550},{"id":4599,"depth":1114,"text":4600},{"id":1101,"depth":1114,"text":1102},"Mémo de révision sur la géolocalisation par satellites.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo.memo",[],{"title":4462,"description":4624},"0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo.memo","hcP2wIaxe82AHQUQ892WFq7OH22ipzxUQOBbo5D-vdo",{"id":4632,"title":4633,"bo":4634,"body":4635,"description":5249,"eval":1123,"extension":1124,"labo":1123,"meta":5250,"navigation":1131,"path":5251,"quizzes":5252,"readingTime":1134,"seo":5253,"stem":5254,"tp":1123,"__hash__":5255},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.memo.md","Décoder une trame NMEA — l'essentiel",[1140],{"type":591,"value":4636,"toc":5242},[4637,4639,4648,4650,4698,4977,4979,5028,5030,5067,5071,5172,5240],[594,4638,4469],{"id":4468},[599,4640,4641,4642,4644,4645,4647],{},"Une trame ",[603,4643,1154],{}," est une ligne de texte ASCII qui transporte une\nposition GPS sous forme de ",[603,4646,1201],{},", lisible à\nl'œil nu.",[594,4649,4482],{"id":4481},[983,4651,4652,4658,4667,4675,4695],{},[986,4653,4654,4655],{},"Format : ",[1169,4656,4657],{},"$GPxxx,champ1,champ2,...,*checksum",[986,4659,4660,4661,4663,4664,4666],{},"Commence toujours par ",[1169,4662,1194],{},", finit par ",[1169,4665,2481],{}," + 2 caractères de vérification.",[986,4668,4669,4670,4674],{},"La trame la plus courante : ",[603,4671,4672],{},[1169,4673,1219],{}," (position + altitude).",[986,4676,4677,4678,4680,4681],{},"Coordonnées au format ",[603,4679,1363],{},", pas en décimal :\n",[983,4682,4683,4689],{},[986,4684,4685,4686,4688],{},"latitude ",[1169,4687,1366],{}," (2 chiffres de degrés)",[986,4690,4691,4692,4694],{},"longitude ",[1169,4693,1370],{}," (3 chiffres de degrés)",[986,4696,4697],{},"Conversion en degrés décimaux :",[745,4699,4701],{"className":4700},[1375],[745,4702,4704,4759],{"className":4703},[748],[745,4705,4707],{"className":4706},[752],[754,4708,4709],{"xmlns":756,"display":1384},[758,4710,4711,4756],{},[761,4712,4713,4733,4735,4748,4750],{},[761,4714,4715,4717,4723,4725,4731],{},[768,4716,1393],{},[1395,4718,4719,4721],{"accent":783},[768,4720,1399],{},[835,4722,1402],{},[768,4724,1405],{},[1395,4726,4727,4729],{"accent":783},[768,4728,1399],{},[835,4730,1402],{},[768,4732,1414],{},[835,4734,843],{},[761,4736,4737,4739,4745],{},[768,4738,1393],{},[1395,4740,4741,4743],{"accent":783},[768,4742,1399],{},[835,4744,1402],{},[768,4746,4747],{},"s",[835,4749,1432],{},[1434,4751,4752,4754],{},[768,4753,1438],{},[764,4755,1441],{},[775,4757,4758],{"encoding":777},"\\text{degrés décimaux} = \\text{degrés} + \\frac{\\text{minutes}}{60}",[745,4760,4762,4851,4906],{"className":4761,"ariaHidden":783},[782],[745,4763,4765,4768,4842,4845,4848],{"className":4764},[787],[745,4766],{"className":4767,"style":1454},[791],[745,4769,4771,4774,4805,4808,4839],{"className":4770},[796,1230],[745,4772,1393],{"className":4773},[796],[745,4775,4777],{"className":4776},[796,1464],[745,4778,4780],{"className":4779},[1468],[745,4781,4783],{"className":4782},[1472],[745,4784,4786,4794],{"className":4785,"style":1477},[1476],[745,4787,4788,4791],{"style":1480},[745,4789],{"className":4790,"style":1485},[1484],[745,4792,1399],{"className":4793},[796],[745,4795,4796,4799],{"style":1480},[745,4797],{"className":4798,"style":1485},[1484],[745,4800,4802],{"className":4801,"style":1498},[1497],[745,4803,1402],{"className":4804},[796],[745,4806,1405],{"className":4807},[796],[745,4809,4811],{"className":4810},[796,1464],[745,4812,4814],{"className":4813},[1468],[745,4815,4817],{"className":4816},[1472],[745,4818,4820,4828],{"className":4819,"style":1477},[1476],[745,4821,4822,4825],{"style":1480},[745,4823],{"className":4824,"style":1485},[1484],[745,4826,1399],{"className":4827},[796],[745,4829,4830,4833],{"style":1480},[745,4831],{"className":4832,"style":1485},[1484],[745,4834,4836],{"className":4835,"style":1498},[1497],[745,4837,1402],{"className":4838},[796],[745,4840,1414],{"className":4841},[796],[745,4843],{"className":4844,"style":910},[800],[745,4846,843],{"className":4847},[914],[745,4849],{"className":4850,"style":910},[800],[745,4852,4854,4857,4897,4900,4903],{"className":4853},[787],[745,4855],{"className":4856,"style":1454},[791],[745,4858,4860,4863,4894],{"className":4859},[796,1230],[745,4861,1393],{"className":4862},[796],[745,4864,4866],{"className":4865},[796,1464],[745,4867,4869],{"className":4868},[1468],[745,4870,4872],{"className":4871},[1472],[745,4873,4875,4883],{"className":4874,"style":1477},[1476],[745,4876,4877,4880],{"style":1480},[745,4878],{"className":4879,"style":1485},[1484],[745,4881,1399],{"className":4882},[796],[745,4884,4885,4888],{"style":1480},[745,4886],{"className":4887,"style":1485},[1484],[745,4889,4891],{"className":4890,"style":1498},[1497],[745,4892,1402],{"className":4893},[796],[745,4895,4747],{"className":4896},[796],[745,4898],{"className":4899,"style":876},[800],[745,4901,1432],{"className":4902},[880],[745,4904],{"className":4905,"style":876},[800],[745,4907,4909,4912],{"className":4908},[787],[745,4910],{"className":4911,"style":1609},[791],[745,4913,4915,4918,4974],{"className":4914},[796],[745,4916],{"className":4917},[1616,1617],[745,4919,4921],{"className":4920},[1434],[745,4922,4924,4966],{"className":4923},[1468,1624],[745,4925,4927,4963],{"className":4926},[1472],[745,4928,4930,4941,4949],{"className":4929,"style":1631},[1476],[745,4931,4932,4935],{"style":1634},[745,4933],{"className":4934,"style":1485},[1484],[745,4936,4938],{"className":4937},[796],[745,4939,1441],{"className":4940},[796],[745,4942,4943,4946],{"style":1646},[745,4944],{"className":4945,"style":1485},[1484],[745,4947],{"className":4948,"style":1654},[1653],[745,4950,4951,4954],{"style":1657},[745,4952],{"className":4953,"style":1485},[1484],[745,4955,4957],{"className":4956},[796],[745,4958,4960],{"className":4959},[796,1230],[745,4961,1438],{"className":4962},[796],[745,4964,1674],{"className":4965},[1673],[745,4967,4969],{"className":4968},[1472],[745,4970,4972],{"className":4971,"style":1681},[1476],[745,4973],{},[745,4975],{"className":4976},[1687,1617],[594,4978,4550],{"id":4549},[626,4980,4981,4991],{},[629,4982,4983],{},[632,4984,4985,4988],{},[635,4986,4987],{},"Trame",[635,4989,4990],{},"Information principale",[648,4992,4993,5002,5010,5019],{},[632,4994,4995,4999],{},[653,4996,4997],{},[1169,4998,1219],{},[653,5000,5001],{},"Position + altitude + heure",[632,5003,5004,5008],{},[653,5005,5006],{},[1169,5007,2526],{},[653,5009,2529],{},[632,5011,5012,5016],{},[653,5013,5014],{},[1169,5015,2546],{},[653,5017,5018],{},"Satellites visibles",[632,5020,5021,5025],{},[653,5022,5023],{},[1169,5024,2556],{},[653,5026,5027],{},"Vitesse et direction",[594,5029,4600],{"id":4599},[983,5031,5032,5045,5060],{},[986,5033,5034,5035],{},"Confondre minutes (NMEA) et fraction de degré (décimal).\n",[983,5036,5037],{},[986,5038,5039,5041,5042,1052],{},[1169,5040,1279],{}," n'est pas 48,07° mais 48 + 7,038\u002F60 ≈ ",[603,5043,5044],{},"48,1173°",[986,5046,5047,5048,2282,5050,5053,5054,2282,5056,5059],{},"Oublier l'hémisphère (",[1169,5049,1292],{},[1169,5051,5052],{},"S"," pour latitude, ",[1169,5055,1318],{},[1169,5057,5058],{},"W"," pour longitude).",[986,5061,5062,5063,5066],{},"Penser que le ",[1169,5064,5065],{},".0"," après les chiffres de degrés est décimal — c'est en fait\nle séparateur entre degrés et minutes.",[594,5068,5070],{"id":5069},"décoder-à-la-main-pseudo-code","Décoder à la main (pseudo-code)",[1225,5072,5074],{"className":2111,"code":5073,"language":2113,"meta":976,"style":976},"trame = \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n\nchamps = decouper_autour_des_virgules(trame)\n\nheure       = champs[1]   # \"123519\"\nlatitude    = champs[2]   # \"4807.038\" → 48° + 7,038′\nhemisphere  = champs[3]   # \"N\"\nlongitude   = champs[4]   # \"01131.000\" → 011° + 31,000′\nmeridien    = champs[5]   # \"E\"\n",[1169,5075,5076,5084,5088,5096,5100,5114,5129,5143,5158],{"__ignoreMap":976},[745,5077,5078,5080,5082],{"class":2118,"line":1134},[745,5079,2122],{"class":2121},[745,5081,843],{"class":2125},[745,5083,2129],{"class":2128},[745,5085,5086],{"class":2118,"line":1114},[745,5087,2134],{"emptyLinePlaceholder":1126},[745,5089,5090,5092,5094],{"class":2118,"line":2137},[745,5091,2140],{"class":2121},[745,5093,843],{"class":2125},[745,5095,2145],{"class":2121},[745,5097,5098],{"class":2118,"line":2148},[745,5099,2134],{"emptyLinePlaceholder":1126},[745,5101,5102,5104,5106,5108,5110,5112],{"class":2118,"line":2153},[745,5103,2156],{"class":2121},[745,5105,843],{"class":2125},[745,5107,2161],{"class":2121},[745,5109,1078],{"class":2164},[745,5111,2167],{"class":2121},[745,5113,2171],{"class":2170},[745,5115,5116,5118,5120,5122,5124,5126],{"class":2118,"line":2174},[745,5117,2177],{"class":2121},[745,5119,843],{"class":2125},[745,5121,2161],{"class":2121},[745,5123,970],{"class":2164},[745,5125,2167],{"class":2121},[745,5127,5128],{"class":2170},"# \"4807.038\" → 48° + 7,038′\n",[745,5130,5131,5133,5135,5137,5139,5141],{"class":2118,"line":2191},[745,5132,2194],{"class":2121},[745,5134,843],{"class":2125},[745,5136,2161],{"class":2121},[745,5138,2201],{"class":2164},[745,5140,2167],{"class":2121},[745,5142,2206],{"class":2170},[745,5144,5145,5147,5149,5151,5153,5155],{"class":2118,"line":2209},[745,5146,2212],{"class":2121},[745,5148,843],{"class":2125},[745,5150,2161],{"class":2121},[745,5152,2219],{"class":2164},[745,5154,2167],{"class":2121},[745,5156,5157],{"class":2170},"# \"01131.000\" → 011° + 31,000′\n",[745,5159,5160,5162,5164,5166,5168,5170],{"class":2118,"line":2227},[745,5161,2230],{"class":2121},[745,5163,843],{"class":2125},[745,5165,2161],{"class":2121},[745,5167,2237],{"class":2164},[745,5169,2167],{"class":2121},[745,5171,2242],{"class":2170},[599,5173,5174,5175,5178,5179,5182,5183,1052],{},"Pour la conversion en degrés décimaux : on prend les ",[603,5176,5177],{},"deux premiers\ncaractères"," pour les degrés, ",[603,5180,5181],{},"le reste"," pour les minutes, et on applique\n",[745,5184,5186,5207],{"className":5185},[748],[745,5187,5189],{"className":5188},[752],[754,5190,5191],{"xmlns":756},[758,5192,5193,5205],{},[761,5194,5195,5197,5199,5201,5203],{},[1743,5196,2274],{},[835,5198,1432],{},[1743,5200,2279],{},[1743,5202,2282],{"mathvariant":1745},[764,5204,1441],{},[775,5206,2287],{"encoding":777},[745,5208,5210,5228],{"className":5209,"ariaHidden":783},[782],[745,5211,5213,5216,5219,5222,5225],{"className":5212},[787],[745,5214],{"className":5215,"style":2297},[791],[745,5217,2274],{"className":5218,"style":2302},[796,2301],[745,5220],{"className":5221,"style":876},[800],[745,5223,1432],{"className":5224},[880],[745,5226],{"className":5227,"style":876},[800],[745,5229,5231,5234,5237],{"className":5230},[787],[745,5232],{"className":5233,"style":2318},[791],[745,5235,2279],{"className":5236,"style":2322},[796,2301],[745,5238,2326],{"className":5239},[796],[2581,5241,2583],{},{"title":976,"searchDepth":1114,"depth":1114,"links":5243},[5244,5245,5246,5247,5248],{"id":4468,"depth":1114,"text":4469},{"id":4481,"depth":1114,"text":4482},{"id":4549,"depth":1114,"text":4550},{"id":4599,"depth":1114,"text":4600},{"id":5069,"depth":1114,"text":5070},"Mémo de révision sur le protocole NMEA 0183.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea.memo",[],{"title":4633,"description":5249},"0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.memo","yFyJki2MFsV3M7JL7o2hW62vC4GkuLQpYQwZ5FN0wmc",{"id":5257,"title":5258,"bo":5259,"body":5260,"description":5434,"eval":1123,"extension":1124,"labo":1123,"meta":5435,"navigation":1131,"path":5436,"quizzes":5437,"readingTime":1134,"seo":5438,"stem":5439,"tp":1123,"__hash__":5440},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques.memo.md","Cartes numériques — l'essentiel",[2606],{"type":591,"value":5261,"toc":5427},[5262,5264,5277,5279,5315,5317,5377,5379,5393,5397],[594,5263,4469],{"id":4468},[599,5265,5266,5267,5270,5271,5273,5274,5276],{},"Une carte numérique est une ",[603,5268,5269],{},"pile de couches activables"," ; ",[603,5272,2628],{},"\nest la carte officielle française, ",[603,5275,2632],{}," est la carte mondiale\ncontributive sous licence libre.",[594,5278,4482],{"id":4481},[983,5280,5281,5293,5298,5303,5312],{},[986,5282,5283,5284,3380,5287,3380,5290,1052],{},"Trois familles de couches : ",[603,5285,5286],{},"fond cartographique",[603,5288,5289],{},"données vectorielles",[603,5291,5292],{},"étiquettes",[986,5294,5295,5297],{},[603,5296,2628],{}," (IGN) : données officielles françaises, cadastre, photos\naériennes historiques.",[986,5299,5300,5302],{},[603,5301,2632],{}," (OSM) : contributif, mondial, libre (licence ODbL).",[986,5304,5305,5306,5308,5309,5311],{},"Un objet OSM = ",[603,5307,2975],{}," (point\u002Fligne\u002Fpolygone) + ",[603,5310,2979],{}," clé=valeur.",[986,5313,5314],{},"Tout internaute inscrit peut éditer OSM ; les modifications sont publiques\net permanentes.",[594,5316,4550],{"id":4549},[626,5318,5319,5329],{},[629,5320,5321],{},[632,5322,5323,5326],{},[635,5324,5325],{},"Besoin",[635,5327,5328],{},"Outil pertinent",[648,5330,5331,5340,5349,5358,5367],{},[632,5332,5333,5336],{},[653,5334,5335],{},"Cadastre, urbanisme, risques",[653,5337,5338],{},[603,5339,2628],{},[632,5341,5342,5345],{},[653,5343,5344],{},"Photos aériennes anciennes",[653,5346,5347],{},[603,5348,2628],{},[632,5350,5351,5354],{},[653,5352,5353],{},"Détails locaux fins (POI, sentiers)",[653,5355,5356],{},[603,5357,2826],{},[632,5359,5360,5363],{},[653,5361,5362],{},"Couverture hors France",[653,5364,5365],{},[603,5366,2826],{},[632,5368,5369,5372],{},[653,5370,5371],{},"Réutilisation libre dans une app",[653,5373,5374,5376],{},[603,5375,2826],{}," (licence ODbL)",[594,5378,4600],{"id":4599},[983,5380,5381,5384,5390],{},[986,5382,5383],{},"Confondre fond satellite (image brute) et carte vectorielle (tracés).",[986,5385,5386,5387,1052],{},"Croire qu'OSM est validé par un comité — c'est un contrôle ",[603,5388,5389],{},"communautaire\na posteriori",[986,5391,5392],{},"Considérer OSM comme « non sérieux » : c'est la base cartographique\nd'innombrables services pros.",[594,5394,5396],{"id":5395},"vocabulaire-à-savoir","Vocabulaire à savoir",[983,5398,5399,5405,5411,5417],{},[986,5400,5401,5404],{},[603,5402,5403],{},"Couche"," : ensemble d'informations cohérent, superposable.",[986,5406,5407,5410],{},[603,5408,5409],{},"Tag"," : paire clé=valeur qui qualifie un objet OSM.",[986,5412,5413,5416],{},[603,5414,5415],{},"Licence libre"," : autorise réutilisation, modification, redistribution.",[986,5418,5419,5422,5423,5426],{},[603,5420,5421],{},"ODbL"," : ",[718,5424,5425],{},"Open Database License",", la licence d'OpenStreetMap.",{"title":976,"searchDepth":1114,"depth":1114,"links":5428},[5429,5430,5431,5432,5433],{"id":4468,"depth":1114,"text":4469},{"id":4481,"depth":1114,"text":4482},{"id":4549,"depth":1114,"text":4550},{"id":4599,"depth":1114,"text":4600},{"id":5395,"depth":1114,"text":5396},"Mémo de révision sur GeoPortail et OpenStreetMap.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fcartes-numeriques.memo",[],{"title":5258,"description":5434},"0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques.memo","nzydcvznP3-e788xvnTAwTcgWUfAeYpzxnlI_lFuLAQ",{"id":5442,"title":5443,"bo":5444,"body":5445,"description":5604,"eval":1123,"extension":1124,"labo":1123,"meta":5605,"navigation":1131,"path":5606,"quizzes":5607,"readingTime":1134,"seo":5608,"stem":5609,"tp":1123,"__hash__":5610},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.memo.md","Itinéraires et graphes — l'essentiel",[3124],{"type":591,"value":5446,"toc":5597},[5447,5449,5456,5458,5499,5501,5546,5548,5567,5571],[594,5448,4469],{"id":4468},[599,5450,5451,5452,5455],{},"Un calcul d'itinéraire = la recherche du ",[603,5453,5454],{},"plus court chemin dans un graphe\npondéré"," dont les sommets sont les intersections et les arêtes les rues.",[594,5457,4482],{"id":4481},[983,5459,5460,5466,5471,5477,5483,5493],{},[986,5461,5462,5465],{},[603,5463,5464],{},"Sommet"," : un point du réseau (intersection, station, profil…).",[986,5467,5468,5470],{},[603,5469,3257],{}," : un lien entre deux sommets (rue, ligne, amitié…).",[986,5472,5473,5476],{},[603,5474,5475],{},"Poids"," d'une arête : son coût (durée, distance, dénivelé…).",[986,5478,5479,5482],{},[603,5480,5481],{},"Graphe pondéré"," : graphe dont les arêtes portent un poids.",[986,5484,5485,5488,5489,5492],{},[603,5486,5487],{},"Plus court chemin"," : la suite d'arêtes dont la ",[603,5490,5491],{},"somme des poids est\nminimale"," entre deux sommets.",[986,5494,5495,5496,5498],{},"Algorithme historique : ",[603,5497,3681],{}," (1959).",[594,5500,4550],{"id":4549},[626,5502,5503,5513],{},[629,5504,5505],{},[632,5506,5507,5510],{},[635,5508,5509],{},"Vous voyez",[635,5511,5512],{},"C'est un graphe avec…",[648,5514,5515,5523,5531,5539],{},[632,5516,5517,5520],{},[653,5518,5519],{},"Un plan de ville",[653,5521,5522],{},"sommets = intersections, arêtes = rues",[632,5524,5525,5528],{},[653,5526,5527],{},"Un plan de métro",[653,5529,5530],{},"sommets = stations, arêtes = tronçons",[632,5532,5533,5536],{},[653,5534,5535],{},"Un réseau social",[653,5537,5538],{},"sommets = profils, arêtes = amitiés",[632,5540,5541,5543],{},[653,5542,37],{},[653,5544,5545],{},"sommets = pages, arêtes = hyperliens",[594,5547,4600],{"id":4599},[983,5549,5550,5557,5560],{},[986,5551,5552,5553,5556],{},"« Le plus court » = le plus court ",[603,5554,5555],{},"selon le poids choisi",", pas toujours\nà vol d'oiseau.",[986,5558,5559],{},"Un même graphe peut être pondéré différemment selon le besoin (durée,\ndistance, dénivelé…).",[986,5561,5562,5563,5566],{},"Un calculateur d'itinéraire ",[603,5564,5565],{},"dépend des données de la carte"," : carte\npérimée ⇒ trajet inadapté.",[594,5568,5570],{"id":5569},"à-enrichir-le-graphe-routier","À enrichir le graphe routier",[983,5572,5573,5579,5585,5591],{},[986,5574,5575,5578],{},[603,5576,5577],{},"Sens uniques"," → arêtes orientées.",[986,5580,5581,5584],{},[603,5582,5583],{},"Interdictions de tourner"," → règles aux intersections.",[986,5586,5587,5590],{},[603,5588,5589],{},"Mode de transport"," → certaines arêtes sont ignorées (piéton, voiture, vélo).",[986,5592,5593,5596],{},[603,5594,5595],{},"Trafic temps réel"," → poids variables selon l'heure.",{"title":976,"searchDepth":1114,"depth":1114,"links":5598},[5599,5600,5601,5602,5603],{"id":4468,"depth":1114,"text":4469},{"id":4481,"depth":1114,"text":4482},{"id":4549,"depth":1114,"text":4550},{"id":4599,"depth":1114,"text":4600},{"id":5569,"depth":1114,"text":5570},"Mémo de révision sur la modélisation d'un itinéraire comme problème sur un graphe.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes.memo",[],{"title":5443,"description":5604},"0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes.memo","Eo_16M11MIFFrEHb2ugUxKqPIcDWMeTqbyeGJTGtvtI",{"id":5612,"title":5613,"bo":5614,"body":5615,"description":5787,"eval":1123,"extension":1124,"labo":1123,"meta":5788,"navigation":1131,"path":5789,"quizzes":5790,"readingTime":1134,"seo":5791,"stem":5792,"tp":1123,"__hash__":5793},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position.memo.md","Confidentialité de la position — l'essentiel",[3894],{"type":591,"value":5616,"toc":5780},[5617,5619,5629,5631,5688,5690,5744,5746,5757,5761],[594,5618,4469],{"id":4468},[599,5620,5621,5622,5625,5626,5628],{},"Le GPS, en lui-même, ",[603,5623,5624],{},"ne transmet rien"," ; ce sont les ",[603,5627,4595],{},"\nauxquelles vous accordez l'accès à votre position qui créent les enjeux de\nconfidentialité.",[594,5630,4482],{"id":4481},[983,5632,5633,5650,5656,5662,5673],{},[986,5634,5635,5636,3380,5639,5642,5643,5646,5647,4175],{},"Trois modes d'autorisation : ",[603,5637,5638],{},"toujours",[603,5640,5641],{},"pendant l'utilisation",",\n",[603,5644,5645],{},"refuser"," (+ une variante moderne : ",[603,5648,5649],{},"une seule fois",[986,5651,5652,5653,1052],{},"Réglages sur iOS : ",[718,5654,5655],{},"Réglages > Confidentialité > Service de localisation",[986,5657,5658,5659,1052],{},"Réglages sur Android : ",[718,5660,5661],{},"Paramètres > Localisation > Autorisations des applis",[986,5663,5664,5665,5668,5669,5672],{},"Une ",[603,5666,5667],{},"donnée de position"," est une ",[603,5670,5671],{},"donnée personnelle"," (RGPD).",[986,5674,5675,5676,3380,5679,3380,5682,3380,5685,5687],{},"Même sans GPS, on peut être localisé via : ",[603,5677,5678],{},"IP",[603,5680,5681],{},"Wi-Fi",[603,5683,5684],{},"antennes\nmobiles",[603,5686,4170],{}," des photos.",[594,5689,4550],{"id":4549},[626,5691,5692,5702],{},[629,5693,5694],{},[632,5695,5696,5699],{},[635,5697,5698],{},"Cas",[635,5700,5701],{},"Réglage adapté",[648,5703,5704,5715,5725,5735],{},[632,5705,5706,5709],{},[653,5707,5708],{},"Navigation guidée en cours",[653,5710,5711,5714],{},[603,5712,5713],{},"Toujours"," (le temps du trajet)",[632,5716,5717,5720],{},[653,5718,5719],{},"Application de carte ouverte",[653,5721,5722],{},[603,5723,5724],{},"Pendant l'utilisation",[632,5726,5727,5730],{},[653,5728,5729],{},"Météo locale ponctuelle",[653,5731,5732],{},[603,5733,5734],{},"Une seule fois",[632,5736,5737,5740],{},[653,5738,5739],{},"Jeu, lampe-torche, calculatrice",[653,5741,5742],{},[603,5743,4072],{},[594,5745,4600],{"id":4599},[983,5747,5748,5751,5754],{},[986,5749,5750],{},"Croire que désactiver le GPS rend invisible — d'autres signaux (Wi-Fi, IP,\nEXIF) suffisent souvent à localiser.",[986,5752,5753],{},"Accepter par défaut « toujours » sans réfléchir au besoin réel.",[986,5755,5756],{},"Ignorer les métadonnées EXIF d'une photo postée publiquement (révèlent\nl'adresse précise de prise de vue).",[594,5758,5760],{"id":5759},"cadre-juridique-fr-ue","Cadre juridique (FR \u002F UE)",[983,5762,5763,5768,5774],{},[986,5764,5765,5767],{},[603,5766,4208],{}," (2018) : consentement explicite, finalité claire, droit\nd'accès\u002Frectification\u002Fsuppression.",[986,5769,5770,5773],{},[603,5771,5772],{},"CNIL"," : autorité française qui reçoit les plaintes et sanctionne.",[986,5775,2742,5776,5779],{},[603,5777,5778],{},"retrait du consentement"," est un droit, à tout moment.",{"title":976,"searchDepth":1114,"depth":1114,"links":5781},[5782,5783,5784,5785,5786],{"id":4468,"depth":1114,"text":4469},{"id":4481,"depth":1114,"text":4482},{"id":4549,"depth":1114,"text":4550},{"id":4599,"depth":1114,"text":4600},{"id":5759,"depth":1114,"text":5760},"Mémo de révision sur les enjeux de confidentialité liés à la géolocalisation.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position.memo",[],{"title":5613,"description":5787},"0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position.memo","MbDGN18BbF0apMRcut-OHNn2cE4QqLbr93k_KSvCHh4",{"id":5795,"title":5796,"bo":5797,"body":5798,"description":6251,"eval":1123,"extension":1124,"labo":1123,"meta":6252,"navigation":1131,"path":6254,"quizzes":6255,"readingTime":1134,"seo":6280,"stem":6281,"tp":1123,"__hash__":6282},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002Fchapitre.memo.md","Localisation, cartographie et mobilité — synthèse",[3124,2606,3894,589,1140],{"type":591,"value":5799,"toc":6246},[5800,5804,5807,5820,5894,5917,5933,5946,5950,6035,6039,6059,6083,6114,6129,6154,6163,6187,6210,6238],[594,5801,5803],{"id":5802},"vue-densemble","Vue d'ensemble",[599,5805,5806],{},"Ce chapitre vous a fait remonter le fil d'un geste devenu banal : ouvrir une\ncarte et lire « vous êtes ici ». Cinq cours, cinq étages d'une même\ninfrastructure.",[599,5808,5809,5810,5813,5814,5816,5817,5819],{},"D'abord la ",[603,5811,5812],{},"technique brute"," : un récepteur GPS ou Galileo écoute en\nsilence les signaux de plusieurs satellites, calcule la durée de leur\ntrajet, et en déduit sa position par ",[603,5815,965],{},". Quatre satellites\nsuffisent à fixer une position 3D précise. Le récepteur est ",[603,5818,4545],{}," :\nil n'émet rien, et les satellites ignorent qui les écoute.",[599,5821,5822,5823,5826,5827,5830,5831,5833,5834,5836,5837,1052],{},"Cette position est ensuite ",[603,5824,5825],{},"publiée"," par le module GNSS sous forme de\n",[603,5828,5829],{},"trames NMEA 0183"," — des chaînes ASCII très simples, faites de champs\nséparés par des virgules. La trame ",[1169,5832,1219],{}," contient en particulier l'heure\nUTC, la latitude, la longitude et l'altitude. Les coordonnées NMEA sont au\nformat ",[603,5835,1363],{}," et se convertissent en degrés décimaux par la\nformule ",[745,5838,5840,5861],{"className":5839},[748],[745,5841,5843],{"className":5842},[752],[754,5844,5845],{"xmlns":756},[758,5846,5847,5859],{},[761,5848,5849,5851,5853,5855,5857],{},[1743,5850,2274],{},[835,5852,1432],{},[1743,5854,2279],{},[1743,5856,2282],{"mathvariant":1745},[764,5858,1441],{},[775,5860,2287],{"encoding":777},[745,5862,5864,5882],{"className":5863,"ariaHidden":783},[782],[745,5865,5867,5870,5873,5876,5879],{"className":5866},[787],[745,5868],{"className":5869,"style":2297},[791],[745,5871,2274],{"className":5872,"style":2302},[796,2301],[745,5874],{"className":5875,"style":876},[800],[745,5877,1432],{"className":5878},[880],[745,5880],{"className":5881,"style":876},[800],[745,5883,5885,5888,5891],{"className":5884},[787],[745,5886],{"className":5887,"style":2318},[791],[745,5889,2279],{"className":5890,"style":2322},[796,2301],[745,5892,2326],{"className":5893},[796],[599,5895,5896,5897,5900,5901,5904,5905,5907,5908,5910,5911,2478,5914,5916],{},"À l'autre bout de la chaîne, le téléphone affiche cette position ",[603,5898,5899],{},"sur une\ncarte numérique"," — non plus une feuille imprimée, mais une ",[603,5902,5903],{},"pile de\ncouches"," activables à volonté. ",[603,5906,2628],{}," sert de référence officielle\nfrançaise (cadastre, plans d'urbanisme, photos aériennes historiques) ;\n",[603,5909,2632],{}," propose une carte mondiale ",[603,5912,5913],{},"contributive",[603,5915,2892],{},",\néditable par n'importe qui, et utilisée comme socle par d'innombrables\nservices.",[599,5918,5919,5920,5923,5924,5926,5927,5929,5930,5932],{},"Cette carte se transforme en ",[603,5921,5922],{},"assistant de mobilité"," par un autre détour\nabstrait : la modélisation du réseau routier comme un ",[603,5925,3315],{},"\n(sommets = intersections, arêtes = rues, poids = durée ou distance). Calculer\nun itinéraire, c'est chercher dans ce graphe le ",[603,5928,3323],{},".\nL'algorithme historique, ",[603,5931,3681],{}," (1959), est encore le moteur de la\nplupart des services aujourd'hui.",[599,5934,5935,5936,5939,5940,5942,5943,5945],{},"Enfin, ce confort de la mobilité numérique soulève une question politique :\n",[603,5937,5938],{},"que faites-vous de votre position, et qui vous la prend ?"," Le GPS ne\ntransmet rien, mais les ",[603,5941,4595],{}," qui y accèdent en font ce qu'elles\nveulent. Les trois modes d'autorisation (toujours \u002F pendant l'utilisation \u002F\nrefuser), couplés au cadre du ",[603,5944,4208],{},", vous donnent les manettes — encore\nfaut-il s'en saisir.",[594,5947,5949],{"id":5948},"carte-des-notions","Carte des notions",[626,5951,5952,5968],{},[629,5953,5954],{},[632,5955,5956,5959,5962,5965],{},[635,5957,5958],{},"Cours",[635,5960,5961],{},"Item BO",[635,5963,5964],{},"Notion-clé",[635,5966,5967],{},"Lien avec les autres cours",[648,5969,5970,5983,5996,6009,6022],{},[632,5971,5972,5975,5977,5980],{},[653,5973,5974],{},"1. GPS et Galileo",[653,5976,589],{},[653,5978,5979],{},"Trilatération, GNSS",[653,5981,5982],{},"Produit les coordonnées brutes que le cours 2 décode",[632,5984,5985,5988,5990,5993],{},[653,5986,5987],{},"2. Décoder une trame NMEA",[653,5989,1140],{},[653,5991,5992],{},"Format texte, degrés-minutes",[653,5994,5995],{},"Sortie du cours 1, entrée des cours 3 & 4",[632,5997,5998,6001,6003,6006],{},[653,5999,6000],{},"3. Cartes numériques",[653,6002,2606],{},[653,6004,6005],{},"Couches, GeoPortail, OSM",[653,6007,6008],{},"Affiche la position et alimente le calcul d'itinéraire",[632,6010,6011,6014,6016,6019],{},[653,6012,6013],{},"4. Itinéraires et graphes",[653,6015,3124],{},[653,6017,6018],{},"Graphe pondéré, plus court chemin",[653,6020,6021],{},"Utilise les données du cours 3",[632,6023,6024,6027,6029,6032],{},[653,6025,6026],{},"5. Confidentialité",[653,6028,3894],{},[653,6030,6031],{},"Modes d'autorisation, RGPD",[653,6033,6034],{},"Question politique adossée à tout ce qui précède",[594,6036,6038],{"id":6037},"auto-évaluation","Auto-évaluation",[968,6040,6042,6047],{"correct":970,"slug":6041},"se-localisation-cartographie-1-q1",[974,6043,6044],{"v-slot:question":976},[599,6045,6046],{},"Combien de satellites au minimum un récepteur doit-il capter pour calculer une position 3D précise (avec correction d'horloge) ?",[974,6048,6049],{"v-slot:choices":976},[983,6050,6051,6053,6055,6057],{},[986,6052,970],{},[986,6054,2201],{},[986,6056,2219],{},[986,6058,2237],{},[968,6060,6062,6067],{"correct":1078,"slug":6061},"se-localisation-cartographie-1-q2",[974,6063,6064],{"v-slot:question":976},[599,6065,6066],{},"Le GPS et le Galileo sont des exemples de…",[974,6068,6069],{"v-slot:choices":976},[983,6070,6071,6074,6077,6080],{},[986,6072,6073],{},"réseaux Wi-Fi mondiaux",[986,6075,6076],{},"systèmes GNSS (Global Navigation Satellite System)",[986,6078,6079],{},"protocoles de cartographie collaborative",[986,6081,6082],{},"antennes mobiles 5G",[968,6084,6086,6098],{"correct":1078,"slug":6085},"se-localisation-cartographie-1-q3",[974,6087,6088],{"v-slot:question":976},[599,6089,6090,6091,6094,6095,6097],{},"Dans une trame NMEA ",[1169,6092,6093],{},"$GPGGA,...,4807.038,N,...",", à quoi correspond ",[1169,6096,1279],{}," ?",[974,6099,6100],{"v-slot:choices":976},[983,6101,6102,6105,6108,6111],{},[986,6103,6104],{},"une latitude de 48,07° Nord",[986,6106,6107],{},"une latitude de 48° 07,038′ Nord (à convertir en degrés décimaux)",[986,6109,6110],{},"une longitude de 4807,038° Nord",[986,6112,6113],{},"l'altitude en mètres",[6115,6116,6121],"self-eval-free-text",{"answer":6117,"slug":6118,"tolerance":6119,"type":6120},"48.1173","se-localisation-cartographie-1-q4","0.001","number",[974,6122,6123],{"v-slot:question":976},[599,6124,6125,6126,6128],{},"Convertissez la latitude NMEA ",[1169,6127,1279],{}," en degrés décimaux (réponse au millième près, sans le symbole °).",[968,6130,6133,6138],{"correct":6131,"slug":6132},"0,1","se-localisation-cartographie-1-q5",[974,6134,6135],{"v-slot:question":976},[599,6136,6137],{},"Quelles affirmations sur OpenStreetMap sont exactes ? (plusieurs réponses possibles)",[974,6139,6140],{"v-slot:choices":976},[983,6141,6142,6145,6148,6151],{},[986,6143,6144],{},"N'importe quel internaute inscrit peut éditer les données",[986,6146,6147],{},"La licence ODbL est une licence libre",[986,6149,6150],{},"Les modifications sont validées par un comité d'experts avant publication",[986,6152,6153],{},"OpenStreetMap est limité à la France",[6115,6155,6158],{"answer":3134,"slug":6156,"case-sensitive":6157},"se-localisation-cartographie-1-q6","false",[974,6159,6160],{"v-slot:question":976},[599,6161,6162],{},"Comment appelle-t-on l'objet mathématique formé de sommets reliés par des arêtes, utilisé pour modéliser un réseau routier ?",[968,6164,6166,6171],{"correct":1078,"slug":6165},"se-localisation-cartographie-1-q7",[974,6167,6168],{"v-slot:question":976},[599,6169,6170],{},"Sur un graphe routier pondéré par la durée, « le plus court chemin » désigne…",[974,6172,6173],{"v-slot:choices":976},[983,6174,6175,6178,6181,6184],{},[986,6176,6177],{},"le chemin le plus court à vol d'oiseau",[986,6179,6180],{},"le chemin dont la somme des durées des tronçons est minimale",[986,6182,6183],{},"le chemin avec le moins d'intersections",[986,6185,6186],{},"le chemin sans aucun sens unique",[968,6188,6190,6194],{"correct":1078,"slug":6189},"se-localisation-cartographie-1-q8",[974,6191,6192],{"v-slot:question":976},[599,6193,1085],{},[974,6195,6196],{"v-slot:choices":976},[983,6197,6198,6201,6204,6207],{},[986,6199,6200],{},"Oui, ils enregistrent chaque récepteur actif",[986,6202,6203],{},"Non, le récepteur est purement passif : il écoute, il n'émet rien",[986,6205,6206],{},"Seulement si vous activez le « mode haute précision »",[986,6208,6209],{},"Seulement les satellites européens (Galileo) le font",[6211,6212,6214,6219],"self-eval-ordering",{"slug":6213},"se-localisation-cartographie-1-q9",[974,6215,6216],{"v-slot:question":976},[599,6217,6218],{},"Ordonnez les étapes du parcours d'une position GPS, du signal satellite jusqu'à l'affichage sur la carte de votre téléphone.",[974,6220,6221],{"v-slot:items":976},[983,6222,6223,6226,6229,6232,6235],{},[986,6224,6225],{},"Les satellites émettent en continu un signal contenant leur identifiant et l'heure d'émission",[986,6227,6228],{},"Le récepteur GNSS du téléphone capte plusieurs signaux et calcule sa position par trilatération",[986,6230,6231],{},"Le module publie la position sous forme de trame NMEA (ou format interne équivalent)",[986,6233,6234],{},"L'application de cartographie reçoit la position et la place sur la pile de couches affichée",[986,6236,6237],{},"L'utilisateur voit le point bleu se positionner à sa position réelle",[6115,6239,6241],{"answer":4208,"slug":6240,"case-sensitive":6157},"se-localisation-cartographie-1-q10",[974,6242,6243],{"v-slot:question":976},[599,6244,6245],{},"Quel est le sigle du règlement européen entré en vigueur en 2018 qui encadre la collecte et l'usage des données personnelles, dont les données de position ?",{"title":976,"searchDepth":1114,"depth":1114,"links":6247},[6248,6249,6250],{"id":5802,"depth":1114,"text":5803},{"id":5948,"depth":1114,"text":5949},{"id":6037,"depth":1114,"text":6038},"Vue d'ensemble du chapitre SE, points-clés à mémoriser, auto-évaluation finale.",{"self_eval_slug":6253},"snt-2nde-se-localisation-cartographie","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fchapitre.memo",[6256,6258,6260,6263,6267,6269,6272,6274,6276,6279],{"slug":6041,"kind":1129,"question":6046,"choices":6257,"correct":970,"multi":1131,"explanation":976},[970,2201,2219,2237],{"slug":6061,"kind":1129,"question":6066,"choices":6259,"correct":1078,"multi":1131,"explanation":976},[6073,6076,6079,6082],{"slug":6085,"kind":1129,"question":6261,"choices":6262,"correct":1078,"multi":1131,"explanation":976},"Dans une trame NMEA $GPGGA,...,4807.038,N,..., à quoi correspond 4807.038 ?",[6104,6107,6110,6113],{"slug":6118,"kind":6264,"question":6265,"answer":6117,"caseSensitive":1131,"tolerance":6266,"inputType":6120,"explanation":976},"free_text","Convertissez la latitude NMEA 4807.038 en degrés décimaux (réponse au millième près, sans le symbole °).",0.001,{"slug":6132,"kind":1129,"question":6137,"choices":6268,"correct":6131,"multi":1126,"explanation":976},[6144,6147,6150,6153],{"slug":6156,"kind":6264,"question":6162,"answer":3134,"caseSensitive":1131,"tolerance":6270,"inputType":6271,"explanation":976},0,"string",{"slug":6165,"kind":1129,"question":6170,"choices":6273,"correct":1078,"multi":1131,"explanation":976},[6177,6180,6183,6186],{"slug":6189,"kind":1129,"question":1085,"choices":6275,"correct":1078,"multi":1131,"explanation":976},[6200,6203,6206,6209],{"slug":6213,"kind":6277,"question":6218,"items":6278,"explanation":976},"ordering",[6225,6228,6231,6234,6237],{"slug":6240,"kind":6264,"question":6245,"answer":4208,"caseSensitive":1131,"tolerance":6270,"inputType":6271,"explanation":976},{"title":5796,"description":6251},"0.snt-2nde\u002Fse-localisation-cartographie\u002Fchapitre.memo","DCdrSYpzPuy4haqTZmeDRGSHx8XlGqUcmaIJTVCwz6k",1788035575358]