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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Edukiak" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Eduki taularen ikusgarritasuna aldatu" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Eduki taularen ikusgarritasuna aldatu</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Erpin geodesiko</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Joan beste hizkuntza batean idatzitako artikulu batera. 25 hizkuntzatan eskuragarri." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet 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data-language-local-name="aragoiera" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/V%C3%A8rtex_geod%C3%A8sic" title="Vèrtex geodèsic – katalana" lang="ca" hreflang="ca" data-title="Vèrtex geodèsic" data-language-autonym="Català" data-language-local-name="katalana" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Geodetick%C3%BD_bod" title="Geodetický bod – txekiera" lang="cs" hreflang="cs" data-title="Geodetický bod" data-language-autonym="Čeština" data-language-local-name="txekiera" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Postament_(landm%C3%A5ling)" title="Postament (landmåling) – daniera" lang="da" hreflang="da" data-title="Postament (landmåling)" data-language-autonym="Dansk" data-language-local-name="daniera" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Trigonometrischer_Punkt" title="Trigonometrischer Punkt – alemana" lang="de" hreflang="de" data-title="Trigonometrischer Punkt" data-language-autonym="Deutsch" data-language-local-name="alemana" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Triangulation_station" title="Triangulation station – ingelesa" lang="en" hreflang="en" data-title="Triangulation station" data-language-autonym="English" data-language-local-name="ingelesa" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Geodezia_vertico" title="Geodezia vertico – esperantoa" lang="eo" hreflang="eo" data-title="Geodezia vertico" data-language-autonym="Esperanto" data-language-local-name="esperantoa" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/V%C3%A9rtice_geod%C3%A9sico" title="Vértice geodésico – gaztelania" lang="es" hreflang="es" data-title="Vértice geodésico" data-language-autonym="Español" data-language-local-name="gaztelania" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kolmiomittaustorni" title="Kolmiomittaustorni – finlandiera" lang="fi" hreflang="fi" data-title="Kolmiomittaustorni" data-language-autonym="Suomi" data-language-local-name="finlandiera" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Poste_de_triangulation" title="Poste de triangulation – frantsesa" lang="fr" hreflang="fr" data-title="Poste de triangulation" data-language-autonym="Français" data-language-local-name="frantsesa" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/V%C3%A9rtice_xeod%C3%A9sico" title="Vértice xeodésico – galiziera" lang="gl" hreflang="gl" data-title="Vértice xeodésico" data-language-autonym="Galego" data-language-local-name="galiziera" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%B6ldm%C3%A9r%C3%A9si_alappont" title="Földmérési alappont – hungariera" lang="hu" hreflang="hu" data-title="Földmérési alappont" data-language-autonym="Magyar" data-language-local-name="hungariera" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Vertice_geodetico" title="Vertice geodetico – italiera" lang="it" hreflang="it" data-title="Vertice geodetico" data-language-autonym="Italiano" data-language-local-name="italiera" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E7%82%B9" title="三角点 – japoniera" lang="ja" hreflang="ja" data-title="三角点" data-language-autonym="日本語" data-language-local-name="japoniera" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90%E1%83%9C%E1%83%92%E1%83%A3%E1%83%9A%E1%83%90%E1%83%AA%E1%83%98%E1%83%98%E1%83%A1_%E1%83%9E%E1%83%A3%E1%83%9C%E1%83%A5%E1%83%A2%E1%83%98" title="ტრიანგულაციის პუნქტი – georgiera" lang="ka" hreflang="ka" data-title="ტრიანგულაციის პუნქტი" data-language-autonym="ქართული" data-language-local-name="georgiera" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Stesen_penyegitigaan" title="Stesen penyegitigaan – malaysiera" lang="ms" hreflang="ms" data-title="Stesen penyegitigaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Punkt_geodezyjny" title="Punkt geodezyjny – poloniera" lang="pl" hreflang="pl" data-title="Punkt geodezyjny" data-language-autonym="Polski" data-language-local-name="poloniera" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/V%C3%A9rtice_geod%C3%A9sico" title="Vértice geodésico – portugesa" lang="pt" hreflang="pt" data-title="Vértice geodésico" data-language-autonym="Português" data-language-local-name="portugesa" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Punct_geodezic" title="Punct geodezic – errumaniera" lang="ro" hreflang="ro" data-title="Punct geodezic" data-language-autonym="Română" data-language-local-name="errumaniera" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%BF%D1%83%D0%BD%D0%BA%D1%82" title="Тригонометрический пункт – errusiera" lang="ru" hreflang="ru" data-title="Тригонометрический пункт" data-language-autonym="Русский" data-language-local-name="errusiera" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Triangulation_station" title="Triangulation station – Simple English" lang="en-simple" hreflang="en-simple" data-title="Triangulation station" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Triangulacijska_to%C4%8Dka" title="Triangulacijska točka – esloveniera" lang="sl" hreflang="sl" data-title="Triangulacijska točka" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%BF%D1%83%D0%BD%D0%BA%D1%82" title="Тригонометричний пункт – ukrainera" lang="uk" hreflang="uk" data-title="Тригонометричний пункт" data-language-autonym="Українська" data-language-local-name="ukrainera" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%89%E8%A7%92%E9%BB%9E" title="三角點 – txinera" lang="zh" hreflang="zh" data-title="三角點" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q131862#sitelinks-wikipedia" title="Aldatu hizkuntzen arteko loturak" class="wbc-editpage">Aldatu loturak</a></span></div> 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Arnotegi_erpin_geodesikoa.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arnotegi_erpin_geodesikoa.jpg/220px-Arnotegi_erpin_geodesikoa.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arnotegi_erpin_geodesikoa.jpg/330px-Arnotegi_erpin_geodesikoa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Arnotegi_erpin_geodesikoa.jpg/440px-Arnotegi_erpin_geodesikoa.jpg 2x" data-file-width="1280" data-file-height="960" /></a><figcaption>Erpin geodesikoa, <a href="/wiki/Arnotegi" title="Arnotegi">Arnotegin</a></figcaption></figure> <p><b>Erpin geodesikoa</b> kokapen zehatz bat adierazten duen seinale bat da. Eta, beste erpin geodesiko batzuekin batera, hiruki sare bat osatzen du. </p><p><a href="/wiki/Geodesia" title="Geodesia">Geodesia</a> lurraren forma, dimentsioak eta grabitate-eremua aztertzeaz arduratzen den zientzia da. </p><p>Ikuspuntu praktikotik begiratuta, honako hau da Geodesiaren baliagarritasun handienetako bat: bere tekniken bidez oso lurralde zabalak irudika daitezkeela mapetan. Puntu-sare bat ezarriz egin daiteke hori. Lurraren azalera osoan sakabanatuta daude, eta zehaztasun handiz ezagutzen ditugu espazioan duten kokapena eta itsasoaren mailaren gainean duten altuera.<sup id="cite_ref-:0_1-0" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Puntu horiei <b>erpin geodesikoak</b> deitzen zaie eta puntu horiek osatzen duten eskeletoan oinarritzen dira lurralde bateko kartografia lortzeko behar diren gainerako lanak.<sup id="cite_ref-:0_1-1" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Erpin geodesiko horien posizioa horrenbesteko zehaztasunarekin jakiteko erreferentziazko sistema aukeratu beharko dugu. Kartografiaren kasuan, Lurraren forma ongien deskribatzen duen azalera matematikoa biraketa-elipsoidea da. Horixe erabiltzen du Bizkaiko Foru Aldundiak, esaterako.<sup id="cite_ref-:0_1-2" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Gero, nahitaezkoa da lurreko gainazal kurbatuan dauden elementuak gainazal lauan jartzea, paperean alegia. Hori proiekzio kartografikoen bitartez lortzen da. Elementu kartografikoak paperean islatzeko aukera emango diguten formula matematikoak dira. U.T.M. (Universal Transversa Mercator) Proiekzioa deiturikoa da. proiekzio horietako bat.<sup id="cite_ref-:0_1-3" class="reference"><a href="#cite_note-:0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Puntu geodesikoak markatzeko, Hego Euskal Herrian eta <a href="/wiki/Espainia" title="Espainia">Espainian</a>, 120 zentimetroko garaiera eta 30eko diametroa duen <a href="/wiki/Zilindro" title="Zilindro">zilindro</a> bat kokatzen dira. Zilindro hau, hormigoizko oinarri kubiko batean sostengatzen da, guztia zuriz margoturik. Ohi, toki altu eta garbietan egoten dira, beste puntu batzuk ikusi ahal izateko. Horregatik ikuspegi oso onak egoten dira toki hauetatik. <a href="/wiki/1975" title="1975">1975etik</a>, <a href="/w/index.php?title=Seinale_Geodesiko_eta_Geofisikoei_buruzko_Legea&action=edit&redlink=1" class="new" title="Seinale Geodesiko eta Geofisikoei buruzko Legea (sortu gabe)">Seinale Geodesiko eta Geofisikoei buruzko Legeak</a> babesten ditu. </p><p>Espainiako erpin geodesikoen sarea, hiru zatitan banatzen da: lehen mailakoak, bigarren mailakoak eta hirugarren mailakoak. Lehen mailakoak, 30 eta 70 kilometro arteko hirukiz osaturik daude. Bigarren mailakoak, lehenengo mailakoetan lagundurik, hirukien alboak 10 eta 25 kilometro artekoak izaten dira, eta, azkenik, hirugarren mailakoek, 5 eta 10 kilometro artekoa. Sare handienetako erpinak, aldi berean, sare txikienetako erpin ere badira. </p> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Erpin_geodesiko&veaction=edit&section=1" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Erpin_geodesiko&action=edit&section=1" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-:0-1">↑ <a href="#cite_ref-:0_1-0"><sup><b>a</b></sup></a> <a href="#cite_ref-:0_1-1"><sup><b>b</b></sup></a> <a href="#cite_ref-:0_1-2"><sup><b>c</b></sup></a> <a href="#cite_ref-:0_1-3"><sup><b>d</b></sup></a> <span class="reference-text"><span class="citation"></span> <span class="citation"> <a rel="nofollow" class="external text" href="https://www.bizkaia.eus/hirigintza/gida2004/06/03-VERTICES%20GEODES.pdf?hash=c5b8d82e5aa1ff93c7bae46716dd1b1d"><i>Bizkaiko sare geodesikoaren mapa. </i></a> Bizkaiko Foru-Aldundia</span>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Erpin_geodesiko&veaction=edit&section=2" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Erpin_geodesiko&action=edit&section=2" title="Edit section's source code: Kanpo estekak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Gaztelaniaz dago aipu honen iturburua"><b>(Gaztelaniaz)</b></span> <a rel="nofollow" class="external text" href="http://www.ign.es">Institutu Geografiko Nazionala</a></li> <li><span style="cursor: help; font-size: 90%; font-family: bold; color: gray" title="Gaztelaniaz dago aipu honen iturburua"><b>(Gaztelaniaz)</b></span> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110307074027/http://gmaps.cartesia.org/vertices.php">Erpin Geodesikoen mapa</a></li> <li><a rel="nofollow" class="external text" href="https://www.bizkaia.eus/hirigintza/gida2004/06/03-VERTICES%20GEODES.pdf?hash=c5b8d82e5aa1ff93c7bae46716dd1b1d">Bizkaiko erpin geodesikoen mapa</a>. 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