[JavaScript] [Google Maps]Tester si un point est dans un Polygone

Bonjour à tous,

Objet
une question existentielle se fait présente sur le forum [APIs Google Maps]
Comment savoir si un point est dans un polygone fermé ?

Sur base des algorithmes trouvés et notamment celui de Darel Rex Finley, le même que SpaceFrog a donné indirectement sur ce post, la fonction est née.

Aucun doute quant à l'existence d'une telle fonction, déclinée en javascript pour la V3 de l'API sur la toile, mais bon je vous livre celle ci dans un fichier de démo.

Fichier
Code:
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<!DOCTYPE html>
<html lang="fr">
<head>
<meta name="viewport" content="initial-scale=1.0, user-scalable=no">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<meta name="Author" content="NoSmoking">
<title>[Google Maps API V3] Tester si un point est dans un Polygone</title>
<style type="text/css">
html, body {
  height : 100%;
  margin: 0;
  padding : 0;
  font-family : Verdana;
  font-size : 1.0em;
  background-color : #fff;
}
#page {
  padding : 10px;
}
#div_main {
  margin : auto;
  width : 802px;
}
h1 {
  color : #4488bb;
  font-size : 1.3em;
  margin : 0;
  padding : 10px;
  border : 1px solid #4488bb;
}
h1 span{
  font-size : .8em;
}
h2 {
  color : #4488bb;
  font-size : 1.15em;
  margin : 10px;
  padding : 0;
}
p {
  font-size : 0.9em;
  line-height : 25px;
  margin : 5px;
  margin-left : 20px;
  padding : 0;
}
code {
  color : #00f;
  font-size : 1.1em;
  font-family : "courier new";
  font-family: monospace;
}
.label{
  display : inline-block;
  width : 100px;
}
#indic_1, #indic_2, #indic_3 {
  display : inline-block;
  color : #fff;
  font-weight : bold;
  width : 25px;
  text-align : center;
  -webkit-border-radius: 25px;
  -moz-border-radius: 25px;
  border-radius: 25px;
}
#position{
  color : #00f;
  font-style : italic;
  line-height : 25px;
}
#div_carte{
  margin : auto;
  width : 760px;
  height: 500px;
  border : 1px solid #808080;
}
.inside {
  background-color : #0f0;
}
.outside {
  background-color : #f00;
}
#lafonction{
  border : 1px dashed #808080;
  background-color : #f8f8f8;
  width : 740px;
  margin : auto;
  padding : 10px;
  overflow : hidden;
  font-family :"Courier New";
  font-size: .9em;
  line-height : 120%;
  word-wrap : break-word;
}
#lafonction span.c4 {color: #f0f}
#lafonction span.c3 {color: #080}
#lafonction span.c2 {color: #09F}
#lafonction span.c1 {color: #00f}
</style>
<script type="text/javascript" src="http://maps.google.com/maps/api/js?sensor=false"></script>
<script type="text/javascript">
// data des polygones
var periphe = [
    [48.90109200399041,2.3572094778320434],
    [48.89996355650762,2.3918850759765746],
    [48.88529142073465,2.3973782400390746],
    [48.87987292830054,2.4066479543945434],
    [48.87174408891387,2.4135144094726684],
    [48.85412707199129,2.4138577322265746],
    [48.847123714948886,2.414201054980481],
    [48.834244018018936,2.4121411184570434],
    [48.829046009477324,2.400468144824231],
    [48.82633379093924,2.389481816699231],
    [48.82045681382785,2.3778088430664184],
    [48.815935593243395,2.3630459646484496],
    [48.815935593243395,2.356522832324231],
    [48.81797019297125,2.352402959277356],
    [48.81638773365275,2.345879826953137],
    [48.817065936620516,2.3354084829589965],
    [48.81853534490713,2.333348546435559],
    [48.82735089009425,2.2930081228515746],
    [48.835147964455714,2.2736103872558715],
    [48.83480898645335,2.2609074453613403],
    [48.83706879647763,2.255242619921887],
    [48.84023235925237,2.253526006152356],
    [48.845429207206244,2.255070958544934],
    [48.850173684392736,2.2519810537597778],
    [48.85356232144678,2.2533543447754028],
    [48.85920954021081,2.261937413623059],
    [48.86225877345302,2.2643406729004028],
    [48.87117953712866,2.273095403125012],
    [48.87558287211646,2.277043614794934],
    [48.877953738121306,2.2803051809570434],
    [48.882695133030396,2.2830517629882934],
    [48.888113319711934,2.2916348318359496],
    [48.88856480877048,2.2945530752441528],
    [48.892063710752296,2.301934514453137],
    [48.89544951180082,2.307256017138684],
    [48.90018924804242,2.3216755728027465],
    [48.901204847337716,2.3573811392089965]
  ];
var cubisme = [
    [49.06191654835642,1.8954403738281371],
    [48.87620382407392,1.9009335378906371],
    [48.8870410168595,2.027276311328137],
    [48.98086500617795,2.030022893359387],
    [48.99348169368928,2.150872502734387],
    [48.84548569172146,2.145379338671887],
    [48.841870554307356,2.021783147265637],
    [48.7622715002571,2.150872502734387],
    [48.841870554307356,2.304681096484387],
    [48.84729316256955,2.227776799609387],
    [49.020506696095374,2.241509709765637]
  ];
var tordu =[
    [48.74959636588999,2.181084905078137],
    [48.60632666079569,2.175591741015637],
    [48.60632666079569,2.290948186328137],
    [48.68073268448994,2.288201604296887],
    [48.69705102284808,2.370599065234387],
    [48.74959636588999,2.367852483203137],
    [48.73872941954967,2.494195256640637],
    [48.68435943891004,2.491448674609387],
    [48.69727762920328,2.370599065234387],
    [48.63696438344719,2.371972356250012],
    [48.60632666079579,2.290604863574231],
    [48.5686281144548,2.4742825369140746],
    [48.769965557311814,2.6129849294921996],
    [48.790778860337895,2.3397000173828246]
  ];
 
if( !google.maps.Polygon.contains){
  // a partir de Point-In-Polygon Algorithm - Determining Whether A Point Is Inside A Complex Polygon
  // toutes les infos sur http://alienryderflex.com/polygon/
  // by Darel Rex Finley et Nathan Mercer
  google.maps.Polygon.prototype.contains = function( point){
    // mise en "cache" si non existant
    if( this.tabLatitude == undefined){
      // recup data du 1st polygone only
      var oData = this.getPath();
      this.tabLatitude  = [];
      this.tabLongitude = [];
      // attention pb closure !!
      var that = this;
      // mise en tableau
      oData.forEach( function( oLatLng/*, indice*/){
        that.tabLatitude.push ( oLatLng.lat());
        that.tabLongitude.push( oLatLng.lng());
      });
    }
    // test si in polygone
    var i, j;
    var lat_i, lat_j, lng_i, lng_j;
    var oddNodes = false;
    var posX = point.latLng.lng();
    var posY = point.latLng.lat();
    var nbPoints = this.tabLatitude.length;
 
    for( i=0, j=1; i < nbPoints; i++, j++){
      if( j == nbPoints){
        j = 0;
      }
      lat_i = this.tabLatitude[i];
      lat_j = this.tabLatitude[j];
      lng_i = this.tabLongitude[i];
      lng_j = this.tabLongitude[j];
      if((( lat_i <  posY) && ( lat_j >= posY)) ||
         (( lat_j <  posY) && ( lat_i >= posY)) &&
         (( lng_i <= posX) || ( lng_j <= posX))) {
        if( lng_i + (posY - lat_i) /(lat_j -lat_i) *(lng_j -lng_i) < posX){
          oddNodes = !oddNodes;
        }
      }
    }
    return oddNodes;
  };
}
 
// mets les donnees au format new google.maps.LatLng
function convertArray( tabVal){
  var i, nb, oLatLng = [];
  for( i =0, nb = tabVal.length; i <nb; i++){
    oLatLng[i] = new google.maps.LatLng( tabVal[i][0], tabVal[i][1]);
  }
  return oLatLng;
}
 
function initPolygone( map, valeur){
  // creation polygone
  var oPolygone = new google.maps.Polygon({
    map : map,
    paths : valeur,
    strokeColor : "#00f",
    strokeOpacity : 0.8,
    strokeWeight : 1,
    fillColor : "#aaaaff",
    fillOpacity : 0.35
  });
  // transfert les evenements a la map
  google.maps.event.addListener( oPolygone, 'click', function( data){
    google.maps.event.trigger( this.getMap(), 'click', data);
  });
  google.maps.event.addListener( oPolygone, 'mousemove', function( data){
    google.maps.event.trigger( this.getMap(), 'mousemove', data);
  });
  return oPolygone;
}
 
function initCarte(){
  var i, nb, oDiv;
  // Option de l'affichage de depart
  var mapOptions = {
    center : new google.maps.LatLng( 48.825, 2.30),
    disableDoubleClickZoom : true,
    draggableCursor : 'crosshair',
    draggingCursor : 'move',
    backgroundColor : '#fff',
    mapTypeControl :  false,
    streetViewControl : false,
    zoom : 10,
    mapTypeId : google.maps.MapTypeId.ROADMAP
  };
  // Chargement de la carte
  var carte = new google.maps.Map( document.getElementById("div_carte"), mapOptions);
  // just for affichage info
  carte.oDivPos   =  document.getElementById("position");
  carte.oDivIndic = [];
  for( i=1; (oDiv = document.getElementById("indic_" +i)) != null; i++){
    carte.oDivIndic.push( oDiv);
  }
  // creation et ajout des polygones
  carte.oPoly = [];
  carte.oPoly.push( initPolygone( carte, convertArray( cubisme)));
  carte.oPoly.push( initPolygone( carte, convertArray( periphe)));
  carte.oPoly.push( initPolygone( carte, convertArray( tordu)));
//  carte.oPoly.push( initPolygone( carte, [/*convertArray( cubisme),*/ convertArray( periphe), convertArray( tordu)]));
 
  // gestion des evenements mouse
  google.maps.event.addListener( carte, 'click', function( data){
    var i, nb, sMsg = '';
    // parcours de tous les polygones de la carte
    for( i=0, nb = this.oPoly.length; i <nb; i++){
      sMsg += '-\240' +(i+1) +'\240';
      sMsg += this.oPoly[i].contains( data) ? 'Yes\240IN' : 'Sorry\240OUT';
      sMsg += '!\n';
    }
    alert( sMsg);
  });
  google.maps.event.addListener( carte, 'mousemove', function( data){
    var i, nb;
    // affichage position curseur
    this.oDivPos.innerHTML = 'lat : ' +data.latLng.toUrlValue().replace(',',', lng : ');
    // affichage in/out
    for( i=0, nb=this.oPoly.length; i <nb; i++){
      this.oDivIndic[i].className = this.oPoly[i].contains( data) ? 'inside' : 'outside';
    }
  });
  google.maps.event.addListener( carte, 'mouseout', function( /*data*/){
    // clear affichage !
    var i, nb;
    for( i=0, nb=this.oPoly.length; i <nb; i++){
      this.oDivIndic[i].className = '';
    }
    this.oDivPos.innerHTML   = '';
  });
}
// init lorsque la page est chargee
google.maps.event.addDomListener(window, 'load', initCarte);
</script>
</head>
<body>
<div id="page">
  <div id="div_main">
    <h1><span>[Google Maps API V3]</span> Tester si un point est dans un Polygone...</h1>
    <h2>Objet</h2>
    <p>
      Tester si un point, au format <code>google.maps.LatLng</code> est &agrave; l'int&eacute;rieur d'un polygone ferm&eacute;.<br>
      L'agorithme est bas&eacute; sur celui de <a href="http://alienryderflex.com/polygon/">Darel Rex Finley</a> et adapt&eacute;, en javascript, aux <code>google.maps.Polygon</code>.
    </p>
    <h2>Utilisation</h2>
    <p>
      Visualisez le r&eacute;sultat en d&eacute;pla&ccedil;ant et/ou cliquant la souris sur la carte
    </p>
    <h2>R&eacute;sultats</h2>
    <p>
      <span class="label">Indicateurs</span>: <span id="indic_1">1</span>&nbsp;<span id="indic_2">2</span>&nbsp;<span id="indic_3">3</span><br>
      <span class="label">Position</span>: <span id="position">&nbsp;</span>
    </p>
    <div id="div_carte"></div>
    <h2>Observations</h2>
    <p>
      Pour savoir si le curseur survole un <code>Polygon</code> il est suffisant d'ajouter l'&eacute;v&eacute;nement <code>mousemove</code> sur le <code>Polygon</code>, ni plus ni moins.<br>
      Dans le cas pr&eacute;sent l'&eacute;v&eacute;nement est remont&eacute; &agrave; la carte, via un <code>google.maps.event.trigger</code>, et c'est le point survol&eacute; qui est pass&eacute; &agrave; la fonction de test, la fonction retournant <code>true</code> ou <code>false</code>.<br>
    </p>
    <h2>La fonction</h2>
<pre id="lafonction"><span class="c1">if</span><span class="c2">(</span> !google.maps.Polygon.contains<span class="c2">)</span><span class="c2">{</span>
  <span class="c3"><em>// a partir de Point-In-Polygon Algorithm - Determining Whether A Point Is Inside A Complex Polygon</em></span>
  <span class="c3"><em>// toutes les infos sur http://alienryderflex.com/polygon/</em></span>
  <span class="c3"><em>// by Darel Rex Finley et Nathan Mercer</em></span>
  google.maps.Polygon.prototype.contains = <span class="c1">function</span><span class="c2">(</span> point<span class="c2">)</span><span class="c2">{</span>
    <span class="c3"><em>// mise en "cache" si non existant</em></span>
    <span class="c1">if</span><span class="c2">(</span> <span class="c1">this</span>.tabLatitude <span class="c2">==</span> undefined<span class="c2">)</span><span class="c2">{</span>
      <span class="c3"><em>// recup data du 1st polygone only</em></span>
      <span class="c1">var</span> oData = <span class="c1">this</span>.getPath<span class="c2">(</span><span class="c2">)</span>;
      <span class="c1">this</span>.tabLatitude = <span class="c2">[</span><span class="c2">]</span>;
      <span class="c1">this</span>.tabLongitude = <span class="c2">[</span><span class="c2">]</span>;
      <span class="c3"><em>// attention pb closure !!</em></span>
      <span class="c1">var</span> that = <span class="c1">this</span>;
      <span class="c3"><em>// mise en tableau</em></span>
      oData.forEach<span class="c2">(</span> <span class="c1">function</span><span class="c2">(</span> oLatLng<span class="c3"><em>/*, indice*/</em></span><span class="c2">)</span><span class="c2">{</span>
        that.tabLatitude.push <span class="c2">(</span> oLatLng.lat<span class="c2">(</span><span class="c2">)</span><span class="c2">)</span>;
        that.tabLongitude.push<span class="c2">(</span> oLatLng.lng<span class="c2">(</span><span class="c2">)</span><span class="c2">)</span>;
      <span class="c2">}</span><span class="c2">)</span>;
    <span class="c2">}</span>
    <span class="c3"><em>// test si in polygone</em></span>
    <span class="c1">var</span> i, j;
    <span class="c1">var</span> lat_i, lat_j, lng_i, lng_j;
    <span class="c1">var</span> oddNodes = <span class="c1">false</span>;
    <span class="c1">var</span> posX = point.latLng.lng<span class="c2">(</span><span class="c2">)</span>;
    <span class="c1">var</span> posY = point.latLng.lat<span class="c2">(</span><span class="c2">)</span>;
    <span class="c1">var</span> nbPoints = <span class="c1">this</span>.tabLatitude.length;
 
    <span class="c1">for</span><span class="c2">(</span> i=<span class="c4">0</span>, j=<span class="c4">1</span>; i &lt; nbPoints; i++, j++<span class="c2">)</span><span class="c2">{</span>
      <span class="c1">if</span><span class="c2">(</span> j <span class="c2">==</span> nbPoints<span class="c2">)</span><span class="c2">{</span>
        j = <span class="c4">0</span>;
      <span class="c2">}</span>
      lat_i = <span class="c1">this</span>.tabLatitude<span class="c2">[</span>i<span class="c2">]</span>;
      lat_j = <span class="c1">this</span>.tabLatitude<span class="c2">[</span>j<span class="c2">]</span>;
      lng_i = <span class="c1">this</span>.tabLongitude<span class="c2">[</span>i<span class="c2">]</span>;
      lng_j = <span class="c1">this</span>.tabLongitude<span class="c2">[</span>j<span class="c2">]</span>;
 
      <span class="c1">if</span><span class="c2">(</span><span class="c2">(</span><span class="c2">(</span> lat_i  &lt; posY<span class="c2">)</span> <span class="c2">&amp;&amp;</span> <span class="c2">(</span> lat_j <span class="c2">&gt;=</span> posY<span class="c2">)</span><span class="c2">)</span> ||
         <span class="c2">(</span><span class="c2">(</span> lat_j  &lt; posY<span class="c2">)</span> <span class="c2">&amp;&amp;</span> <span class="c2">(</span> lat_i <span class="c2">&gt;=</span> posY<span class="c2">)</span><span class="c2">)</span> <span class="c2">&amp;&amp;</span>
         <span class="c2">(</span><span class="c2">(</span> lng_i <span class="c2">&lt;=</span> posX<span class="c2">)</span> || <span class="c2">(</span> lng_j <span class="c2">&lt;=</span> posX<span class="c2">)</span><span class="c2">)</span><span class="c2">)</span> <span class="c2">{</span>
        <span class="c1">if</span><span class="c2">(</span> lng_i + <span class="c2">(</span>posY - lat_i<span class="c2">)</span> /<span class="c2">(</span>lat_j -lat_i<span class="c2">)</span> *<span class="c2">(</span>lng_j -lng_i<span class="c2">)</span> &lt; posX<span class="c2">)</span><span class="c2">{</span>
          oddNodes = !oddNodes;
        <span class="c2">}</span>
      <span class="c2">}</span>
    <span class="c2">}</span>
    <span class="c1">return</span> oddNodes;
  <span class="c2">}</span>;
<span class="c2">}</span>
</pre>
    <br>
  </div>
</div>
</body>
</html>
il suffit de copier/coller et de tester.

Observation
Ma recherche sur la toile a sûrement été mal menée, cela en fera juste une de plus.

A vos remarques!

edit 06.08.2011 déjà!!
oubli de simplification de la fonction, le traitement sur un getPaths() n'est pas justifié, les essais menés ayant montrés qu'elle n'a pas de sens, au moins sous cette forme!