地理坐标偏移 - 机场跑道图

Question

我正在尝试生成机场跑道图，如下所示：

每个机场都有一个跑道列表，如下所示：

const runways = [
    {
      identifier1: "110L",
      identifier2: "28R",
      length: 3107,
      width: 75,

      latitude1: 37.66247544,
      longitude1: -122.12726156,

      latitude2: 37.65822686,
      longitude2: -122.11795339,
    },
    {
      identifier1: "10R",
      identifier2: "28L",
      length: 5694,
      width: 150,
      
      latitude1: 37.66204453,
      longitude1: -122.12979078,

      latitude2: 37.65426,
      longitude2: -122.11273375,
    },
  ];

如您所见，每条跑道都有起点和终点地理点。对于视觉效果，我使用 svg-airports，上面的跑道示例表示为：

<airport-diagram width="200" height="200">
  <airport-runway
    length-ft="3107"
    true-heading="119"
    offset-angle="29"
    offset-x="300"
    offset-y="1000"
  >
    <runway-id name="10L" pattern="left"></runway-id>
    <runway-id name="28R" pattern="right"></runway-id>
  </airport-runway>
  <airport-runway
    length-ft="5694"
    true-heading="119"
    offset-angle="29"
    offset-x="300"
    offset-y="-1000"
  >
    <runway-id name="10R" pattern="right"></runway-id>
    <runway-id name="28L" pattern="left"></runway-id>
  </airport-runway>
</airport-diagram>

如您所见，每条跑道都有以下值

长度
真航向
偏移角度
偏移-x
偏移-y

我能够提供长度，因为我已经从我的 airport 中获得了该信息，并且我正在计算真实航向（方位角）如下：

function radians(n) {
  return n * (Math.PI / 180);
}
function degrees(n) {
  return n * (180 / Math.PI);
}

function getBearing(startLat, startLong, endLat, endLong) {
  startLat = radians(startLat);
  startLong = radians(startLong);
  endLat = radians(endLat);
  endLong = radians(endLong);

  var dLong = endLong - startLong;

  var dPhi = Math.log(
    Math.tan(endLat / 2.0 + Math.PI / 4.0) /
      Math.tan(startLat / 2.0 + Math.PI / 4.0)
  );
  if (Math.abs(dLong) > Math.PI) {
    if (dLong > 0.0) dLong = -(2.0 * Math.PI - dLong);
    else dLong = 2.0 * Math.PI + dLong;
  }

  return (degrees(Math.atan2(dLong, dPhi)) + 180.0) % 180.0;
}

问题是，我可以根据跑道之间的地理坐标计算offset-angle、offset-x和offset-y吗？

P.S：偏移值以英尺为单位。

Answer 1

将longitude/latitude转换为笛卡尔坐标。那么它应该很容易。我认为转换是问题所在。

对于机场（相对较小），可以使用简单的equirectangular projection。

<!doctype html>
<html>
<body>
   <script src="t.js"></script>
   <script src="svg-airports-1.0.js" async></script>
</body>
</html>

// t.js
// important parts within ////// commments
const runways = [
   {
      identifier1: "110L",
      identifier2: "28R",
      length: 3107,
      width: 75,
      latitude1: 37.66247544,
      longitude1: -122.12726156,
      latitude2: 37.65822686,
      longitude2: -122.11795339,
   }, {
      identifier1: "10R",
      identifier2: "28L",
      length: 5694,
      width: 150,
      latitude1: 37.66204453,
      longitude1: -122.12979078,
      latitude2: 37.65426,
      longitude2: -122.11273375,
   },
];

function runways2html(runways,scale=1.0) {
   //
   airport = document.createElement("airport-diagram")
   document.body.appendChild(airport)
   //////////////////////////////////////////////////////////////////////
   const radians = n => n * (Math.PI / 180)
   const degrees = n => n * (180 / Math.PI)
   const avg = (v1,v2) => .5*(v1+v2)
   const lon2x = lon => R*(lon-lon0)*cosLat0
   const lat2y = lat => R*(lat-lat0)
   //
   var lons = runways.map(({longitude1,longitude2}) => [longitude1,longitude2]).flat().map(v => radians(v))
   var lats = runways.map(({latitude1,latitude2}) => [latitude1,latitude2]).flat().map(v => radians(v))
   var lonMax = Math.max(...lons)
   var lonMin = Math.min(...lons)
   var latMax = Math.max(...lats)
   var latMin = Math.min(...lats)
   var lon0 = avg(lonMin,lonMax)
   var lat0 = avg(latMin,latMax)
   var cosLat0 = Math.cos(lat0)
   var R = 20902000 // Earth radius in feet (??)
   //////////////////////////////////////////////////////////////////////
   var [xMin,xMax] = [lonMin,lonMax].map(lon2x)
   var [yMin,yMax] = [latMin,latMax].map(lat2y)
   var width = xMax-xMin
   var height = yMax-yMin
   var [width,height] = [width,height].map(v => v*scale)
   airport.setAttribute("width",width)
   airport.setAttribute("height",height)
   //
   runways.forEach(runway => {
      var {
         identifier1,
         identifier2,
         length,
         width,
         latitude1,
         longitude1,
         latitude2,
         longitude2,
      } = runway
      //////////////////////////////////////////////////////////////////////
      var [longitude1,longitude2,latitude1,latitude2] = [longitude1,longitude2,latitude1,latitude2].map(v => radians(v))
      var [x1,x2] = [longitude1,longitude2].map(lon2x)
      var [y1,y2] = [latitude1,latitude2].map(lat2y)
      var heading = Math.atan2(x2-x1,y2-y1)
      heading = degrees(heading)
      var x = avg(x1,x2)
      var y = avg(y1,y2)
      //////////////////////////////////////////////////////////////////////
      var runway = document.createElement("airport-runway")
      runway.setAttribute("length-ft",length)
      runway.setAttribute("true-heading",heading)
      runway.setAttribute("offset-angle",0)
      runway.setAttribute("offset-x",x)
      runway.setAttribute("offset-y",y)
      var [id1,id2] = [0,1].map(i => document.createElement("runway-id"))
      id1.setAttribute("name",identifier1)
      id1.setAttribute("pattern",identifier1.endsWith("L")?"left":"right") // ??
      id2.setAttribute("name",identifier2)
      id2.setAttribute("pattern",identifier1.endsWith("L")?"right":"left") // ??
      runway.appendChild(id1)
      runway.appendChild(id2)
      airport.appendChild(runway)
   })
}

runways2html(runways,0.2)

地理坐标偏移 - 机场跑道图

Geo Coordinates offset - airport runways diagram

javascript

math

svg

geo

coordinates