Sphere Mollweide

<!--
  示例：球面摩尔威投影
  要点：Mollweide 公式把经纬度投到等积椭圆世界图，纬度用迭代解出
  依赖：OpenLayers 10.3.1 · jsDelivr CDN（底图 OSM，无 Key）
  替代：官方用 proj4 注册全球投影，这里直接用公式在离屏 canvas 上绘制
-->
<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta name="robots" content="noindex,follow">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>球面摩尔威投影</title>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/ol@10.3.1/ol.css">
<style>
  html,body{height:100%;margin:0}
  body{display:flex;flex-direction:column;overflow:hidden;
       font:13px/1.6 -apple-system,"Segoe UI","PingFang SC",sans-serif;color:#16181d}
  .bar{flex:0 0 auto;padding:8px 12px;background:#f6f7f9;border-bottom:1px solid #e3e6ea;
       display:flex;gap:14px;align-items:center;font-size:12px;color:#58606e;flex-wrap:wrap}
  .bar b{color:#16181d;font-weight:600}
  .wrap{position:relative;flex:1 1 auto;min-height:0}
  #map{position:absolute;inset:0;background:#eef0f3}
  .panel{position:absolute;right:12px;bottom:12px;background:#fff;border:1px solid #e3e6ea;
         border-radius:8px;box-shadow:0 4px 16px rgba(16,24,40,.12);padding:8px}
  .panel h5{margin:0 0 6px;font-size:12px;color:#58606e;font-weight:600}
  .panel canvas{display:block;border-radius:4px}
</style>
</head>
<body>
<div class="bar">
  <span>投影 <b>Mollweide</b></span>
  <span>红点为北京，绿线为每 30° 经纬网</span>
</div>
<div class="wrap">
  <div id="map"></div>
  <div class="panel">
    <h5>等积椭圆世界图</h5>
    <canvas id="world" width="320" height="180"></canvas>
  </div>
</div>
<script src="https://cdn.jsdelivr.net/npm/ol@10.3.1/dist/ol.js"></script>
<script>
(function () {
  'use strict';
  if (!window.ol) {
    document.getElementById('map').textContent = 'OpenLayers 加载失败，请检查 cdn.jsdelivr.net 是否可访问';
    return;
  }

  var R = 6371008.8;
  var D2R = Math.PI / 180;

  /* Mollweide 正解：θ 由 2θ + sin2θ = π sinφ 迭代得到 */
  function mollweide(lon, lat) {
    var phi = lat * D2R;
    var theta = phi;
    for (var i = 0; i < 12; i++) {
      var denom = 2 + 2 * Math.cos(2 * theta);
      if (Math.abs(denom) < 1e-9) break;
      theta -= (2 * theta + Math.sin(2 * theta) - Math.PI * Math.sin(phi)) / denom;
    }
    var k = 2 * Math.SQRT2 / Math.PI;
    return [
      R * k * (lon * D2R) * Math.cos(theta),
      R * Math.SQRT2 * Math.sin(theta)
    ];
  }

  var canvas = document.getElementById('world');
  var W = canvas.width;
  var H = canvas.height;
  var renderer = ol.render.toContext(canvas.getContext('2d'), {
    size: [W, H],
    pixelRatio: 1
  });

  var maxX = R * 2 * Math.SQRT2;
  var maxY = R * Math.SQRT2;
  function project(lon, lat) {
    var p = mollweide(lon, lat);
    return [
      W / 2 + p[0] / maxX * (W - 16),
      H / 2 - p[1] / maxY * (H - 16)
    ];
  }

  /* 经纬网 */
  renderer.setStyle(new ol.style.Style({
    stroke: new ol.style.Stroke({ color: 'rgba(47,143,91,.55)', width: 1 })
  }));

  for (var lonLine = -180; lonLine <= 180; lonLine += 30) {
    var meridian = [];
    for (var latLine = -90; latLine <= 90; latLine += 3) {
      meridian.push(project(lonLine, latLine));
    }
    renderer.drawGeometry(new ol.geom.LineString(meridian));
  }

  for (var latLine2 = -60; latLine2 <= 60; latLine2 += 30) {
    var parallel = [];
    for (var lonLine2 = -180; lonLine2 <= 180; lonLine2 += 3) {
      parallel.push(project(lonLine2, latLine2));
    }
    renderer.drawGeometry(new ol.geom.LineString(parallel));
  }

  /* 世界边界椭圆 */
  renderer.setStyle(new ol.style.Style({
    stroke: new ol.style.Stroke({ color: '#8a92a1', width: 1.5 })
  }));
  renderer.drawGeometry(new ol.geom.Polygon([[
    [W / 2 - (W - 16) / 2, H / 2],
    [W / 2, H / 2 - (H - 16) / 2],
    [W / 2 + (W - 16) / 2, H / 2],
    [W / 2, H / 2 + (H - 16) / 2],
    [W / 2 - (W - 16) / 2, H / 2]
  ]]));

  /* 北京位置 */
  var bj = project(116.391, 39.907);
  renderer.setStyle(new ol.style.Style({
    image: new ol.style.Circle({
      radius: 4,
      fill: new ol.style.Fill({ color: '#d64545' }),
      stroke: new ol.style.Stroke({ color: '#fff', width: 1.5 })
    }),
    text: new ol.style.Text({
      text: '北京',
      offsetY: -12,
      font: '500 11px sans-serif',
      fill: new ol.style.Fill({ color: '#d64545' })
    })
  }));
  renderer.drawGeometry(new ol.geom.Point(bj));

  /* 左侧地图仍用常规墨卡托视图，标注同一个城市 */
  var map = new ol.Map({
    target: 'map',
    layers: [
      new ol.layer.Tile({ source: new ol.source.XYZ({url: 'https://server.arcgisonline.com/ArcGIS/rest/services/World_Street_Map/MapServer/tile/{z}/{y}/{x}', attributions: 'Tiles © Esri'}) }),
      new ol.layer.Vector({
        source: new ol.source.Vector({
          features: [new ol.Feature({
            geometry: new ol.geom.Point(ol.proj.fromLonLat([116.391, 39.907]))
          })]
        }),
        style: new ol.style.Style({
          image: new ol.style.Circle({
            radius: 7,
            fill: new ol.style.Fill({ color: '#d64545' }),
            stroke: new ol.style.Stroke({ color: '#fff', width: 2 })
          })
        })
      })
    ],
    view: new ol.View({ center: ol.proj.fromLonLat([116.391, 39.907]), zoom: 4 }),
    controls: ol.control.defaults.defaults({ attribution: false, rotate: false })
  });
})();
</script>
</body>
</html>