Openlayers raster reprojection 栅格重投影原理分析

背景

OpenLayers 3 新版本可以以不一样于服务器提供的坐标系显示来自WMS，WMTS，静态图像和许多其余来源的栅格数据。图像的地图投影的转换直接在Web浏览器中进行。任何Proj4js支持的坐标参考系统中的视图都是可能的，而且之前不兼容的图层如今能够组合和覆盖。

Raster Reproject意义

能够在浏览器端实现不一样资源在不一样投影下的转换，再也不依赖于服务端处理，好比在Geoserver中指定投影类型，仍是至关给力的

效果图

还能够看如下效果对比图

3857使用web Mercator 中国区域是方形，Reproject到4326时，就有些扁了，在相同的中心点，缩放级别下，地图的视察范围也不太一致，4326通过压扁后，能显示更多的范围。

再来一张放大后的，变形明显。

分析过程

以reprojection-image为例说明，使用的是三角仿射变换triangle affine transformation。

三角形动态计算，以正好铺满当前视口

不一样的缩放级别1

不一样的缩放级别2

不一样的缩放级别3

不一样的缩放级别4

不一样的比例尺下会更新三角格网的大小，以刚好平分地图视口，至少两个三角

每一个三角形单独进行Reproject，不一样三角之间互不影响

对三角格网渲染进行Degbu过滤后示意

渲染其中一部分三角

这个图能方便明白Reproject原理

• 首先划分三角格网
• 根据位置，计算每一个三角网对应的原始raster位置和区域，内部使用数学方法，求出转换参数，对每一个三角网进行转换，这里其实并无对每一个像素进行Reproject，而是以三角为最小单位，进行Reproject, 理论上只要三角足够小，经过积分是能够达到一样的效果的，相比像素角度的处理效率也会高不少
• 将多个三角进行无缘拼接

核心实现

三角Reproject

源码ol/reproj.js, render funcction

/** * Renders the source data into new canvas based on the triangulation. * * @param {number} width Width of the canvas. * @param {number} height Height of the canvas. * @param {number} pixelRatio Pixel ratio. * @param {number} sourceResolution Source resolution. * @param {import("./extent.js").Extent} sourceExtent Extent of the data source. * @param {number} targetResolution Target resolution. * @param {import("./extent.js").Extent} targetExtent Target extent. * @param {import("./reproj/Triangulation.js").default} triangulation * Calculated triangulation. * @param {Array<{extent: import("./extent.js").Extent, * image: (HTMLCanvasElement|HTMLImageElement|HTMLVideoElement)}>} sources * Array of sources. * @param {number} gutter Gutter of the sources. * @param {boolean=} opt_renderEdges Render reprojection edges. * @return {HTMLCanvasElement} Canvas with reprojected data. */
export function render(width, height, pixelRatio, sourceResolution, sourceExtent, targetResolution, targetExtent, triangulation, sources, gutter, opt_renderEdges) {

  var context = createCanvasContext2D(Math.round(pixelRatio * width),
    Math.round(pixelRatio * height));

  if (sources.length === 0) {
    return context.canvas;
  }

  context.scale(pixelRatio, pixelRatio);

  var sourceDataExtent = createEmpty();
  sources.forEach(function(src, i, arr) {
    extend(sourceDataExtent, src.extent);
  });

  var canvasWidthInUnits = getWidth(sourceDataExtent);
  var canvasHeightInUnits = getHeight(sourceDataExtent);
  
  // 加载image的内部canvas
  var stitchContext = createCanvasContext2D(
    Math.round(pixelRatio * canvasWidthInUnits / sourceResolution),
    Math.round(pixelRatio * canvasHeightInUnits / sourceResolution));

  var stitchScale = pixelRatio / sourceResolution;

  sources.forEach(function(src, i, arr) {
    var xPos = src.extent[0] - sourceDataExtent[0];
    var yPos = -(src.extent[3] - sourceDataExtent[3]);
    var srcWidth = getWidth(src.extent);
    var srcHeight = getHeight(src.extent);

    stitchContext.drawImage(
      src.image,
      gutter, gutter,
      src.image.width - 2 * gutter, src.image.height - 2 * gutter,
      xPos * stitchScale, yPos * stitchScale,
      srcWidth * stitchScale, srcHeight * stitchScale);
  });

  var targetTopLeft = getTopLeft(targetExtent);

  // 对三角进行循环处理
  triangulation.getTriangles().forEach(function(triangle, i, arr) {

    /* Calculate affine transform (src -> dst) * Resulting matrix can be used to transform coordinate * from `sourceProjection` to destination pixels. * * To optimize number of context calls and increase numerical stability, * we also do the following operations: * trans(-topLeftExtentCorner), scale(1 / targetResolution), scale(1, -1) * here before solving the linear system so [ui, vi] are pixel coordinates. * * Src points: xi, yi * Dst points: ui, vi * Affine coefficients: aij * * | x0 y0 1 0 0 0 | |a00| |u0| * | x1 y1 1 0 0 0 | |a01| |u1| * | x2 y2 1 0 0 0 | x |a02| = |u2| * | 0 0 0 x0 y0 1 | |a10| |v0| * | 0 0 0 x1 y1 1 | |a11| |v1| * | 0 0 0 x2 y2 1 | |a12| |v2| */
    var source = triangle.source;
    var target = triangle.target;
    var x0 = source[0][0], y0 = source[0][1];
    var x1 = source[1][0], y1 = source[1][1];
    var x2 = source[2][0], y2 = source[2][1];
    var u0 = (target[0][0] - targetTopLeft[0]) / targetResolution;
    var v0 = -(target[0][1] - targetTopLeft[1]) / targetResolution;
    var u1 = (target[1][0] - targetTopLeft[0]) / targetResolution;
    var v1 = -(target[1][1] - targetTopLeft[1]) / targetResolution;
    var u2 = (target[2][0] - targetTopLeft[0]) / targetResolution;
    var v2 = -(target[2][1] - targetTopLeft[1]) / targetResolution;

    // Shift all the source points to improve numerical stability
    // of all the subsequent calculations. The [x0, y0] is used here.
    // This is also used to simplify the linear system.
    var sourceNumericalShiftX = x0;
    var sourceNumericalShiftY = y0;
    x0 = 0;
    y0 = 0;
    x1 -= sourceNumericalShiftX;
    y1 -= sourceNumericalShiftY;
    x2 -= sourceNumericalShiftX;
    y2 -= sourceNumericalShiftY;

    var augmentedMatrix = [
      [x1, y1, 0, 0, u1 - u0],
      [x2, y2, 0, 0, u2 - u0],
      [0, 0, x1, y1, v1 - v0],
      [0, 0, x2, y2, v2 - v0]
    ];
    var affineCoefs = solveLinearSystem(augmentedMatrix);
    if (!affineCoefs) {
      return;
    }
    context.save();
    context.beginPath();
    var centroidX = (u0 + u1 + u2) / 3;
    var centroidY = (v0 + v1 + v2) / 3;
    var p0 = enlargeClipPoint(centroidX, centroidY, u0, v0);
    var p1 = enlargeClipPoint(centroidX, centroidY, u1, v1);
    var p2 = enlargeClipPoint(centroidX, centroidY, u2, v2);

    // 设置三角的切割范围，只显示这个范围内的图片，多个三角拼接起来就是总体图像
    context.moveTo(p1[0], p1[1]);
    context.lineTo(p0[0], p0[1]);
    context.lineTo(p2[0], p2[1]);
    context.clip();

    // 最关键的三个方法，经过一系列转换，保证在相应的比例尺下在当前范围内
    // 显示正确的Reproject图像
    // 直接设置下面3个参数，很差容易能达到想要的效果
    // 能够经过将相同的参数输出在本地，进行调试，观察三角内的图像
    context.transform(
      affineCoefs[0], affineCoefs[2], affineCoefs[1], affineCoefs[3], u0, v0);

    context.translate(sourceDataExtent[0] - sourceNumericalShiftX,
      sourceDataExtent[3] - sourceNumericalShiftY);

    context.scale(sourceResolution / pixelRatio,
      -sourceResolution / pixelRatio);

    context.drawImage(stitchContext.canvas, 0, 0);
    context.restore();
  });

  // 调试使用，是否显示三角
  if (opt_renderEdges) {
    context.save();

    context.strokeStyle = 'black';
    context.lineWidth = 1;

    triangulation.getTriangles().forEach(function(triangle, i, arr) {
      var target = triangle.target;
      var u0 = (target[0][0] - targetTopLeft[0]) / targetResolution;
      var v0 = -(target[0][1] - targetTopLeft[1]) / targetResolution;
      var u1 = (target[1][0] - targetTopLeft[0]) / targetResolution;
      var v1 = -(target[1][1] - targetTopLeft[1]) / targetResolution;
      var u2 = (target[2][0] - targetTopLeft[0]) / targetResolution;
      var v2 = -(target[2][1] - targetTopLeft[1]) / targetResolution;

      context.beginPath();
      context.moveTo(u1, v1);
      context.lineTo(u0, v0);
      context.lineTo(u2, v2);
      context.closePath();
      context.stroke();
    });

    context.restore();
  }
  return context.canvas;
}
复制代码

我以其中一个三角的计算参数为示例，能够看到参数仍是比较复杂的

context.moveTo(1136, 199);
context.lineTo(850, 200);
context.lineTo(1136, 401);
context.clip();

context.transform(
  0.011129369548469296, 0.00006403305449769778, 0.00009456173415458175, -0.0111338055978892, 851.2500000000001, 200.00000000000063);

context.translate(-413988.7802610396,
  835088.5497620346);

context.scale(351.73160173160176,
  -351.73160173160176);

context.drawImage(stitchContext.canvas, 0, 0);
context.restore();
复制代码

其中，进行仿射变换的转换过程及数学原理，还须要进一步研究。

参考

• tutorials-raster-reprojection
• reprojection-image