EPSG:2163 Coordinates by mbostock

Use the brush to select extent coordinates interactively.

The gdalwarp utility can crop the warped output image using the -te argument, which specifies a geographic extent as xmin ymin xmax ymax coordinates in the target projection. For example, the extent -2030000 -1250000 -1300000 -40400 shown above encompasses California when using EPSG:2163, the U.S. National Atlas projection.

The trick to computing these coordinates is to know the scale of the underlying Lambert azimuthal equal-area projection: 6,370,997 meters, as shown in the human-readable projection definition. From there, it is possible to translate between pixel space and EPSG:2163 coordinates.

function te(projection) {
  var radius = 6370997,
      scale = projection.scale(),
      rotate = projection.rotate(),
      translate = projection.translate(),
      offset = projection.rotate([0, 0]).translate([0, 0])([0, 0]);

  projection.rotate(rotate).translate(translate);

  return [
    Math.round((-offset[0] - translate[0]) / scale * radius),
    Math.round((offset[1] + translate[1] - height) / scale * radius),
    Math.round((-offset[0] - translate[0] + width) / scale * radius),
    Math.round((offset[1] + translate[1]) / scale * radius)
  ];
}

index.html

<!DOCTYPE html>
<meta charset="utf-8">
<style>

body {
  position: relative;
  height: 500px;
}

#info {
  position: absolute;
  left: 10px;
  bottom: 10px;
}

.graticule {
  fill: none;
  stroke: #777;
  stroke-width: .5px;
  stroke-opacity: .5;
}

.land {
  fill: #333;
}

.state-boundary {
  fill: none;
  stroke: #fff;
}

.brush .extent {
  fill: red;
  fill-opacity: .1;
  stroke: red;
}

</style>
<div id="info"></div>
<script src="//d3js.org/d3.v3.min.js"></script>
<script src="//d3js.org/topojson.v1.min.js"></script>
<script>

var width = 960,
    height = 500,
    formatNumber = d3.format(".3r");

var projection = d3.geo.azimuthalEqualArea()
    .rotate([100, -45])
    .scale(1050)
    .translate([width / 2, height / 2 - 110]);

var extent = te(projection);

var brush = d3.svg.brush()
    .x(d3.scale.linear().domain([extent[0], extent[2]]).range([0, width]))
    .y(d3.scale.linear().domain([extent[1], extent[3]]).range([height, 0]))
    .extent([[-2030000, -1250000], [-1300000, -40400]])
    .on("brush", brushed);

var path = d3.geo.path()
    .projection(projection);

var graticule = d3.geo.graticule()
    .extent([[-140, 20], [-60, 60]])
    .step([2, 2]);

var info = d3.select("#info");

var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height);

svg.append("path")
    .datum(graticule)
    .attr("class", "graticule")
    .attr("d", path);

d3.json("/mbostock/raw/4090846/us.json", function(error, us) {
  if (error) throw error;

  svg.insert("path", ".graticule")
      .datum(topojson.feature(us, us.objects.land))
      .attr("class", "land")
      .attr("d", path);

  svg.insert("path", ".graticule")
      .datum(topojson.mesh(us, us.objects.states, function(a, b) { return a !== b; }))
      .attr("class", "state-boundary")
      .attr("d", path);

  svg.append("g")
      .attr("class", "brush")
      .call(brush)
      .call(brushed);
});

function brushed() {
  var e = brush.extent();
  info.text(formatNumber(e[0][0])
      + " " + formatNumber(e[0][1])
      + " " + formatNumber(e[1][0])
      + " " + formatNumber(e[1][1]));
}

function te(projection) {
  var radius = 6370997,
      scale = projection.scale(),
      rotate = projection.rotate(),
      translate = projection.translate(),
      offset = projection.rotate([0, 0]).translate([0, 0])([0, 0]);

  projection.rotate(rotate).translate(translate);

  return [
    Math.round((-offset[0] - translate[0]) / scale * radius),
    Math.round((offset[1] + translate[1] - height) / scale * radius),
    Math.round((-offset[0] - translate[0] + width) / scale * radius),
    Math.round((offset[1] + translate[1]) / scale * radius)
  ];
}

</script>