Add d3.geo.albersUsa.invert.

2013-02-18 12:50:11 +00:00 · 2013-02-18 12:50:11 +00:00 · 4ce9bffe91
--- a/d3.js
+++ b/d3.js
@ -5475,6 +5475,7 @@ d3 = function() {
    var alaska = d3.geo.albers().rotate([ 160, 0 ]).center([ 0, 60 ]).parallels([ 55, 65 ]);
    var hawaii = d3.geo.albers().rotate([ 160, 0 ]).center([ 0, 20 ]).parallels([ 8, 18 ]);
    var puertoRico = d3.geo.albers().rotate([ 60, 0 ]).center([ 0, 10 ]).parallels([ 8, 18 ]);
+    var alaskaInvert, hawaiiInvert, puertoRicoInvert;
    function albersUsa(coordinates) {
      return projection(coordinates)(coordinates);
    }
@ -5482,6 +5483,9 @@ d3 = function() {
      var lon = point[0], lat = point[1];
      return lat > 50 ? alaska : lon < -140 ? hawaii : lat < 21 ? puertoRico : lower48;
    }
+    albersUsa.invert = function(coordinates) {
+      return alaskaInvert(coordinates) || hawaiiInvert(coordinates) || puertoRicoInvert(coordinates) || lower48.invert(coordinates);
+    };
    albersUsa.scale = function(x) {
      if (!arguments.length) return lower48.scale();
      lower48.scale(x);
@ -5497,10 +5501,25 @@ d3 = function() {
      alaska.translate([ dx - .4 * dz, dy + .17 * dz ]);
      hawaii.translate([ dx - .19 * dz, dy + .2 * dz ]);
      puertoRico.translate([ dx + .58 * dz, dy + .43 * dz ]);
+      alaskaInvert = d3_geo_albersUsaInvert(alaska, [ [ -180, 50 ], [ -130, 72 ] ]);
+      hawaiiInvert = d3_geo_albersUsaInvert(hawaii, [ [ -164, 18 ], [ -154, 24 ] ]);
+      puertoRicoInvert = d3_geo_albersUsaInvert(puertoRico, [ [ -67.5, 17.5 ], [ -65, 19 ] ]);
      return albersUsa;
    };
    return albersUsa.scale(lower48.scale());
  };
+  function d3_geo_albersUsaInvert(projection, extent) {
+    var a = projection(extent[0]), b = projection([ .5 * (extent[0][0] + extent[1][0]), extent[0][1] ]), c = projection([ extent[1][0], extent[0][1] ]), d = projection(extent[1]);
+    var dya = b[1] - a[1], dxa = b[0] - a[0], dyb = c[1] - b[1], dxb = c[0] - b[0];
+    var ma = dya / dxa, mb = dyb / dxb;
+    var cx = .5 * (ma * mb * (a[1] - c[1]) + mb * (a[0] + b[0]) - ma * (b[0] + c[0])) / (mb - ma), cy = (.5 * (a[0] + b[0]) - cx) / ma + .5 * (a[1] + b[1]);
+    var dx0 = d[0] - cx, dy0 = d[1] - cy, dx1 = a[0] - cx, dy1 = a[1] - cy, r0 = dx0 * dx0 + dy0 * dy0, r1 = dx1 * dx1 + dy1 * dy1;
+    var a0 = Math.atan2(dy0, dx0), a1 = Math.atan2(dy1, dx1);
+    return function(coordinates) {
+      var dx = coordinates[0] - cx, dy = coordinates[1] - cy, r = dx * dx + dy * dy, a = Math.atan2(dy, dx);
+      if (r0 < r && r < r1 && a0 < a && a < a1) return projection.invert(coordinates);
+    };
+  }
  function d3_geo_albers(φ0, φ1) {
    var sinφ0 = Math.sin(φ0), n = (sinφ0 + Math.sin(φ1)) / 2, C = 1 + sinφ0 * (2 * n - sinφ0), ρ0 = Math.sqrt(C) / n;
    function albers(λ, φ) {
--- a/d3.min.js
+++ b/d3.min.js
--- a/src/geo/albers-usa.js
+++ b/src/geo/albers-usa.js
@ -1,6 +1,4 @@
-// TODO composite invert
-
-// A composite projection for the United States, 960x500. The set of standard
+// A composite projection for the United States, 960×500. The set of standard
 // parallels for each region comes from USGS, which is published here:
 // http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers
 d3.geo.albersUsa = function() {
@ -21,6 +19,10 @@ d3.geo.albersUsa = function() {
      .center([0, 10])
      .parallels([8, 18]);

+  var alaskaInvert,
+      hawaiiInvert,
+      puertoRicoInvert;
+
  function albersUsa(coordinates) {
    return projection(coordinates)(coordinates);
  }
@ -34,6 +36,10 @@ d3.geo.albersUsa = function() {
        : lower48;
  }

+  albersUsa.invert = function(coordinates) {
+    return alaskaInvert(coordinates) || hawaiiInvert(coordinates) || puertoRicoInvert(coordinates) || lower48.invert(coordinates);
+  };
+
  albersUsa.scale = function(x) {
    if (!arguments.length) return lower48.scale();
    lower48.scale(x);
@ -52,8 +58,52 @@ d3.geo.albersUsa = function() {
    alaska.translate([dx - .40 * dz, dy + .17 * dz]);
    hawaii.translate([dx - .19 * dz, dy + .20 * dz]);
    puertoRico.translate([dx + .58 * dz, dy + .43 * dz]);
+
+    alaskaInvert = d3_geo_albersUsaInvert(alaska, [[-180, 50], [-130, 72]]);
+    hawaiiInvert = d3_geo_albersUsaInvert(hawaii, [[-164, 18], [-154, 24]]);
+    puertoRicoInvert = d3_geo_albersUsaInvert(puertoRico, [[-67.5, 17.5], [-65, 19]]);
+
    return albersUsa;
  };

  return albersUsa.scale(lower48.scale());
 };
+
+function d3_geo_albersUsaInvert(projection, extent) {
+  var a = projection(extent[0]),
+      b = projection([.5 * (extent[0][0] + extent[1][0]), extent[0][1]]),
+      c = projection([extent[1][0], extent[0][1]]),
+      d = projection(extent[1]);
+
+  var dya = b[1]- a[1],
+      dxa = b[0]- a[0],
+      dyb = c[1]- b[1],
+      dxb = c[0]- b[0];
+
+  var ma = dya / dxa,
+      mb = dyb / dxb;
+
+  // Find center of circle going through points [a, b, c].
+  var cx = .5 * (ma * mb * (a[1] - c[1]) + mb * (a[0] + b[0]) - ma * (b[0] + c[0])) / (mb - ma),
+      cy = (.5 * (a[0] + b[0]) - cx) / ma + .5 * (a[1] + b[1]);
+
+  // Radial distance² from center.
+  var dx0 = d[0] - cx,
+      dy0 = d[1] - cy,
+      dx1 = a[0] - cx,
+      dy1 = a[1] - cy,
+      r0 = dx0 * dx0 + dy0 * dy0,
+      r1 = dx1 * dx1 + dy1 * dy1;
+
+  // Angular extent.
+  var a0 = Math.atan2(dy0, dx0),
+      a1 = Math.atan2(dy1, dx1);
+
+  return function(coordinates) {
+    var dx = coordinates[0] - cx,
+        dy = coordinates[1] - cy,
+        r = dx * dx + dy * dy,
+        a = Math.atan2(dy, dx);
+    if (r0 < r && r < r1 && a0 < a && a < a1) return projection.invert(coordinates);
+  };
+}
--- a/test/geo/albers-test.js
+++ b/test/geo/albers-test.js
@ -7,9 +7,7 @@ var suite = vows.describe("d3.geo.albers");

 suite.addBatch({
  "albers": {
-    topic: function() {
-      return d3.geo.albers();
-    },
+    topic: d3.geo.albers,
    "Arctic": function(albers) {
      var coords = albers([0, 85]);
      assert.inDelta(coords[0], 1031.393796, 1e-6);
--- a/test/geo/albers-usa-test.js
+++ b/test/geo/albers-usa-test.js
@ -0,0 +1,28 @@
+require("../env");
+
+var vows = require("vows"),
+    assert = require("assert");
+
+var suite = vows.describe("d3.geo.albersUsa");
+
+suite.addBatch({
+  "albersUsa": {
+    topic: d3.geo.albersUsa,
+    "Washington": equalInverse([-120.5, 47.5], [215.478997, 51.976493]),
+    "San Francisco": equalInverse([-122.42, 37.78], [150.072677, 211.257829]),
+    "Juneau, Alaska": equalInverse([-134.22, 58.43], [217.366590, 409.498517]),
+    "Honolulu, Hawaii": equalInverse([-157.82, 21.30], [325.696002, 427.278824]),
+    "San Juan, Puerto Rico": equalInverse([-66.07, 18.45], [909.159250, 456.394827])
+  }
+});
+
+suite.export(module);
+
+function equalInverse(location, point) {
+  return function(projection) {
+    var projected;
+    assert.inDelta(projected = projection(location), point, 1e-6);
+    assert.inDelta(projection.invert(projected), location, 1e-6);
+    assert.inDelta(projection(projection.invert(point)), point, 1e-6);
+  };
+};