Wagner customizable projection, by Tobias Jung

closes #139

README.md

@@ -745,6 +745,29 @@ The Van der Grinten III projection.
 
 The Van der Grinten IV projection.
 
+<a href="#geoWagner" name="geoWagner">#</a> d3.<b>geoWagner</b>() [<>](https://github.com/d3/d3-geo-projection/blob/master/src/wagner.js "Source")
+<br><a href="#geoWagnerRaw" name="geoWagnerRaw">#</a> d3.<b>geoWagnerRaw</b>
+
+[<img src="https://raw.githubusercontent.com/d3/d3-geo-projection/master/img/wagner.png" width="480" height="250">](https://map-projections.net/d3-customizable-wagner/)
+
+The Wagner projection is customizable: default values produce the Wagner VIII projection.
+
+<a href="#wagner_poleline" name="wagner_poleline">#</a> <i>wagner</i>.<b>poleline</b>([<i>poleline</i>])
+
+Defaults to 65°.
+
+<a href="#wagner_parallels" name="wagner_parallels">#</a> <i>wagner</i>.<b>parallels</b>([<i>parallels</i>])
+
+Defaults to 60°.
+
+<a href="#wagner_inflation" name="wagner_inflation">#</a> <i>wagner</i>.<b>inflation</b>([<i>inflation</i>])
+
+Defaults to 20.
+
+<a href="#wagner_ratio" name="wagner_ratio">#</a> <i>wagner</i>.<b>ratio</b>([<i>ratio</i>])
+
+Defaults to 200.
+
 <a href="#geoWagner4" name="geoWagner4">#</a> d3.<b>geoWagner4</b>() [<>](https://github.com/d3/d3-geo-projection/blob/master/src/wagner4.js "Source")
 <br><a href="#geoWagner4Raw" name="geoWagner4Raw">#</a> d3.<b>geoWagner4Raw</b>
 

src/index.js

@@ -88,6 +88,7 @@ export {default as geoVanDerGrinten, vanDerGrintenRaw as geoVanDerGrintenRaw} fr
 export {default as geoVanDerGrinten2, vanDerGrinten2Raw as geoVanDerGrinten2Raw} from "./vanDerGrinten2";
 export {default as geoVanDerGrinten3, vanDerGrinten3Raw as geoVanDerGrinten3Raw} from "./vanDerGrinten3";
 export {default as geoVanDerGrinten4, vanDerGrinten4Raw as geoVanDerGrinten4Raw} from "./vanDerGrinten4";
+export {default as geoWagner, wagnerRaw as geoWagnerRaw} from "./wagner.js";
 export {default as geoWagner4, wagner4Raw as geoWagner4Raw} from "./wagner4.js";
 export {default as geoWagner6, wagner6Raw as geoWagner6Raw} from "./wagner6.js";
 export {default as geoWagner7, wagner7Raw as geoWagner7Raw} from "./wagner7.js";

src/wagner.js

@@ -0,0 +1,89 @@
+import {geoProjectionMutator as projectionMutator} from "d3-geo";
+import {acos, asin, atan2, cos, degrees, epsilon, halfPi, max, min, pi, radians, sin, sqrt, tan} from "./math";
+
+function wagnerFormula(cx, cy, m1, m2, n) {
+  function forward(lambda, phi) {
+    var s = m1 * sin(m2 * phi),
+        c0 = sqrt(1 - s * s),
+        c1 = sqrt(2 / (1 + c0 * cos(lambda *= n)));
+    return [
+      cx * c0 * c1 * sin(lambda),
+      cy * s * c1
+    ];
+  }
+
+  forward.invert = function(x, y) {
+    var t1 = x / cx,
+        t2 = y / cy,
+        p = sqrt(t1 * t1 + t2 * t2),
+        c = 2 * asin(p / 2);
+    return [
+      atan2(x * tan(c), cx * p) / n,
+      p && asin(y * sin(c) / (cy * m1 * p)) / m2
+    ];
+  };
+
+  return forward;
+}
+
+export function wagnerRaw(poleline, parallels, inflation, ratio) {
+  // 60 is always used as reference parallel
+  var phi1 = pi / 3;
+
+  // sanitizing the input values
+  // poleline and parallels may approximate but never equal 0
+  poleline = max(poleline, epsilon);
+  parallels = max(parallels, epsilon);
+  // poleline must be <= 90; parallels may approximate but never equal 180
+  poleline = min(poleline, halfPi);
+  parallels = min(parallels, pi - epsilon);
+  // 0 <= inflation <= 99.999
+  inflation = max(inflation, 0);
+  inflation = min(inflation, 100 - epsilon);
+  // ratio > 0.
+  // sensible values, i.e. something that renders a map which still can be
+  // recognized as world map, are e.g. 20 <= ratio <= 1000.
+  ratio = max(ratio, epsilon);
+
+  // convert values from boehm notation
+  // areal inflation e.g. from 0 to 1 or 20 to 1.2:
+  var vinflation = inflation/100 + 1;
+  // axial ratio e.g. from 200 to 2:
+  var vratio  = ratio / 100;
+  // the other ones are a bit more complicated...
+  var m2 = acos(vinflation * cos(phi1)) / phi1,
+      m1 = sin(poleline) / sin(m2 * halfPi),
+      n = parallels / pi,
+      k = sqrt(vratio * sin(poleline / 2) / sin(parallels / 2)),
+      cx = k / sqrt(n * m1 * m2),
+      cy = 1 / (k * sqrt(n * m1 * m2));
+
+  return wagnerFormula(cx, cy, m1, m2, n);
+}
+
+export default function() {
+  // default values generate wagner8
+  var poleline = 65 * radians,
+      parallels = 60 * radians,
+      inflation = 20,
+      ratio = 200,
+      mutate = projectionMutator(wagnerRaw),
+      projection = mutate(poleline, parallels, inflation, ratio);
+
+  projection.poleline = function(_) {
+    return arguments.length ? mutate(poleline = +_ * radians, parallels, inflation, ratio) : poleline * degrees;
+  };
+
+  projection.parallels = function(_) {
+    return arguments.length ? mutate(poleline, parallels = +_ * radians, inflation, ratio) : parallels * degrees;
+  };
+  projection.inflation = function(_) {
+    return arguments.length ? mutate(poleline, parallels, inflation = +_, ratio) : inflation;
+  };
+  projection.ratio = function(_) {
+    return arguments.length ? mutate(poleline, parallels, inflation, ratio = +_) : ratio;
+  };
+
+  return projection
+    .scale(163.775);
+}

test/compare-images

@@ -88,6 +88,7 @@ for i in \
     vanDerGrinten2 \
     vanDerGrinten3 \
     vanDerGrinten4 \
+    wagner \
     wagner4 \
     wagner6 \
     wagner7 \

test/invert-test.js

@@ -94,6 +94,7 @@ var points = [[0, 0], [30.3, 24.1], [-10, 42], [-2, -5], [0,-55]];
   d3.geoVanDerGrinten2,
   d3.geoVanDerGrinten3,
   d3.geoVanDerGrinten4,
+  d3.geoWagner,
   d3.geoWagner4,
   d3.geoWagner6,
   d3.geoWagner7,