From 717ed0cd6cc0a03d6f829b079e05bb301916343e Mon Sep 17 00:00:00 2001
From: Mike Bostock <mbostock@gmail.com>
Date: Mon, 3 Oct 2016 13:32:49 -0700
Subject: [PATCH] Use cylindrical projection when appropriate.

---
 src/projection/conicEqualArea.js       | 14 +++++---------
 src/projection/cylindricalEqualArea.js | 15 +++++++++++++++
 2 files changed, 20 insertions(+), 9 deletions(-)
 create mode 100644 src/projection/cylindricalEqualArea.js

diff --git a/src/projection/conicEqualArea.js b/src/projection/conicEqualArea.js
index de3aff5..c408bb1 100644
--- a/src/projection/conicEqualArea.js
+++ b/src/projection/conicEqualArea.js
@@ -1,18 +1,14 @@
 import {abs, asin, atan2, cos, epsilon, sign, sin, sqrt} from "../math";
 import {conicProjection} from "./conic";
+import {cylindricalEqualAreaRaw} from "./cylindricalEqualArea";
 
 export function conicEqualAreaRaw(y0, y1) {
-  var sy0 = sin(y0),
-      n = (sy0 + sin(y1)) / 2,
-      c = 1 + sy0 * (2 * n - sy0);
+  var sy0 = sin(y0), n = (sy0 + sin(y1)) / 2;
 
-  // gracefully handle the limit case where the two standard parallels
-  // are symetrical with the Equator
-  if (abs(n) < epsilon) {
-    n = (n < 0 ? -1 : 1) * epsilon;
-  }
+  // Are the parallels symmetrical around the Equator?
+  if (abs(n) < epsilon) return cylindricalEqualAreaRaw(y0);
 
-  var r0 = sqrt(c) / n;
+  var c = 1 + sy0 * (2 * n - sy0), r0 = sqrt(c) / n;
 
   function project(x, y) {
     var r = sqrt(c - 2 * n * sin(y)) / n;
diff --git a/src/projection/cylindricalEqualArea.js b/src/projection/cylindricalEqualArea.js
new file mode 100644
index 0000000..3074818
--- /dev/null
+++ b/src/projection/cylindricalEqualArea.js
@@ -0,0 +1,15 @@
+import {asin, cos, sin} from "../math";
+
+export function cylindricalEqualAreaRaw(phi0) {
+  var cosPhi0 = cos(phi0);
+
+  function forward(lambda, phi) {
+    return [lambda * cosPhi0, sin(phi) / cosPhi0];
+  }
+
+  forward.invert = function(x, y) {
+    return [x / cosPhi0, asin(y * cosPhi0)];
+  };
+
+  return forward;
+}