Better handling of ambiguous centroids.

Rather than doing something like picking the last seen point, return
an undefined centroid if it is ambiguous.

Users can decide what to do, e.g. when picking an origin for a rotating
globe, using the last coordinate in a MultiPoint or LineString seems
reasonable in an ambiguous situation.

d3.js

@@ -5891,7 +5891,10 @@
   d3.geo.centroid = function(object) {
     d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
     d3.geo.stream(object, d3_geo_centroid);
-    return d3_geo_centroidW ? [ Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees, Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / Math.sqrt(d3_geo_centroidX * d3_geo_centroidX + d3_geo_centroidY * d3_geo_centroidY + d3_geo_centroidZ * d3_geo_centroidZ)))) * d3_degrees ] : null;
+    var m;
+    if (d3_geo_centroidW && Math.abs(m = Math.sqrt(d3_geo_centroidX * d3_geo_centroidX + d3_geo_centroidY * d3_geo_centroidY + d3_geo_centroidZ * d3_geo_centroidZ)) > ε) {
+      return [ Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees, Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / m))) * d3_degrees ];
+    }
   };
   var d3_geo_centroidW, d3_geo_centroidX, d3_geo_centroidY, d3_geo_centroidZ;
   var d3_geo_centroid = {

src/geo/centroid.js

@@ -1,12 +1,15 @@
 d3.geo.centroid = function(object) {
   d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
   d3.geo.stream(object, d3_geo_centroid);
-  // TODO fallback to [0, 0] e.g. for sphere, equator?
   // TODO mixed geometries
-  return d3_geo_centroidW ? [
+  var m;
-    Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees,
+  if (d3_geo_centroidW &&
-    Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / Math.sqrt(d3_geo_centroidX * d3_geo_centroidX + d3_geo_centroidY * d3_geo_centroidY + d3_geo_centroidZ * d3_geo_centroidZ)))) * d3_degrees
+      Math.abs(m = Math.sqrt(d3_geo_centroidX * d3_geo_centroidX + d3_geo_centroidY * d3_geo_centroidY + d3_geo_centroidZ * d3_geo_centroidZ)) > ε) {
-  ] : null;
+    return [
+      Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees,
+      Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / m))) * d3_degrees
+    ];
+  }
 };
 
 var d3_geo_centroidW,

test/geo/centroid-test.js

@@ -13,9 +13,21 @@ suite.addBatch({
     "Point": function(centroid) {
       assert.deepEqual(centroid({type: "Point", coordinates: [0, 0]}), [0, 0]);
     },
-    "MultiPoint": function(centroid) {
+    "MultiPoint": {
-      assert.inDelta(centroid({type: "MultiPoint", coordinates: [[0, 0], [1, 2]]}), [0.499847, 1.000038], 1e-6);
+      "": function(centroid) {
-      assert.deepEqual(centroid({type: "MultiPoint", coordinates: [[179, 0], [-179, 0]]}), [180, 0]);
+        assert.inDelta(centroid({type: "MultiPoint", coordinates: [[0, 0], [1, 2]]}), [0.499847, 1.000038], 1e-6);
+      },
+      "antimeridian": function(centroid) {
+        assert.deepEqual(centroid({type: "MultiPoint", coordinates: [[179, 0], [-179, 0]]}), [180, 0]);
+      },
+      "rings": {
+        "equator": function(centroid) {
+          assert.isUndefined(centroid({type: "MultiPoint", coordinates: [[0, 0], [90, 0], [180, 0], [-90, 0]]}));
+        },
+        "polar": function(centroid) {
+          assert.isUndefined(centroid({type: "MultiPoint", coordinates: [[0, 0], [0, 90], [180, 0], [0, -90]]}));
+        }
+      }
     },
     "LineString": function(centroid) {
       assert.inDelta(centroid({type: "LineString", coordinates: [[0, 0], [1, 0]]}), [.5, 0], 1e-6);
@@ -25,8 +37,8 @@ suite.addBatch({
       assert.inDelta(centroid({type: "LineString", coordinates: [[-60, -1], [60, 1]]}), [0, 0], 1e-6);
       assert.inDelta(centroid({type: "LineString", coordinates: [[179, -1], [-179, 1]]}), [180, 0], 1e-6);
       assert.inDelta(centroid({type: "LineString", coordinates: [[-179, 0], [0, 0], [179, 0]]}), [0, 0], 1e-6);
-      assert.inDelta(centroid({type: "LineString", coordinates: [[0, -90], [0, 90]]}), [0, 0], 1e-6);
+      assert.inDelta(centroid({type: "LineString", coordinates: [[-180, -90], [0, 0], [0, 90]]}), [0, 0], 1e-6);
-      assert.inDelta(centroid({type: "LineString", coordinates: [[-180, -90], [0, 90]]}), [-90, 0], 1e-6);
+      assert.isUndefined(centroid({type: "LineString", coordinates: [[0, -90], [0, 90]]}));
     },
     "MultiLineString": function(centroid) {
       assert.inDelta(centroid({type: "MultiLineString", coordinates: [[[0, 0], [0, 2]]]}), [0, 1], 1e-6);