diff --git a/d3.js b/d3.js
index 33670336..b9b90991 100644
--- a/d3.js
+++ b/d3.js
@@ -1298,12 +1298,12 @@ d3 = function() {
     }
     return d3_rgb(vv(h + 120), vv(h), vv(h - 120));
   }
-  var π = Math.PI, ε = 1e-6, d3_radians = π / 180, d3_degrees = 180 / π;
+  var π = Math.PI, ε = 1e-6, ε2 = ε * ε, d3_radians = π / 180, d3_degrees = 180 / π;
   function d3_sgn(x) {
     return x > 0 ? 1 : x < 0 ? -1 : 0;
   }
   function d3_acos(x) {
-    return Math.acos(Math.max(-1, Math.min(1, x)));
+    return x > 1 ? 0 : x < -1 ? π : Math.acos(x);
   }
   function d3_asin(x) {
     return x > 1 ? π / 2 : x < -1 ? -π / 2 : Math.asin(x);
@@ -2170,7 +2170,7 @@ d3 = function() {
     d[2] /= l;
   }
   function d3_geo_spherical(cartesian) {
-    return [ Math.atan2(cartesian[1], cartesian[0]), Math.asin(Math.max(-1, Math.min(1, cartesian[2]))) ];
+    return [ Math.atan2(cartesian[1], cartesian[0]), d3_asin(cartesian[2]) ];
   }
   function d3_geo_sphericalEqual(a, b) {
     return Math.abs(a[0] - b[0]) < ε && Math.abs(a[1] - b[1]) < ε;
@@ -2304,27 +2304,24 @@ d3 = function() {
     };
   }();
   d3.geo.centroid = function(object) {
-    d3_geo_centroidDimension = d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
+    d3_geo_centroidW0 = d3_geo_centroidW1 = d3_geo_centroidX0 = d3_geo_centroidY0 = d3_geo_centroidZ0 = d3_geo_centroidX1 = d3_geo_centroidY1 = d3_geo_centroidZ1 = d3_geo_centroidX2 = d3_geo_centroidY2 = d3_geo_centroidZ2 = 0;
     d3.geo.stream(object, d3_geo_centroid);
-    var m;
-    return 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 ? [ Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees, Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / m))) * d3_degrees ] : [ NaN, NaN ];
+    var x = d3_geo_centroidX2, y = d3_geo_centroidY2, z = d3_geo_centroidZ2, m = x * x + y * y + z * z;
+    if (m < ε2) {
+      x = d3_geo_centroidX1, y = d3_geo_centroidY1, z = d3_geo_centroidZ1;
+      if (d3_geo_centroidW1 < ε) x = d3_geo_centroidX0, y = d3_geo_centroidY0, z = d3_geo_centroidZ0;
+      m = x * x + y * y + z * z;
+      if (m < ε2) return [ NaN, NaN ];
+    }
+    return [ Math.atan2(y, x) * d3_degrees, d3_asin(z / Math.sqrt(m)) * d3_degrees ];
   };
-  var d3_geo_centroidDimension, d3_geo_centroidW, d3_geo_centroidX, d3_geo_centroidY, d3_geo_centroidZ;
+  var d3_geo_centroidW0, d3_geo_centroidW1, d3_geo_centroidX0, d3_geo_centroidY0, d3_geo_centroidZ0, d3_geo_centroidX1, d3_geo_centroidY1, d3_geo_centroidZ1, d3_geo_centroidX2, d3_geo_centroidY2, d3_geo_centroidZ2;
   var d3_geo_centroid = {
-    sphere: function() {
-      if (d3_geo_centroidDimension < 2) {
-        d3_geo_centroidDimension = 2;
-        d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-      }
-    },
+    sphere: d3_noop,
     point: d3_geo_centroidPoint,
     lineStart: d3_geo_centroidLineStart,
     lineEnd: d3_geo_centroidLineEnd,
     polygonStart: function() {
-      if (d3_geo_centroidDimension < 2) {
-        d3_geo_centroidDimension = 2;
-        d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-      }
       d3_geo_centroid.lineStart = d3_geo_centroidRingStart;
     },
     polygonEnd: function() {
@@ -2332,36 +2329,18 @@ d3 = function() {
     }
   };
   function d3_geo_centroidPoint(λ, φ) {
-    if (d3_geo_centroidDimension) return;
-    ++d3_geo_centroidW;
     λ *= d3_radians;
     var cosφ = Math.cos(φ *= d3_radians);
-    d3_geo_centroidX += (cosφ * Math.cos(λ) - d3_geo_centroidX) / d3_geo_centroidW;
-    d3_geo_centroidY += (cosφ * Math.sin(λ) - d3_geo_centroidY) / d3_geo_centroidW;
-    d3_geo_centroidZ += (Math.sin(φ) - d3_geo_centroidZ) / d3_geo_centroidW;
+    d3_geo_centroidPointXYZ(cosφ * Math.cos(λ), cosφ * Math.sin(λ), Math.sin(φ));
   }
-  function d3_geo_centroidRingStart() {
-    var λ00, φ00;
-    d3_geo_centroidDimension = 1;
-    d3_geo_centroidLineStart();
-    d3_geo_centroidDimension = 2;
-    var linePoint = d3_geo_centroid.point;
-    d3_geo_centroid.point = function(λ, φ) {
-      linePoint(λ00 = λ, φ00 = φ);
-    };
-    d3_geo_centroid.lineEnd = function() {
-      d3_geo_centroid.point(λ00, φ00);
-      d3_geo_centroidLineEnd();
-      d3_geo_centroid.lineEnd = d3_geo_centroidLineEnd;
-    };
+  function d3_geo_centroidPointXYZ(x, y, z) {
+    ++d3_geo_centroidW0;
+    d3_geo_centroidX0 += (x - d3_geo_centroidX0) / d3_geo_centroidW0;
+    d3_geo_centroidY0 += (y - d3_geo_centroidY0) / d3_geo_centroidW0;
+    d3_geo_centroidZ0 += (z - d3_geo_centroidZ0) / d3_geo_centroidW0;
   }
   function d3_geo_centroidLineStart() {
     var x0, y0, z0;
-    if (d3_geo_centroidDimension > 1) return;
-    if (d3_geo_centroidDimension < 1) {
-      d3_geo_centroidDimension = 1;
-      d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-    }
     d3_geo_centroid.point = function(λ, φ) {
       λ *= d3_radians;
       var cosφ = Math.cos(φ *= d3_radians);
@@ -2369,19 +2348,51 @@ d3 = function() {
       y0 = cosφ * Math.sin(λ);
       z0 = Math.sin(φ);
       d3_geo_centroid.point = nextPoint;
+      d3_geo_centroidPointXYZ(x0, y0, z0);
     };
     function nextPoint(λ, φ) {
       λ *= d3_radians;
       var cosφ = Math.cos(φ *= d3_radians), x = cosφ * Math.cos(λ), y = cosφ * Math.sin(λ), z = Math.sin(φ), w = Math.atan2(Math.sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z);
-      d3_geo_centroidW += w;
-      d3_geo_centroidX += w * (x0 + (x0 = x));
-      d3_geo_centroidY += w * (y0 + (y0 = y));
-      d3_geo_centroidZ += w * (z0 + (z0 = z));
+      d3_geo_centroidW1 += w;
+      d3_geo_centroidX1 += w * (x0 + (x0 = x));
+      d3_geo_centroidY1 += w * (y0 + (y0 = y));
+      d3_geo_centroidZ1 += w * (z0 + (z0 = z));
+      d3_geo_centroidPointXYZ(x0, y0, z0);
     }
   }
   function d3_geo_centroidLineEnd() {
     d3_geo_centroid.point = d3_geo_centroidPoint;
   }
+  function d3_geo_centroidRingStart() {
+    var λ00, φ00, x0, y0, z0;
+    d3_geo_centroid.point = function(λ, φ) {
+      λ00 = λ, φ00 = φ;
+      d3_geo_centroid.point = nextPoint;
+      λ *= d3_radians;
+      var cosφ = Math.cos(φ *= d3_radians);
+      x0 = cosφ * Math.cos(λ);
+      y0 = cosφ * Math.sin(λ);
+      z0 = Math.sin(φ);
+      d3_geo_centroidPointXYZ(x0, y0, z0);
+    };
+    d3_geo_centroid.lineEnd = function() {
+      nextPoint(λ00, φ00);
+      d3_geo_centroid.lineEnd = d3_geo_centroidLineEnd;
+      d3_geo_centroid.point = d3_geo_centroidPoint;
+    };
+    function nextPoint(λ, φ) {
+      λ *= d3_radians;
+      var cosφ = Math.cos(φ *= d3_radians), x = cosφ * Math.cos(λ), y = cosφ * Math.sin(λ), z = Math.sin(φ), cx = y0 * z - z0 * y, cy = z0 * x - x0 * z, cz = x0 * y - y0 * x, m = Math.sqrt(cx * cx + cy * cy + cz * cz), u = x0 * x + y0 * y + z0 * z, v = m && -d3_acos(u) / m, w = Math.atan2(m, u);
+      d3_geo_centroidX2 += v * cx;
+      d3_geo_centroidY2 += v * cy;
+      d3_geo_centroidZ2 += v * cz;
+      d3_geo_centroidW1 += w;
+      d3_geo_centroidX1 += w * (x0 + (x0 = x));
+      d3_geo_centroidY1 += w * (y0 + (y0 = y));
+      d3_geo_centroidZ1 += w * (z0 + (z0 = z));
+      d3_geo_centroidPointXYZ(x0, y0, z0);
+    }
+  }
   function d3_true() {
     return true;
   }
@@ -3146,29 +3157,22 @@ d3 = function() {
     }
   };
   function d3_geo_pathCentroidPoint(x, y) {
-    if (d3_geo_centroidDimension) return;
-    d3_geo_centroidX += x;
-    d3_geo_centroidY += y;
-    ++d3_geo_centroidZ;
+    d3_geo_centroidX0 += x;
+    d3_geo_centroidY0 += y;
+    ++d3_geo_centroidZ0;
   }
   function d3_geo_pathCentroidLineStart() {
     var x0, y0;
-    if (d3_geo_centroidDimension !== 1) {
-      if (d3_geo_centroidDimension < 1) {
-        d3_geo_centroidDimension = 1;
-        d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-      } else return;
-    }
     d3_geo_pathCentroid.point = function(x, y) {
       d3_geo_pathCentroid.point = nextPoint;
-      x0 = x, y0 = y;
+      d3_geo_pathCentroidPoint(x0 = x, y0 = y);
     };
     function nextPoint(x, y) {
       var dx = x - x0, dy = y - y0, z = Math.sqrt(dx * dx + dy * dy);
-      d3_geo_centroidX += z * (x0 + x) / 2;
-      d3_geo_centroidY += z * (y0 + y) / 2;
-      d3_geo_centroidZ += z;
-      x0 = x, y0 = y;
+      d3_geo_centroidX1 += z * (x0 + x) / 2;
+      d3_geo_centroidY1 += z * (y0 + y) / 2;
+      d3_geo_centroidZ1 += z;
+      d3_geo_pathCentroidPoint(x0 = x, y0 = y);
     }
   }
   function d3_geo_pathCentroidLineEnd() {
@@ -3176,20 +3180,20 @@ d3 = function() {
   }
   function d3_geo_pathCentroidRingStart() {
     var x00, y00, x0, y0;
-    if (d3_geo_centroidDimension < 2) {
-      d3_geo_centroidDimension = 2;
-      d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-    }
     d3_geo_pathCentroid.point = function(x, y) {
       d3_geo_pathCentroid.point = nextPoint;
-      x00 = x0 = x, y00 = y0 = y;
+      d3_geo_pathCentroidPoint(x00 = x0 = x, y00 = y0 = y);
     };
     function nextPoint(x, y) {
-      var z = y0 * x - x0 * y;
-      d3_geo_centroidX += z * (x0 + x);
-      d3_geo_centroidY += z * (y0 + y);
-      d3_geo_centroidZ += z * 3;
-      x0 = x, y0 = y;
+      var dx = x - x0, dy = y - y0, z = Math.sqrt(dx * dx + dy * dy);
+      d3_geo_centroidX1 += z * (x0 + x) / 2;
+      d3_geo_centroidY1 += z * (y0 + y) / 2;
+      d3_geo_centroidZ1 += z;
+      z = y0 * x - x0 * y;
+      d3_geo_centroidX2 += z * (x0 + x);
+      d3_geo_centroidY2 += z * (y0 + y);
+      d3_geo_centroidZ2 += z * 3;
+      d3_geo_pathCentroidPoint(x0 = x, y0 = y);
     }
     d3_geo_pathCentroid.lineEnd = function() {
       nextPoint(x00, y00);
@@ -3328,9 +3332,9 @@ d3 = function() {
       return d3_geo_pathAreaSum;
     };
     path.centroid = function(object) {
-      d3_geo_centroidDimension = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
+      d3_geo_centroidX0 = d3_geo_centroidY0 = d3_geo_centroidZ0 = d3_geo_centroidX1 = d3_geo_centroidY1 = d3_geo_centroidZ1 = d3_geo_centroidX2 = d3_geo_centroidY2 = d3_geo_centroidZ2 = 0;
       d3.geo.stream(object, projectStream(d3_geo_pathCentroid));
-      return d3_geo_centroidZ ? [ d3_geo_centroidX / d3_geo_centroidZ, d3_geo_centroidY / d3_geo_centroidZ ] : undefined;
+      return d3_geo_centroidZ2 ? [ d3_geo_centroidX2 / d3_geo_centroidZ2, d3_geo_centroidY2 / d3_geo_centroidZ2 ] : d3_geo_centroidZ1 ? [ d3_geo_centroidX1 / d3_geo_centroidZ1, d3_geo_centroidY1 / d3_geo_centroidZ1 ] : d3_geo_centroidZ0 ? [ d3_geo_centroidX0 / d3_geo_centroidZ0, d3_geo_centroidY0 / d3_geo_centroidZ0 ] : [ NaN, NaN ];
     };
     path.bounds = function(object) {
       d3_geo_pathBoundsX1 = d3_geo_pathBoundsY1 = -(d3_geo_pathBoundsX0 = d3_geo_pathBoundsY0 = Infinity);
@@ -3531,11 +3535,11 @@ d3 = function() {
     var cosδφ = Math.cos(δφ), sinδφ = Math.sin(δφ), cosδγ = Math.cos(δγ), sinδγ = Math.sin(δγ);
     function rotation(λ, φ) {
       var cosφ = Math.cos(φ), x = Math.cos(λ) * cosφ, y = Math.sin(λ) * cosφ, z = Math.sin(φ), k = z * cosδφ + x * sinδφ;
-      return [ Math.atan2(y * cosδγ - k * sinδγ, x * cosδφ - z * sinδφ), Math.asin(Math.max(-1, Math.min(1, k * cosδγ + y * sinδγ))) ];
+      return [ Math.atan2(y * cosδγ - k * sinδγ, x * cosδφ - z * sinδφ), d3_asin(k * cosδγ + y * sinδγ) ];
     }
     rotation.invert = function(λ, φ) {
       var cosφ = Math.cos(φ), x = Math.cos(λ) * cosφ, y = Math.sin(λ) * cosφ, z = Math.sin(φ), k = z * cosδγ - y * sinδγ;
-      return [ Math.atan2(y * cosδγ + z * sinδγ, x * cosδφ + k * sinδφ), Math.asin(Math.max(-1, Math.min(1, k * cosδφ - x * sinδφ))) ];
+      return [ Math.atan2(y * cosδγ + z * sinδγ, x * cosδφ + k * sinδφ), d3_asin(k * cosδφ - x * sinδφ) ];
     };
     return rotation;
   }
diff --git a/d3.min.js b/d3.min.js
index f64c9450..ebadc83c 100644
--- a/d3.min.js
+++ b/d3.min.js
@@ -1,5 +1,5 @@
-d3=function(){function n(n){return null!=n&&!isNaN(n)}function t(n){return n.length}function e(n){for(var t=1;n*t%1;)t*=10;return t}function r(n,t){try{for(var e in t)Object.defineProperty(n.prototype,e,{value:t[e],enumerable:!1})}catch(r){n.prototype=t}}function i(){}function u(){}function a(n,t,e){return function(){var r=e.apply(t,arguments);return r===t?n:r}}function o(){}function c(n){function t(){for(var t,r=e,i=-1,u=r.length;++i<u;)(t=r[i].on)&&t.apply(this,arguments);return n}var e=[],r=new i;return t.on=function(t,i){var u,a=r.get(t);return arguments.length<2?a&&a.on:(a&&(a.on=null,e=e.slice(0,u=e.indexOf(a)).concat(e.slice(u+1)),r.remove(t)),i&&e.push(r.set(t,{on:i})),n)},t}function l(){ua.event.stopPropagation(),ua.event.preventDefault()}function f(){for(var n,t=ua.event;n=t.sourceEvent;)t=n;return t}function s(n,t){function e(){n.on(t,null)}n.on(t,function(){l(),e()},!0),setTimeout(e,0)}function h(n){for(var t=new o,e=0,r=arguments.length;++e<r;)t[arguments[e]]=c(t);return 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diff --git a/src/geo/centroid.js b/src/geo/centroid.js
index e68343cb..b764e9fd 100644
--- a/src/geo/centroid.js
+++ b/src/geo/centroid.js
@@ -1,37 +1,51 @@
+import "../core/noop";
 import "../math/trigonometry";
 import "geo";
 import "stream";
 
 d3.geo.centroid = function(object) {
-  d3_geo_centroidDimension = d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
+  d3_geo_centroidW0 = d3_geo_centroidW1 =
+  d3_geo_centroidX0 = d3_geo_centroidY0 = d3_geo_centroidZ0 =
+  d3_geo_centroidX1 = d3_geo_centroidY1 = d3_geo_centroidZ1 =
+  d3_geo_centroidX2 = d3_geo_centroidY2 = d3_geo_centroidZ2 = 0;
   d3.geo.stream(object, d3_geo_centroid);
-  var m;
-  return 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
-      ? [Math.atan2(d3_geo_centroidY, d3_geo_centroidX) * d3_degrees, Math.asin(Math.max(-1, Math.min(1, d3_geo_centroidZ / m))) * d3_degrees]
-      : [NaN, NaN];
+
+  var x = d3_geo_centroidX2,
+      y = d3_geo_centroidY2,
+      z = d3_geo_centroidZ2,
+      m = x * x + y * y + z * z;
+
+  // If the area-weighted centroid is undefined, fall back to length-weighted centroid.
+  if (m < ε2) {
+    x = d3_geo_centroidX1, y = d3_geo_centroidY1, z = d3_geo_centroidZ1;
+    // If the feature has zero length, fall back to arithmetic mean of point vectors.
+    if (d3_geo_centroidW1 < ε) x = d3_geo_centroidX0, y = d3_geo_centroidY0, z = d3_geo_centroidZ0;
+    m = x * x + y * y + z * z;
+    // If the feature still has an undefined centroid, then return.
+    if (m < ε2) return [NaN, NaN];
+  }
+
+  return [Math.atan2(y, x) * d3_degrees, d3_asin(z / Math.sqrt(m)) * d3_degrees];
 };
 
-var d3_geo_centroidDimension,
-    d3_geo_centroidW,
-    d3_geo_centroidX,
-    d3_geo_centroidY,
-    d3_geo_centroidZ;
+var d3_geo_centroidW0,
+    d3_geo_centroidW1,
+    d3_geo_centroidX0,
+    d3_geo_centroidY0,
+    d3_geo_centroidZ0,
+    d3_geo_centroidX1,
+    d3_geo_centroidY1,
+    d3_geo_centroidZ1,
+    d3_geo_centroidX2,
+    d3_geo_centroidY2,
+    d3_geo_centroidZ2;
 
 var d3_geo_centroid = {
-  sphere: function() {
-    if (d3_geo_centroidDimension < 2) {
-      d3_geo_centroidDimension = 2;
-      d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-    }
-  },
+  sphere: d3_noop,
   point: d3_geo_centroidPoint,
   lineStart: d3_geo_centroidLineStart,
   lineEnd: d3_geo_centroidLineEnd,
   polygonStart: function() {
-    if (d3_geo_centroidDimension < 2) {
-      d3_geo_centroidDimension = 2;
-      d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-    }
     d3_geo_centroid.lineStart = d3_geo_centroidRingStart;
   },
   polygonEnd: function() {
@@ -41,42 +55,21 @@ var d3_geo_centroid = {
 
 // Arithmetic mean of Cartesian vectors.
 function d3_geo_centroidPoint(λ, φ) {
-  if (d3_geo_centroidDimension) return;
-  ++d3_geo_centroidW;
   λ *= d3_radians;
   var cosφ = Math.cos(φ *= d3_radians);
-  d3_geo_centroidX += (cosφ * Math.cos(λ) - d3_geo_centroidX) / d3_geo_centroidW;
-  d3_geo_centroidY += (cosφ * Math.sin(λ) - d3_geo_centroidY) / d3_geo_centroidW;
-  d3_geo_centroidZ += (Math.sin(φ) - d3_geo_centroidZ) / d3_geo_centroidW;
+  d3_geo_centroidPointXYZ(cosφ * Math.cos(λ), cosφ * Math.sin(λ), Math.sin(φ));
 }
 
-function d3_geo_centroidRingStart() {
-  var λ00, φ00; // first point
-
-  d3_geo_centroidDimension = 1;
-  d3_geo_centroidLineStart();
-  d3_geo_centroidDimension = 2;
-
-  var linePoint = d3_geo_centroid.point;
-  d3_geo_centroid.point = function(λ, φ) {
-    linePoint(λ00 = λ, φ00 = φ);
-  };
-  d3_geo_centroid.lineEnd = function() {
-    d3_geo_centroid.point(λ00, φ00);
-    d3_geo_centroidLineEnd();
-    d3_geo_centroid.lineEnd = d3_geo_centroidLineEnd;
-  };
+function d3_geo_centroidPointXYZ(x, y, z) {
+  ++d3_geo_centroidW0;
+  d3_geo_centroidX0 += (x - d3_geo_centroidX0) / d3_geo_centroidW0;
+  d3_geo_centroidY0 += (y - d3_geo_centroidY0) / d3_geo_centroidW0;
+  d3_geo_centroidZ0 += (z - d3_geo_centroidZ0) / d3_geo_centroidW0;
 }
 
 function d3_geo_centroidLineStart() {
   var x0, y0, z0; // previous point
 
-  if (d3_geo_centroidDimension > 1) return;
-  if (d3_geo_centroidDimension < 1) {
-    d3_geo_centroidDimension = 1;
-    d3_geo_centroidW = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-  }
-
   d3_geo_centroid.point = function(λ, φ) {
     λ *= d3_radians;
     var cosφ = Math.cos(φ *= d3_radians);
@@ -84,6 +77,7 @@ function d3_geo_centroidLineStart() {
     y0 = cosφ * Math.sin(λ);
     z0 = Math.sin(φ);
     d3_geo_centroid.point = nextPoint;
+    d3_geo_centroidPointXYZ(x0, y0, z0);
   };
 
   function nextPoint(λ, φ) {
@@ -95,13 +89,61 @@ function d3_geo_centroidLineStart() {
         w = Math.atan2(
           Math.sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w),
           x0 * x + y0 * y + z0 * z);
-    d3_geo_centroidW += w;
-    d3_geo_centroidX += w * (x0 + (x0 = x));
-    d3_geo_centroidY += w * (y0 + (y0 = y));
-    d3_geo_centroidZ += w * (z0 + (z0 = z));
+    d3_geo_centroidW1 += w;
+    d3_geo_centroidX1 += w * (x0 + (x0 = x));
+    d3_geo_centroidY1 += w * (y0 + (y0 = y));
+    d3_geo_centroidZ1 += w * (z0 + (z0 = z));
+    d3_geo_centroidPointXYZ(x0, y0, z0);
   }
 }
 
 function d3_geo_centroidLineEnd() {
   d3_geo_centroid.point = d3_geo_centroidPoint;
 }
+
+// See J. E. Brock, The Inertia Tensor for a Spherical Triangle,
+// J. Applied Mechanics 42, 239 (1975).
+function d3_geo_centroidRingStart() {
+  var λ00, φ00, // first point
+      x0, y0, z0; // previous point
+
+  d3_geo_centroid.point = function(λ, φ) {
+    λ00 = λ, φ00 = φ;
+    d3_geo_centroid.point = nextPoint;
+    λ *= d3_radians;
+    var cosφ = Math.cos(φ *= d3_radians);
+    x0 = cosφ * Math.cos(λ);
+    y0 = cosφ * Math.sin(λ);
+    z0 = Math.sin(φ);
+    d3_geo_centroidPointXYZ(x0, y0, z0);
+  };
+
+  d3_geo_centroid.lineEnd = function() {
+    nextPoint(λ00, φ00);
+    d3_geo_centroid.lineEnd = d3_geo_centroidLineEnd;
+    d3_geo_centroid.point = d3_geo_centroidPoint;
+  };
+
+  function nextPoint(λ, φ) {
+    λ *= d3_radians;
+    var cosφ = Math.cos(φ *= d3_radians),
+        x = cosφ * Math.cos(λ),
+        y = cosφ * Math.sin(λ),
+        z = Math.sin(φ),
+        cx = y0 * z - z0 * y,
+        cy = z0 * x - x0 * z,
+        cz = x0 * y - y0 * x,
+        m = Math.sqrt(cx * cx + cy * cy + cz * cz),
+        u = x0 * x + y0 * y + z0 * z,
+        v = m && -d3_acos(u) / m, // area weight
+        w = Math.atan2(m, u); // line weight
+    d3_geo_centroidX2 += v * cx;
+    d3_geo_centroidY2 += v * cy;
+    d3_geo_centroidZ2 += v * cz;
+    d3_geo_centroidW1 += w;
+    d3_geo_centroidX1 += w * (x0 + (x0 = x));
+    d3_geo_centroidY1 += w * (y0 + (y0 = y));
+    d3_geo_centroidZ1 += w * (z0 + (z0 = z));
+    d3_geo_centroidPointXYZ(x0, y0, z0);
+  }
+}
diff --git a/src/geo/path-centroid.js b/src/geo/path-centroid.js
index e7bf36fe..cda58970 100644
--- a/src/geo/path-centroid.js
+++ b/src/geo/path-centroid.js
@@ -22,33 +22,25 @@ var d3_geo_pathCentroid = {
 };
 
 function d3_geo_pathCentroidPoint(x, y) {
-  if (d3_geo_centroidDimension) return;
-  d3_geo_centroidX += x;
-  d3_geo_centroidY += y;
-  ++d3_geo_centroidZ;
+  d3_geo_centroidX0 += x;
+  d3_geo_centroidY0 += y;
+  ++d3_geo_centroidZ0;
 }
 
 function d3_geo_pathCentroidLineStart() {
   var x0, y0;
 
-  if (d3_geo_centroidDimension !== 1) {
-    if (d3_geo_centroidDimension < 1) {
-      d3_geo_centroidDimension = 1;
-      d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-    } else return;
-  }
-
   d3_geo_pathCentroid.point = function(x, y) {
     d3_geo_pathCentroid.point = nextPoint;
-    x0 = x, y0 = y;
+    d3_geo_pathCentroidPoint(x0 = x, y0 = y);
   };
 
   function nextPoint(x, y) {
     var dx = x - x0, dy = y - y0, z = Math.sqrt(dx * dx + dy * dy);
-    d3_geo_centroidX += z * (x0 + x) / 2;
-    d3_geo_centroidY += z * (y0 + y) / 2;
-    d3_geo_centroidZ += z;
-    x0 = x, y0 = y;
+    d3_geo_centroidX1 += z * (x0 + x) / 2;
+    d3_geo_centroidY1 += z * (y0 + y) / 2;
+    d3_geo_centroidZ1 += z;
+    d3_geo_pathCentroidPoint(x0 = x, y0 = y);
   }
 }
 
@@ -59,24 +51,24 @@ function d3_geo_pathCentroidLineEnd() {
 function d3_geo_pathCentroidRingStart() {
   var x00, y00, x0, y0;
 
-  if (d3_geo_centroidDimension < 2) {
-    d3_geo_centroidDimension = 2;
-    d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
-  }
-
   // For the first point, …
   d3_geo_pathCentroid.point = function(x, y) {
     d3_geo_pathCentroid.point = nextPoint;
-    x00 = x0 = x, y00 = y0 = y;
+    d3_geo_pathCentroidPoint(x00 = x0 = x, y00 = y0 = y);
   };
 
   // For subsequent points, …
   function nextPoint(x, y) {
-    var z = y0 * x - x0 * y;
-    d3_geo_centroidX += z * (x0 + x);
-    d3_geo_centroidY += z * (y0 + y);
-    d3_geo_centroidZ += z * 3;
-    x0 = x, y0 = y;
+    var dx = x - x0, dy = y - y0, z = Math.sqrt(dx * dx + dy * dy);
+    d3_geo_centroidX1 += z * (x0 + x) / 2;
+    d3_geo_centroidY1 += z * (y0 + y) / 2;
+    d3_geo_centroidZ1 += z;
+
+    z = y0 * x - x0 * y;
+    d3_geo_centroidX2 += z * (x0 + x);
+    d3_geo_centroidY2 += z * (y0 + y);
+    d3_geo_centroidZ2 += z * 3;
+    d3_geo_pathCentroidPoint(x0 = x, y0 = y);
   }
 
   // For the last point, return to the start.
diff --git a/src/geo/path.js b/src/geo/path.js
index 25e0f99c..bf424805 100644
--- a/src/geo/path.js
+++ b/src/geo/path.js
@@ -38,9 +38,14 @@ d3.geo.path = function() {
   };
 
   path.centroid = function(object) {
-    d3_geo_centroidDimension = d3_geo_centroidX = d3_geo_centroidY = d3_geo_centroidZ = 0;
+    d3_geo_centroidX0 = d3_geo_centroidY0 = d3_geo_centroidZ0 =
+    d3_geo_centroidX1 = d3_geo_centroidY1 = d3_geo_centroidZ1 =
+    d3_geo_centroidX2 = d3_geo_centroidY2 = d3_geo_centroidZ2 = 0;
     d3.geo.stream(object, projectStream(d3_geo_pathCentroid));
-    return d3_geo_centroidZ ? [d3_geo_centroidX / d3_geo_centroidZ, d3_geo_centroidY / d3_geo_centroidZ] : undefined;
+    return d3_geo_centroidZ2 ? [d3_geo_centroidX2 / d3_geo_centroidZ2, d3_geo_centroidY2 / d3_geo_centroidZ2]
+        : d3_geo_centroidZ1 ? [d3_geo_centroidX1 / d3_geo_centroidZ1, d3_geo_centroidY1 / d3_geo_centroidZ1]
+        : d3_geo_centroidZ0 ? [d3_geo_centroidX0 / d3_geo_centroidZ0, d3_geo_centroidY0 / d3_geo_centroidZ0]
+        : [NaN, NaN];
   };
 
   path.bounds = function(object) {
diff --git a/src/geo/rotation.js b/src/geo/rotation.js
index 68d65532..8c399486 100644
--- a/src/geo/rotation.js
+++ b/src/geo/rotation.js
@@ -52,7 +52,7 @@ function d3_geo_rotationφγ(δφ, δγ) {
         k = z * cosδφ + x * sinδφ;
     return [
       Math.atan2(y * cosδγ - k * sinδγ, x * cosδφ - z * sinδφ),
-      Math.asin(Math.max(-1, Math.min(1, k * cosδγ + y * sinδγ)))
+      d3_asin(k * cosδγ + y * sinδγ)
     ];
   }
 
@@ -64,7 +64,7 @@ function d3_geo_rotationφγ(δφ, δγ) {
         k = z * cosδγ - y * sinδγ;
     return [
       Math.atan2(y * cosδγ + z * sinδγ, x * cosδφ + k * sinδφ),
-      Math.asin(Math.max(-1, Math.min(1, k * cosδφ - x * sinδφ)))
+      d3_asin(k * cosδφ - x * sinδφ)
     ];
   };
 
diff --git a/src/geo/spherical.js b/src/geo/spherical.js
index f5908fe7..50e4838c 100644
--- a/src/geo/spherical.js
+++ b/src/geo/spherical.js
@@ -3,7 +3,7 @@ import "../math/trigonometry";
 function d3_geo_spherical(cartesian) {
   return [
     Math.atan2(cartesian[1], cartesian[0]),
-    Math.asin(Math.max(-1, Math.min(1, cartesian[2])))
+    d3_asin(cartesian[2])
   ];
 }
 
diff --git a/src/math/trigonometry.js b/src/math/trigonometry.js
index ac00181b..23cd1974 100644
--- a/src/math/trigonometry.js
+++ b/src/math/trigonometry.js
@@ -1,5 +1,6 @@
 var π = Math.PI,
     ε = 1e-6,
+    ε2 = ε * ε,
     d3_radians = π / 180,
     d3_degrees = 180 / π;
 
@@ -8,7 +9,7 @@ function d3_sgn(x) {
 }
 
 function d3_acos(x) {
-  return Math.acos(Math.max(-1, Math.min(1, x)));
+  return x > 1 ? 0 : x < -1 ? π : Math.acos(x);
 }
 
 function d3_asin(x) {
diff --git a/test/geo/centroid-test.js b/test/geo/centroid-test.js
index b0074ae2..39ce203d 100644
--- a/test/geo/centroid-test.js
+++ b/test/geo/centroid-test.js
@@ -52,28 +52,86 @@ suite.addBatch({
       assert.inDelta(centroid({type: "MultiLineString", coordinates: [[[0, 0], [0, 2]]]}), [0, 1], 1e-6);
     },
 
-    "an empty line is treated as a point": function(centroid) {
-      assert.inDelta(centroid({type: "LineString", coordinates: [[1, 1], [1, 1]]}), [1, 1], 1e-6); // TODO
-      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Point", coordinates: [0, 0]}, {type: "LineString", coordinates: [[1, 2], [1, 2]]}]}), [0.499847, 1.000038], 1e-6);
+    "a line of zero length is treated as points": function(centroid) {
+      assert.inDelta(centroid({type: "LineString", coordinates: [[1, 1], [1, 1]]}), [1, 1], 1e-6);
+      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Point", coordinates: [0, 0]}, {type: "LineString", coordinates: [[1, 2], [1, 2]]}]}), [0.666534, 1.333408], 1e-6);
     },
 
-    "an empty polygon is treated as a point": function(centroid) {
-      assert.inDelta(centroid({type: "Polygon", coordinates: [[[1, 1], [1, 1], [1, 1], [1, 1]]]}), [1, 1], 1e-6); // TODO
-      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Point", coordinates: [0, 0]}, {type: "Polygon", coordinates: [[[1, 2], [1, 2], [1, 2], [1, 2]]]}]}), [0.499847, 1.000038], 1e-6);
+    "an empty polygon with non-zero extent is treated as a line": function(centroid) {
+      assert.inDelta(centroid({type: "Polygon", coordinates: [[[1, 1], [2, 1], [3, 1], [2, 1], [1, 1]]]}), [2, 1.000076], 1e-6);
+      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Point", coordinates: [0, 0]}, {type: "Polygon", coordinates: [[[1, 2], [1, 2], [1, 2], [1, 2]]]}]}), [0.799907, 1.600077], 1e-6);
+    },
+
+    "an empty polygon with zero extent is treated as a point": function(centroid) {
+      assert.inDelta(centroid({type: "Polygon", coordinates: [[[1, 1], [1, 1], [1, 1], [1, 1]]]}), [1, 1], 1e-6);
+      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Point", coordinates: [0, 0]}, {type: "Polygon", coordinates: [[[1, 2], [1, 2], [1, 2], [1, 2]]]}]}), [0.799907, 1.600077], 1e-6);
+    },
+
+    "the centroid of the equator is ambiguous": function(centroid) {
+      assert.ok(centroid({type: "LineString", coordinates: [[0, 0], [120, 0], [-120, 0], [0, 0]]}).every(isNaN));
     },
 
-    // TODO Don’t treat a polygon as a line string.
     "the centroid of a polygon is the (spherical) average of its surface": function(centroid) {
       assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -90], [0, 0], [0, 90], [1, 0], [0, -90]]]}), [.5, 0], 1e-6);
-      assert.inDelta(centroid(_.geo.circle().angle(5).origin([0, 45])()), [0, 45], 1e-6);
       assert.inDelta(centroid({type: "Polygon", coordinates: [_.range(-180, 180 + 1 / 2, 1).map(function(x) { return [x, -60]; })]})[1], -90, 1e-6);
       assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -10], [0, 10], [10, 10], [10, -10], [0, -10]]]}), [5, 0], 1e-6);
     },
 
-    // TODO Actually test multiple polygons here.
     "the centroid of a set of polygons is the (spherical) average of its surface": function(centroid) {
-      assert.inDelta(centroid({type: "MultiPolygon", coordinates: [[[[0, -90], [0, 0], [0, 90], [1, 0], [0, -90]]]]}), [.5, 0], 1e-6);
-      assert.inDelta(centroid({type: "GeometryCollection", geometries: [{type: "Polygon", coordinates: [[[0, -90], [0, 0], [0, 90], [1, 0], [0, -90]]]}]}), [.5, 0], 1e-6);
+      var circle = _.geo.circle();
+      assert.inDelta(centroid({
+        type: "MultiPolygon",
+        coordinates: [
+          circle.angle(45).origin([0, 0])().coordinates,
+          circle.angle(60).origin([180, 0])().coordinates
+        ]
+      }), [180, 0], 1e-6);
+    },
+
+    "the centroid of a lune is the (spherical) average of its surface": function(centroid) {
+      assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -90], [0, 0], [0, 90], [1, 0], [0, -90]]]}), [.5, 0], 1e-6);
+    },
+
+    "the centroid of a small circle is its origin": {
+      "5°": function(centroid) {
+        assert.inDelta(centroid(_.geo.circle().angle(5).origin([30, 45])()), [30, 45], 1e-6);
+      },
+      "135°": function(centroid) {
+        assert.inDelta(centroid(_.geo.circle().angle(135).origin([30, 45])()), [30, 45], 1e-6);
+      },
+      "South Pole": function(centroid) {
+        assert.equal(centroid({type: "Polygon", coordinates: [_.range(-180, 180 + 1 / 2, 1).map(function(x) { return [x, -60]; })]})[1], -90);
+      },
+      "equator": function(centroid) {
+        assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -10], [0, 10], [10, 10], [10, -10], [0, -10]]]}), [5, 0], 1e-6);
+      },
+      "equator with coincident points": function(centroid) {
+        assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -10], [0, 10], [0, 10], [10, 10], [10, -10], [0, -10]]]}), [5, 0], 1e-6);
+      },
+      "other": function(centroid) {
+        assert.inDelta(centroid({type: "Polygon", coordinates: [[[-180, 0], [-180, 10], [-179, 10], [-179, 0], [-180, 0]]]}), [-179.5, 4.987448], 1e-6);
+      },
+      "concentric rings": function(centroid) {
+        var circle = _.geo.circle().origin([0, 45]),
+            coordinates = circle.angle(60)().coordinates;
+        coordinates.push(circle.angle(45)().coordinates[0].reverse());
+        assert.inDelta(centroid({type: "Polygon", coordinates: coordinates}), [0, 45], 1e-6);
+      }
+    },
+
+    "the centroid of a spherical square on the equator": function(centroid) {
+      assert.inDelta(centroid({type: "Polygon", coordinates: [[[0, -10], [0, 10], [10, 10], [10, -10], [0, -10]]]}), [5, 0], 1e-6);
+    },
+
+    "the centroid of a spherical square touching the antimeridian": function(centroid) {
+      assert.inDelta(centroid({type: "Polygon", coordinates: [[[-180, 0], [-180, 10], [-179, 10], [-179, 0], [-180, 0]]]}), [-179.5, 4.987448], 1e-6);
+    },
+
+    "concentric rings": function(centroid) {
+      var circle = _.geo.circle().origin([0, 45]),
+          coordinates = circle.angle(60)().coordinates;
+      coordinates.push(circle.angle(45)().coordinates[0].reverse());
+      assert.inDelta(centroid({type: "Polygon", coordinates: coordinates}), [0, 45], 1e-6);
     },
 
     "the centroid of a sphere is ambiguous": function(centroid) {
@@ -81,7 +139,7 @@ suite.addBatch({
     },
 
     "the centroid of a feature is the centroid of its constituent geometry": function(centroid) {
-      assert.inDelta(centroid({type: "Feature", geometry: {type: "LineString", coordinates: [[1, 1], [1, 1]]}}), [1, 1], 1e-6); // TODO
+      assert.inDelta(centroid({type: "Feature", geometry: {type: "LineString", coordinates: [[1, 1], [1, 1]]}}), [1, 1], 1e-6);
       assert.inDelta(centroid({type: "Feature", geometry: {type: "Point", coordinates: [1, 1]}}), [1, 1], 1e-6);
       assert.inDelta(centroid({type: "Feature", geometry: {type: "Polygon", coordinates: [[[0, -90], [0, 0], [0, 90], [1, 0], [0, -90]]]}}), [.5, 0], 1e-6);
     },
@@ -105,23 +163,23 @@ suite.addBatch({
         {type: "Polygon", coordinates: [[[-180, 0], [-180, 1], [-179, 1], [-179, 0], [-180, 0]]]},
         {type: "LineString", coordinates: [[179, 0], [180, 0]]},
         {type: "Point", coordinates: [0, 0]}
-      ]}), [-179.5, 0.5], 1e-6);
+      ]}), [-179.5, 0.500006], 1e-6);
       assert.inDelta(centroid({type: "GeometryCollection", geometries: [
         {type: "Point", coordinates: [0, 0]},
         {type: "LineString", coordinates: [[179, 0], [180, 0]]},
         {type: "Polygon", coordinates: [[[-180, 0], [-180, 1], [-179, 1], [-179, 0], [-180, 0]]]}
-      ]}), [-179.5, 0.5], 1e-6);
+      ]}), [-179.5, 0.500006], 1e-6);
     },
 
-    "the centroid of the sphere and a point only considers the sphere": function(centroid) {
-      assert.ok(centroid({type: "GeometryCollection", geometries: [
+    "the centroid of the sphere and a point is the point": function(centroid) {
+      assert.deepEqual(centroid({type: "GeometryCollection", geometries: [
         {type: "Sphere"},
         {type: "Point", coordinates: [0, 0]}
-      ]}).every(isNaN));
-      assert.ok(centroid({type: "GeometryCollection", geometries: [
+      ]}), [0, 0]);
+      assert.deepEqual(centroid({type: "GeometryCollection", geometries: [
         {type: "Point", coordinates: [0, 0]},
         {type: "Sphere"}
-      ]}).every(isNaN));
+      ]}), [0, 0]);
     }
   }
 });
diff --git a/test/geo/path-test.js b/test/geo/path-test.js
index 396be29f..6cd90cfb 100644
--- a/test/geo/path-test.js
+++ b/test/geo/path-test.js
@@ -130,7 +130,7 @@ suite.addBatch({
           assert.deepEqual(centroid({type: "Point", coordinates: [0, 0]}), [480, 250]);
         },
         "of an empty multipoint": function(centroid) {
-          assert.isUndefined(centroid({type: "MultiPoint", coordinates: []}));
+          assert.ok(centroid({type: "MultiPoint", coordinates: []}).every(isNaN));
         },
         "of a singleton multipoint": function(centroid) {
           assert.deepEqual(centroid({type: "MultiPoint", coordinates: [[0, 0]]}), [480, 250]);
@@ -139,15 +139,15 @@ suite.addBatch({
           assert.deepEqual(centroid({type: "MultiPoint", coordinates: [[-122, 37], [-74, 40]]}), [-10, 57.5]);
         },
         "of an empty linestring": function(centroid) {
-          assert.isUndefined(centroid({type: "LineString", coordinates: []}));
+          assert.ok(centroid({type: "LineString", coordinates: []}).every(isNaN));
         },
         "of a linestring with two points": function(centroid) {
           assert.deepEqual(centroid({type: "LineString", coordinates: [[100, 0], [0, 0]]}), [730, 250]);
           assert.deepEqual(centroid({type: "LineString", coordinates: [[0, 0], [100, 0], [101, 0]]}), [732.5, 250]);
         },
         "of a linestring with two points, one unique": function(centroid) {
-          assert.isUndefined(centroid({type: "LineString", coordinates: [[-122, 37], [-122, 37]]}));
-          assert.isUndefined(centroid({type: "LineString", coordinates: [[ -74, 40], [ -74, 40]]}));
+          assert.deepEqual(centroid({type: "LineString", coordinates: [[-122, 37], [-122, 37]]}), [-130, 65]);
+          assert.deepEqual(centroid({type: "LineString", coordinates: [[-74, 40], [-74, 40]]}), [110, 50]);
         },
         "of a linestring with three points; two unique": function(centroid) {
           assert.deepEqual(centroid({type: "LineString", coordinates: [[-122, 37], [-74, 40], [-74, 40]]}), [-10, 57.5]);
@@ -162,7 +162,7 @@ suite.addBatch({
           assert.deepEqual(centroid({type: "Polygon", coordinates: [[[100, 0], [100, 1], [101, 1], [101, 0], [100, 0]]]}), [982.5, 247.5]);
         },
         "of a zero-area polygon": function(centroid) {
-          assert.isUndefined(centroid({type: "Polygon", coordinates: [[[1, 0], [2, 0], [3, 0], [1, 0]]]}));
+          assert.deepEqual(centroid({type: "Polygon", coordinates: [[[1, 0], [2, 0], [3, 0], [1, 0]]]}), [490, 250]);
         },
         "of a polygon with two rings, one with zero area": function(centroid) {
           assert.deepEqual(centroid({type: "Polygon", coordinates: [
@@ -180,7 +180,7 @@ suite.addBatch({
           }), [479.642857, 250], 1e-6);
         },
         "of an empty multipolygon": function(centroid) {
-          assert.isUndefined(centroid({type: "MultiPolygon", coordinates: []}));
+          assert.ok(centroid({type: "MultiPolygon", coordinates: []}).every(isNaN));
         },
         "of a singleton multipolygon": function(centroid) {
           assert.deepEqual(centroid({type: "MultiPolygon", coordinates: [[[[100, 0], [100, 1], [101, 1], [101, 0], [100, 0]]]]}), [982.5, 247.5]);
@@ -294,9 +294,7 @@ suite.addBatch({
           [[109.378, 189.584], [797.758, 504.660]], 1e-3);
       },
       "centroid of a line string": function(p) {
-        var centroid = p.centroid({type: "LineString", coordinates: [[-122, 37], [-74, 40], [-100, 0]]});
-        assert.inDelta(centroid[0], 545.131, 1e-3);
-        assert.inDelta(centroid[1], 253.860, 1e-3);
+        assert.inDelta(p.centroid({type: "LineString", coordinates: [[-122, 37], [-74, 40], [-100, 0]]}), [545.131, 253.860], 1e-3);
       }
     },