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      d3_geo_pathCentroid.point = nextPoint;

      d3_geo_pathCentroidPoint(x00 = x0 = x, y00 = y0 = y);

    };

    function nextPoint(x, 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);

    };

      d3_geo_pathCentroid.point = nextPoint;

      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_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() {

    d3_geo_pathCentroid.point = d3_geo_pathCentroidPoint;