Remove antimeridian-polar cuts.

See #49.

The threshold had to be rather low, 1e-2, for this to work with
world-atlas.

lib/topojson/topology.js

@@ -51,9 +51,59 @@ module.exports = function(objects, options) {
   if (!system) { system = systems[oversize ? "cartesian" : "spherical"]; if (options) options["coordinate-system"] = system.name; }
   if (system === systems.spherical && oversize) throw new Error("spherical coordinates outside of [±180°, ±90°]");
 
-  // When near the spherical coordinate limits, clamp to nice round values.
-  // This avoids quantized coordinates that are slightly outside the limits.
+  // Remove polar antimeridian cuts, i.e. all sequences:
+  // [±180°, *]+, [*, ±90°]+, [±180, *]+.
   if (system === systems.spherical) {
+    each({
+      polygon: function(polygon) {
+        for (var j = 0, m = polygon.length; j < m; ++j) {
+          var line = polygon[j],
+              i = -1,
+              n = line.length,
+              a = false,
+              b = false,
+              c = false,
+              i0 = -1;
+          for (i = 0; i < n; ++i) {
+            var point = line[i],
+                antimeridian = Math.abs(Math.abs(point[0]) - 180) < 1e-2,
+                polar = Math.abs(Math.abs(point[1]) - 90) < 1e-2;
+            if (antimeridian || polar) {
+              if (!(a || b || c)) i0 = i;
+              if (antimeridian) {
+                if (a) c = true;
+                else a = true;
+              }
+              if (polar) b = true;
+            }
+            if (!antimeridian && !polar || i === n - 1) {
+              if (a && b && c) {
+                line.splice(i0, i - i0);
+                n -= i - i0;
+                i = i0;
+              }
+              a = b = c = false;
+            }
+          }
+        }
+      }
+    });
+
+    // Recompute bounding box.
+    x1 = y1 = -(x0 = y0 = Infinity);
+    each({
+      point: function(point) {
+        var x = point[0],
+            y = point[1];
+        if (x < x0) x0 = x;
+        if (x > x1) x1 = x;
+        if (y < y0) y0 = y;
+        if (y > y1) y1 = y;
+      }
+    });
+
+    // When near the spherical coordinate limits, clamp to nice round values.
+    // This avoids quantized coordinates that are slightly outside the limits.
     if (x0 < -180 + ε) x0 = -180;
     if (x1 > 180 - ε) x1 = 180;
     if (y0 < -90 + ε) y0 = -90;

test/topology-test.js

@@ -547,6 +547,45 @@ suite.addBatch({
       ]);
       assert.deepEqual(topology.objects.abe, {type: "LineString", arcs: [0, 1]});
       assert.deepEqual(topology.objects.bcdb, {type: "Polygon", arcs: [[2]]});
+    },
+
+    //
+    // A-----B-----C-----D-----E
+    // |                       |
+    // |                       |
+    // J-----I-----H-----G-----F
+    "a polygon surrounding the South pole with a cut along the antimeridian": function() {
+      var topology = topojson.topology({
+        polygon: {type: "Polygon", coordinates: [[
+          [-180, -80], [-90, -80], [0, -80], [90, -80], [180, -80],
+          [180, -90], [90, -90], [0, -90], [-90, -90], [-180, -90],
+          [-180, -80]
+        ]]}}, {quantization: 4});
+      assert.deepEqual(topology.arcs, [
+        [[0, 0], [1, 0], [1, 0], [1, 0], [-3, 0]]
+      ]);
+      assert.deepEqual(topology.objects.polygon, {type: "Polygon", arcs: [[0]]});
+    },
+
+    //
+    // B-----C-----D-----E-----F
+    // |                       |
+    // |                       |
+    // A                       G
+    // |                       |
+    // |                       |
+    // L-----K-----J-----I-----H
+    "a large polygon surrounding the South pole with a cut along the antimeridian": function() {
+      var topology = topojson.topology({
+        polygon: {type: "Polygon", coordinates: [[
+          [-180, -85], [-180, -80], [-90, -80], [0, -80], [90, -80], [180, -80],
+          [180, -85], [180, -90], [90, -90], [0, -90], [-90, -90], [-180, -90],
+          [-180, -85]
+        ]]}}, {quantization: 4});
+      assert.deepEqual(topology.arcs, [
+        [[0, 0], [0, 3], [1, 0], [1, 0], [1, 0], [-3, -3]]
+      ]);
+      assert.deepEqual(topology.objects.polygon, {type: "Polygon", arcs: [[0]]});
     }
   }
 });