diff --git a/client/glyph.js b/client/glyph.js
index 2aec9408..0ce07968 100644
--- a/client/glyph.js
+++ b/client/glyph.js
@@ -8,7 +8,7 @@ var COLORS = ['#0074D9', '#2ECC40', '#FFDC00', '#FF4136', '#7FDBFF',
 function change_glyph(method, glyph) {
   glyph = glyph || Session.get('glyph.data');
   Meteor.call(method, glyph, function(error, data) {
-    data.d = Glyphs.get_svg_path(data);
+    data.render = get_glyph_render_data(data);
 
     data.manual = data.manual || {};
     data.manual.bridges_added = data.manual.bridges_added || [];
@@ -178,7 +178,7 @@ Template.glyph.helpers({
     return Session.get('glyph.show_strokes') ? 'black' : 'gray';
   },
   d: function() {
-    return Session.get('glyph.data').d;
+    return Session.get('glyph.data').render.d;
   },
   show_strokes: function() {
     return !!Session.get('glyph.show_strokes');
@@ -194,6 +194,7 @@ Template.glyph.helpers({
     return result;
   },
   bridges: function() {
+    return [];
     var glyph = Session.get('glyph.data');
     var removed = {};
     for (var i = 0; i < glyph.manual.bridges_removed.length; i++) {
@@ -216,15 +217,12 @@ Template.glyph.helpers({
   },
   points: function() {
     var glyph = Session.get('glyph.data');
-    var corners = {};
-    for (var i = 0; i < glyph.extractor.corners.length; i++) {
-      corners[to_point(glyph.extractor.corners[i]).coordinates] = true;
-    }
     var result = [];
-    for (var i = 0; i < glyph.extractor.points.length; i++) {
-      var point = to_point(glyph.extractor.points[i]);
-      point.color = corners[point.coordinates] ? 'red' : 'black';
-      point.z_index = corners[point.coordinates] ? 1 : 0;
+    for (var i = 0; i < glyph.render.endpoints.length; i++) {
+      var endpoint = glyph.render.endpoints[i];
+      var point = to_point(endpoint.point);
+      point.color = endpoint.corner ? 'red' : 'black';
+      point.z_index = endpoint.corner ? 1 : 0;
       if (point.coordinates === Session.get('glyph.selected_point')) {
         point.color = 'purple';
       }
diff --git a/lib/glyphs.js b/lib/glyphs.js
index 22268ac8..558d12dd 100644
--- a/lib/glyphs.js
+++ b/lib/glyphs.js
@@ -14,112 +14,3 @@ Glyphs.get_svg_path = function(glyph) {
   }
   return terms.join(' ');
 }
-
-// Error out if the condition does not hold.
-function assert(condition, message) {
-  if (!condition) {
-    console.error(message);
-    throw new Error;
-  }
-}
-
-function clone(point) {
-  return [point[0], point[1]];
-}
-
-function equal(point1, point2) {
-  return point1[0] === point2[0] && point1[1] === point2[1];
-}
-
-function valid(point) {
-  return point[0] !== undefined && point[1] !== undefined;
-}
-
-// Takes a non-empty list of SVG commands that may contain multiple contours.
-// Returns a list of lists of path segment objects that each form one contour.
-// Each path segment has three keys: start, end, and control.
-function split_path(path) {
-  assert(path.length >= 2);
-  assert(path[0].type === 'M', 'Path did not start with M!');
-  assert(path[path.length - 1].type === 'Z', 'Path did not end with Z!');
-
-  var result = [[]];
-  var start = [path[0].x, path[0].y];
-  var current = clone(start);
-  assert(valid(current));
-
-  for (var i = 1; i < path.length; i++) {
-    var command = path[i];
-    if (command.type === 'M' || command.type === 'Z') {
-      assert(start.x === current.x && start.y === current.y, 'Open contour!');
-      assert(result[result.length -1].length > 0, 'Empty contour!');
-      if (command.type === 'Z') {
-        assert(i === path.length - 1, 'Path ended early!');
-        return result;
-      }
-      var start = [command.x, command.y];
-      var current = clone(start);
-      assert(valid(current));
-      continue;
-    }
-    assert(command.type === 'Q' || command.type === 'L',
-           'Got unexpected TTF command: ' + command.type);
-    var segment = {
-      'start': clone(current),
-      'end': [command.x, command.y],
-      'control': [command.x1, command.y1],
-    };
-    assert(valid(segment.end));
-    if (equal(segment.start, segment.end)) {
-      continue;
-    }
-    if (!valid(segment.control) ||
-        equal(segment.start, segment.control) ||
-        equal(segment.end, segment.control)) {
-      delete segment.control;
-    }
-    result[result.length - 1].push(segment);
-    current = clone(segment.end);
-  }
-}
-
-// Takes a list of paths. Returns them oriented the way a TTF glyph should be:
-// exterior contours counter-clockwise and interior contours clockwise.
-function orient_paths(paths) {
-  var max_area = 0;
-  for (var i = 0; i < paths.length; i++) {
-    var area = get_2x_area(paths[i]);
-    if (Math.abs(area) > max_area) {
-      max_area = area;
-    }
-  }
-  if (max_area < 0) {
-    // The paths are reversed. Flip each one.
-    var result = [];
-    for (var i = 0; i < paths.length; i++) {
-      var path = paths[i];
-      for (var j = 0; j < paths.length; j++) {
-        var ref = [path[j].start, path[j].end];
-        path[j].start = ref[1];
-        path[j].end = ref[0];
-      }
-      path[j].reverse();
-    }
-  }
-  return paths;
-}
-
-// Returns twice the area contained in the path. The result is positive iff the
-// path winds in the counter-clockwise direction.
-function get_2x_area(path) {
-  var area = 0;
-  for (var i = 0; i < path.length; i++) {
-    var segment = path[i];
-    area += (segment.end.x - segment.start.x)*(segment.end.y + segment.start.y);
-  }
-  return area;
-}
-
-split_and_orient_path = function(path) {
-  return orient_paths(split_path(path));
-}
diff --git a/lib/stroke_extractor.js b/lib/stroke_extractor.js
new file mode 100644
index 00000000..2919e9e2
--- /dev/null
+++ b/lib/stroke_extractor.js
@@ -0,0 +1,173 @@
+var MIN_CORNER_ANGLE = 0.1*Math.PI;
+var MIN_CORNER_TANGENT_DISTANCE = 4;
+
+// Error out if the condition does not hold.
+function assert(condition, message) {
+  if (!condition) {
+    console.error(message);
+    throw new Error;
+  }
+}
+
+// Helper methods for use with "points", which are just pairs of integers.
+var Point = {
+  angle: function(point) {
+    return Math.atan2(point[1], point[0]);
+  },
+  clone: function(point) {
+    return [point[0], point[1]];
+  },
+  distance2: function(point1, point2) {
+    var diff = Point.subtract(point1, point2);
+    return Math.pow(diff[0], 2) + Math.pow(diff[1], 2);
+  },
+  equal: function(point1, point2) {
+    return point1[0] === point2[0] && point1[1] === point2[1];
+  },
+  subtract: function(point1, point2) {
+    return [point1[0] - point2[0], point1[1] - point2[1]];
+  },
+  valid: function(point) {
+    return point[0] !== undefined && point[1] !== undefined;
+  },
+};
+
+// Helper methods for use with angles, which are floats in [-pi, pi).
+var Angle = {
+  subtract: function(angle1, angle2) {
+    var result = angle1 - angle2;
+    if (result < -Math.PI) {
+      result += 2*Math.PI;
+    }
+    if (result >= Math.PI) {
+      result -= 2*Math.PI;
+    }
+    return result;
+  },
+};
+
+// Takes a non-empty list of SVG commands that may contain multiple contours.
+// Returns a list of lists of path segment objects that each form one contour.
+// Each path segment has three keys: start, end, and control.
+function split_path(path) {
+  assert(path.length >= 2);
+  assert(path[0].type === 'M', 'Path did not start with M!');
+  assert(path[path.length - 1].type === 'Z', 'Path did not end with Z!');
+
+  var result = [[]];
+  var start = [path[0].x, path[0].y];
+  var current = Point.clone(start);
+  assert(Point.valid(current));
+
+  for (var i = 1; i < path.length; i++) {
+    var command = path[i];
+    if (command.type === 'M' || command.type === 'Z') {
+      assert(start.x === current.x && start.y === current.y, 'Open contour!');
+      assert(result[result.length -1].length > 0, 'Empty contour!');
+      if (command.type === 'Z') {
+        assert(i === path.length - 1, 'Path ended early!');
+        return result;
+      }
+      result.push([]);
+      var start = [command.x, command.y];
+      var current = Point.clone(start);
+      assert(Point.valid(current));
+      continue;
+    }
+    assert(command.type === 'Q' || command.type === 'L',
+           'Got unexpected TTF command: ' + command.type);
+    var segment = {
+      'start': Point.clone(current),
+      'end': [command.x, command.y],
+      'control': [command.x1, command.y1],
+    };
+    assert(Point.valid(segment.end));
+    if (Point.equal(segment.start, segment.end)) {
+      continue;
+    }
+    if (!Point.valid(segment.control) ||
+        Point.equal(segment.start, segment.control) ||
+        Point.equal(segment.end, segment.control)) {
+      delete segment.control;
+    }
+    result[result.length - 1].push(segment);
+    current = Point.clone(segment.end);
+  }
+}
+
+// Takes a list of paths. Returns them oriented the way a TTF glyph should be:
+// exterior contours counter-clockwise and interior contours clockwise.
+function orient_paths(paths) {
+  var max_area = 0;
+  for (var i = 0; i < paths.length; i++) {
+    var area = get_2x_area(paths[i]);
+    if (Math.abs(area) > max_area) {
+      max_area = area;
+    }
+  }
+  if (max_area < 0) {
+    // The paths are reversed. Flip each one.
+    var result = [];
+    for (var i = 0; i < paths.length; i++) {
+      var path = paths[i];
+      for (var j = 0; j < paths.length; j++) {
+        var ref = [path[j].start, path[j].end];
+        path[j].start = ref[1];
+        path[j].end = ref[0];
+      }
+      path[j].reverse();
+    }
+  }
+  return paths;
+}
+
+// Returns twice the area contained in the path. The result is positive iff the
+// path winds in the counter-clockwise direction.
+function get_2x_area(path) {
+  var area = 0;
+  for (var i = 0; i < path.length; i++) {
+    var segment = path[i];
+    area += (segment.end.x - segment.start.x)*(segment.end.y + segment.start.y);
+  }
+  return area;
+}
+
+function Endpoint(paths, index) {
+  this.index = index;
+  var path = paths[index[0]];
+  var n = path.length;
+  this.segments = [path[(index[1] + n - 1) % n], path[index[1]]];
+  this.point = this.segments[0].end;
+  assert(Point.valid(this.point), this.point);
+  assert(Point.equal(this.point, this.segments[1].start), path);
+  this.tangents = [
+    Point.subtract(this.segments[0].end, this.segments[0].start),
+    Point.subtract(this.segments[1].end, this.segments[1].start),
+  ];
+  var threshold = Math.pow(MIN_CORNER_TANGENT_DISTANCE, 2);
+  if (this.segments[0].control !== undefined &&
+      Point.distance2(this.point, this.segments[0].control) > threshold) {
+    this.tangents[0] = Point.subtract(this.point, this.segments[0].control);
+  }
+  if (this.segments[1].control !== undefined &&
+      Point.distance2(this.point, this.segments[1].control) > threshold) {
+    this.tangents[1] = Point.subtract(this.segments[1].control, this.point);
+  }
+  this.angles = this.tangents.map(Point.angle);
+  var diff = Angle.subtract(this.angles[1], this.angles[0]);
+  this.corner = diff < -MIN_CORNER_ANGLE;
+  return this;
+}
+
+// Exports go below this fold.
+
+this.get_glyph_render_data = function(glyph) {
+  var paths = orient_paths(split_path(glyph.path));
+  var endpoints = [];
+  for (var i = 0; i < paths.length; i++) {
+    for (var j = 0; j < paths[i].length; j++) {
+      endpoints.push(new Endpoint(paths, [i, j]));
+    }
+  }
+  return {d: Glyphs.get_svg_path(glyph), endpoints: endpoints};
+}