diff --git a/geometry/CMakeLists.txt b/geometry/CMakeLists.txt
index 5e236e6328..b182deacd3 100644
--- a/geometry/CMakeLists.txt
+++ b/geometry/CMakeLists.txt
@@ -11,6 +11,8 @@ set(
   cellid.hpp
   clipping.cpp
   clipping.hpp
+  convex_hull.cpp
+  convex_hull.hpp
   covering.hpp
   covering_utils.hpp
   distance.hpp
diff --git a/geometry/convex_hull.cpp b/geometry/convex_hull.cpp
new file mode 100644
index 0000000000..adc878ab28
--- /dev/null
+++ b/geometry/convex_hull.cpp
@@ -0,0 +1,69 @@
+#include "geometry/convex_hull.hpp"
+
+#include "geometry/robust_orientation.hpp"
+
+#include "base/stl_helpers.hpp"
+
+#include <algorithm>
+
+using namespace std;
+
+namespace m2
+{
+namespace
+{
+double const kEps = 1e-9;
+
+// Checks whether (p1 - p) x (p2 - p) > 0.
+bool IsCCW(PointD const & p1, PointD const & p2, PointD const & p)
+{
+  return robust::OrientedS(p1, p2, p) > kEps;
+}
+
+bool ContinuesHull(vector<PointD> const & hull, PointD const & p)
+{
+  auto const n = hull.size();
+  if (n < 2)
+    return true;
+
+  auto const & p1 = hull[n - 2];
+  auto const & p2 = hull[n - 1];
+
+  // Checks whether (p2 - p1) x (p - p2) > 0.
+  return robust::OrientedS(p1, p, p2) < -kEps;
+}
+}  // namespace
+
+vector<PointD> BuildConvexHull(vector<PointD> points)
+{
+  my::SortUnique(points);
+
+  auto const n = points.size();
+
+  if (n < 2)
+    return points;
+
+  iter_swap(points.begin(), min_element(points.begin(), points.end()));
+
+  auto const pivot = points[0];
+
+  sort(points.begin() + 1, points.end(), [&pivot](PointD const & lhs, PointD const & rhs) {
+    if (IsCCW(lhs, rhs, pivot))
+      return true;
+    if (IsCCW(rhs, lhs, pivot))
+      return false;
+    return lhs.SquareLength(pivot) < rhs.SquareLength(pivot);
+  });
+
+  vector<PointD> hull;
+
+  for (auto const & p : points)
+  {
+    while (!ContinuesHull(hull, p))
+      hull.pop_back();
+    hull.push_back(p);
+  }
+
+  return hull;
+}
+}  // namespace m2
diff --git a/geometry/convex_hull.hpp b/geometry/convex_hull.hpp
new file mode 100644
index 0000000000..a7021a6539
--- /dev/null
+++ b/geometry/convex_hull.hpp
@@ -0,0 +1,13 @@
+#pragma once
+
+#include "geometry/point2d.hpp"
+
+#include <vector>
+
+namespace m2
+{
+// Builds a convex hull around |points|.
+//
+// Complexity: O(n * log(n)), where n is the number of points.
+std::vector<PointD> BuildConvexHull(std::vector<PointD> points);
+}  // namespace m2
diff --git a/geometry/geometry.pro b/geometry/geometry.pro
index 8dfd043d5c..6989dd6507 100644
--- a/geometry/geometry.pro
+++ b/geometry/geometry.pro
@@ -12,6 +12,7 @@ SOURCES += \
   algorithm.cpp \
   angles.cpp \
   clipping.cpp \
+  convex_hull.cpp \
   distance_on_sphere.cpp \
   latlon.cpp \
   nearby_points_sweeper.cpp \
@@ -31,6 +32,7 @@ HEADERS += \
   any_rect2d.hpp \
   avg_vector.hpp \
   cellid.hpp \
+  convex_hull.hpp \
   covering.hpp \
   covering_utils.hpp \
   distance.hpp \
diff --git a/geometry/geometry_tests/CMakeLists.txt b/geometry/geometry_tests/CMakeLists.txt
index 2740fb3df5..2df35b473f 100644
--- a/geometry/geometry_tests/CMakeLists.txt
+++ b/geometry/geometry_tests/CMakeLists.txt
@@ -10,6 +10,7 @@ set(
   cellid_test.cpp
   clipping_test.cpp
   common_test.cpp
+  convex_hull_tests.cpp
   covering_test.cpp
   distance_on_sphere_test.cpp
   distance_test.cpp
diff --git a/geometry/geometry_tests/convex_hull_tests.cpp b/geometry/geometry_tests/convex_hull_tests.cpp
new file mode 100644
index 0000000000..cad2cc40e7
--- /dev/null
+++ b/geometry/geometry_tests/convex_hull_tests.cpp
@@ -0,0 +1,43 @@
+#include "testing/testing.hpp"
+
+#include "geometry/convex_hull.hpp"
+#include "geometry/point2d.hpp"
+
+#include <vector>
+
+using namespace m2;
+using namespace std;
+
+namespace
+{
+UNIT_TEST(ConvexHull_Smoke)
+{
+  TEST_EQUAL(BuildConvexHull({}), vector<PointD>{}, ());
+  TEST_EQUAL(BuildConvexHull({PointD(0, 0)}), vector<PointD>{PointD(0, 0)}, ());
+  TEST_EQUAL(BuildConvexHull({PointD(0, 0), PointD(0, 0)}), vector<PointD>{PointD(0, 0)}, ());
+
+  TEST_EQUAL(BuildConvexHull({PointD(0, 0), PointD(1, 1), PointD(0, 0)}),
+             vector<PointD>({PointD(0, 0), PointD(1, 1)}), ());
+
+  TEST_EQUAL(BuildConvexHull({PointD(0, 0), PointD(1, 1), PointD(2, 2)}),
+             vector<PointD>({PointD(0, 0), PointD(2, 2)}), ());
+
+  {
+    int const kXMax = 100;
+    int const kYMax = 200;
+    vector<PointD> points;
+    for (int x = 0; x <= kXMax; ++x)
+    {
+      for (int y = 0; y <= kYMax; ++y)
+        points.emplace_back(x, y);
+    }
+    TEST_EQUAL(BuildConvexHull(points), vector<PointD>({PointD(0, 0), PointD(kXMax, 0),
+                                                        PointD(kXMax, kYMax), PointD(0, kYMax)}),
+               ());
+  }
+
+  TEST_EQUAL(
+      BuildConvexHull({PointD(0, 0), PointD(0, 5), PointD(10, 5), PointD(3, 3), PointD(10, 0)}),
+      vector<PointD>({PointD(0, 0), PointD(10, 0), PointD(10, 5), PointD(0, 5)}), ());
+}
+}  // namespace
diff --git a/geometry/geometry_tests/geometry_tests.pro b/geometry/geometry_tests/geometry_tests.pro
index bba8723348..8612172643 100644
--- a/geometry/geometry_tests/geometry_tests.pro
+++ b/geometry/geometry_tests/geometry_tests.pro
@@ -25,6 +25,7 @@ SOURCES += \
   cellid_test.cpp \
   clipping_test.cpp \
   common_test.cpp \
+  convex_hull_tests.cpp \
   covering_test.cpp \
   distance_on_sphere_test.cpp \
   distance_test.cpp \