diff --git a/geometry/geometry.pro b/geometry/geometry.pro
index eaeb7e42b8..0a97c2fefd 100644
--- a/geometry/geometry.pro
+++ b/geometry/geometry.pro
@@ -28,3 +28,4 @@ HEADERS += \
   simplification.hpp \
   transformations.hpp \
   tree4d.hpp \
+  polygon.hpp \
diff --git a/geometry/geometry_tests/geometry_tests.pro b/geometry/geometry_tests/geometry_tests.pro
index 322c5d1cb8..ba26c8c323 100644
--- a/geometry/geometry_tests/geometry_tests.pro
+++ b/geometry/geometry_tests/geometry_tests.pro
@@ -29,3 +29,4 @@ SOURCES += \
   simplification_test.cpp \
   transformations_test.cpp \
   tree_test.cpp \
+  polygon_test.cpp \
diff --git a/geometry/geometry_tests/polygon_test.cpp b/geometry/geometry_tests/polygon_test.cpp
new file mode 100644
index 0000000000..c877e93057
--- /dev/null
+++ b/geometry/geometry_tests/polygon_test.cpp
@@ -0,0 +1,61 @@
+#include "../../testing/testing.hpp"
+#include "../polygon.hpp"
+#include "../point2d.hpp"
+#include "../../base/macros.hpp"
+
+namespace
+{
+typedef m2::PointD P;
+}
+
+UNIT_TEST(IsSegmentInCone)
+{
+  TEST(IsSegmentInCone(P(0,0),  P( 0, 3), P(-1,-1), P(1,-1)), ());
+  TEST(IsSegmentInCone(P(0,0),  P( 2, 3), P(-1,-1), P(1,-1)), ());
+  TEST(IsSegmentInCone(P(0,0),  P(-3, 3), P(-1,-1), P(1,-1)), ());
+  TEST(IsSegmentInCone(P(0,0),  P(-3, 0), P(-1,-1), P(1,-1)), ());
+  TEST(IsSegmentInCone(P(0,0),  P( 3, 0), P(-1,-1), P(1,-1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P( 0,-1), P(-1,-1), P(1,-1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P( 1,-3), P(-1,-1), P(1,-1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P(-1,-3), P(-1,-1), P(1,-1)), ());
+
+  TEST(IsSegmentInCone(P(0,0),  P( 0, 3), P(-1,1), P(1,1)), ());
+  TEST(IsSegmentInCone(P(0,0),  P( 2, 3), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P(-3, 3), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P(-3, 0), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P( 3, 0), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P( 0,-1), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P( 1,-3), P(-1,1), P(1,1)), ());
+  TEST(!IsSegmentInCone(P(0,0), P(-1,-3), P(-1,1), P(1,1)), ());
+}
+
+UNIT_TEST(IsDiagonalVisible)
+{
+  P polyA [] = { P(0,0), P(3,0), P(3,2), P(2,2), P(2,1), P(0,1) };
+  vector<P> poly(&polyA[0], &polyA[0] + ARRAY_SIZE(polyA));
+  // TODO: Reverse directions.
+
+  TEST(!IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 0, poly.begin() + 2), ());
+  TEST(!IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 0, poly.begin() + 3), ());
+  TEST( IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 0, poly.begin() + 4), ());
+  TEST(!IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 5, poly.begin() + 3), ());
+  TEST(!IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 5, poly.begin() + 2), ());
+  TEST( IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 5, poly.begin() + 1), ());
+  TEST( IsDiagonalVisible(poly.begin(), poly.end(), poly.begin() + 1, poly.begin() + 5), ());
+}
+
+UNIT_TEST(FindSingleStrip)
+{
+  {
+    P poly [] = { P(0,0), P(3,0), P(3,2), P(2,2), P(2,1), P(0,1) };
+    size_t const n = ARRAY_SIZE(poly);
+    TEST_NOT_EQUAL(
+          FindSingleStrip(n, IsDiagonalVisibleFunctor<P const *>(&poly[0], &poly[0] + n)), n, ());
+  }
+  {
+    P poly [] = { P(0,0), P(2, -1), P(3,-1), P(3,2), P(2,2), P(2,1), P(0,1) };
+    size_t const n = ARRAY_SIZE(poly);
+    TEST_EQUAL(
+          FindSingleStrip(n, IsDiagonalVisibleFunctor<P const *>(&poly[0], &poly[0] + n)), n, ());
+  }
+}
diff --git a/geometry/polygon.hpp b/geometry/polygon.hpp
new file mode 100644
index 0000000000..bb1e63245c
--- /dev/null
+++ b/geometry/polygon.hpp
@@ -0,0 +1,82 @@
+#pragma once
+
+#include "../base/assert.hpp"
+#include "../base/base.hpp"
+#include "../base/math.hpp"
+#include "../base/stl_add.hpp"
+
+// If polygon with n vertices is a single strip, return the start index of the strip or n otherwise.
+template <typename IsVisibleF>
+size_t FindSingleStrip(size_t const n, IsVisibleF isVisible)
+{
+  for (size_t i = 0; i < n; ++i)
+  {
+    // Searching for a strip only in a single direction, because the opposite direction
+    // is traversed from the last vertex of the possible strip.
+    size_t a = my::PrevModN(i, n);
+    size_t b = my::NextModN(i, n);
+    for (size_t j = 2; j < n; ++j)
+    {
+      ASSERT_NOT_EQUAL(a, b, ());
+      if (!isVisible(a, b))
+        break;
+      if (j & 1)
+        a = my::PrevModN(a, n);
+      else
+        b = my::NextModN(b, n);
+    }
+    if (a == b)
+      return i;
+  }
+  return n;
+}
+
+// Is segment (v, v1) in cone (vPrev, v, vNext)? Orientation CCW.
+template <typename PointT> bool IsSegmentInCone(PointT v, PointT v1, PointT vPrev, PointT vNext)
+{
+  PointT const diff = v1 - v;
+  PointT const edgeL = vPrev - v;
+  PointT const edgeR = vNext - v;
+  double const cpLR = CrossProduct(edgeR, edgeL);
+  ASSERT(!my::AlmostEqual(cpLR, 0.0),
+         ("vPrev, v, vNext shouldn't be collinear!", edgeL, edgeR, v, v1, vPrev, vNext));
+  if (cpLR > 0)
+  {
+    // vertex is convex
+    return CrossProduct(diff, edgeR) < 0 && CrossProduct(diff, edgeL) > 0;
+  }
+  else
+  {
+    // vertex is reflex
+    return CrossProduct(diff, edgeR) < 0 || CrossProduct(diff, edgeL) > 0;
+  }
+}
+
+// Is diagonal (i0, i1) visible in polygon [beg, end).
+template <typename IterT>
+bool IsDiagonalVisible(IterT const beg, IterT const end, IterT const i0, IterT const i1)
+{
+  // TODO: Orientation CCW!!
+  if (!IsSegmentInCone(*i0, *i1, *PrevIterInCycle(i0, beg, end), *NextIterInCycle(i0, beg, end)))
+    return false;
+
+  for (IterT j0 = beg, j1 = PrevIterInCycle(beg, beg, end); j0 != end; j1 = j0++)
+    if (j0 != i0 && j0 != i1 && j1 != i0 && j1 != i1 && SegmentsIntersect(*i0, *i1, *j0, *j1))
+      return false;
+
+  return true;
+}
+
+template <typename IterT> class IsDiagonalVisibleFunctor
+{
+public:
+  IsDiagonalVisibleFunctor(IterT const beg, IterT const end) : m_Beg(beg), m_End(end) {}
+
+  bool operator () (size_t a, size_t b) const
+  {
+    return IsDiagonalVisible(m_Beg, m_End, m_Beg + a, m_End + b);
+  }
+
+private:
+  IterT m_Beg, m_End;
+};