One Month In Minsk. Made in Belarus.

1 files changed, 342 insertions, 0 deletions

diff --git a/geometry/covering.hpp b/geometry/covering.hpp
new file mode 100644
index 0000000000..8da2cbd6a2
--- /dev/null
+++ b/geometry/covering.hpp
@@ -0,0 +1,342 @@
+#pragma once
+#include "../geometry/point2d.hpp"
+#include "../base/assert.hpp"
+#include "../base/base.hpp"
+#include "../base/logging.hpp"
+#include "../base/set_operations.hpp"
+#include "../base/stl_add.hpp"
+#include "../std/algorithm.hpp"
+#include "../std/array.hpp"
+#include "../std/functional.hpp"
+#include "../std/iterator.hpp"
+#include "../std/map.hpp"
+#include "../std/queue.hpp"
+#include "../std/utility.hpp"
+#include "../std/vector.hpp"
+
+namespace covering
+{
+
+enum CellTriangleIntersection
+{
+  CELL_TRIANGLE_NO_INTERSECTION = 0,
+  CELL_TRIANGLE_INTERSECT = 1,
+  CELL_INSIDE_TRIANGLE = 2,
+  TRIANGLE_INSIDE_CELL = 3
+};
+
+template <class CellIdT>
+CellTriangleIntersection IntersectCellWithTriangle(
+    CellIdT const cell, m2::PointD const & a, m2::PointD const & b, m2::PointD const & c)
+{
+  pair<uint32_t, uint32_t> const xy = cell.XY();
+  uint32_t const r = cell.Radius();
+  m2::PointD const cellCorners[4] =
+  {
+    m2::PointD(xy.first - r, xy.second - r),
+    m2::PointD(xy.first - r, xy.second + r),
+    m2::PointD(xy.first + r, xy.second + r),
+    m2::PointD(xy.first + r, xy.second - r)
+  };
+  for (int i = 0; i < 4; ++i)
+  {
+    m2::PointD const & p1 = cellCorners[i];
+    m2::PointD const & p2 = cellCorners[i == 0 ? 3 : i - 1];
+    if (m2::SegmentsIntersect(a, b, p1, p2)) return CELL_TRIANGLE_INTERSECT;
+    if (m2::SegmentsIntersect(b, c, p1, p2)) return CELL_TRIANGLE_INTERSECT;
+    if (m2::SegmentsIntersect(c, a, p1, p2)) return CELL_TRIANGLE_INTERSECT;
+  }
+  if (xy.first - r <= a.x && a.x <= xy.first + r && xy.second - r <= a.y && a.y <= xy.second + r)
+    return TRIANGLE_INSIDE_CELL;
+  if (m2::IsPointStrictlyInsideTriangle(cellCorners[0], a, b, c))
+    return CELL_INSIDE_TRIANGLE;
+  return CELL_TRIANGLE_NO_INTERSECTION;
+}
+
+template <class CellIdT, typename F>
+void CoverTriangle(m2::PointD const & a, m2::PointD const & b, m2::PointD const & c,
+                   F const & output, uint8_t const level = CellIdT::DEPTH_LEVELS - 1,
+                   CellIdT const startCell = CellIdT::Root())
+{
+  ASSERT_LESS_OR_EQUAL(startCell.Level(), level, (a, b, c));
+  CellTriangleIntersection intersection = IntersectCellWithTriangle(startCell, a, b, c);
+
+  if (intersection == CELL_TRIANGLE_NO_INTERSECTION)
+    return;
+
+  if (startCell.Level() == level || intersection == CELL_INSIDE_TRIANGLE)
+  {
+    output(startCell);
+    return;
+  }
+
+  for (uint8_t child = 0; child < 4; ++child)
+    CoverTriangle(a, b, c, output, level, startCell.Child(child));
+}
+
+template <class CellIdT>
+class Covering
+{
+public:
+  typedef CellIdT CellId;
+  typedef typename CellId::LessQueueOrder LessQueueOrder;
+
+  Covering() : m_Size(0) {}
+
+  explicit Covering(CellId cell) : m_Size(1)
+  {
+    m_Covering[cell.Level()].push_back(cell);
+  }
+
+  explicit Covering(vector<CellId> const & v)
+  {
+    for (size_t i = 0; i < v.size(); ++i)
+      m_Covering[v[i].Level()].push_back(v[i]);
+    Sort();
+    Unique();
+    RemoveDuplicateChildren();
+    RemoveFullSquares();
+    m_Size = CalculateSize();
+  }
+
+  // Cover triangle.
+  Covering(m2::PointD const & a, m2::PointD const & b, m2::PointD const & c,
+           int level = CellId::DEPTH_LEVELS - 1)
+  {
+    // TODO: ASSERT(a != b), ASSERT(b != c), ASSERT(a != c) ?
+    ASSERT(0 <= level && level <= CellId::DEPTH_LEVELS, (level, CellId::Root()));
+    CoverTriangleInfo info;
+    info.m_pCovering = this;
+    info.m_A = a;
+    info.m_B = b;
+    info.m_C = c;
+    info.m_Level = level;
+    CoverTriangleImpl(info, CellId::Root());
+    Sort();
+    RemoveFullSquares();
+    m_Size = CalculateSize();
+  }
+
+  size_t Size() const
+  {
+    ASSERT_EQUAL(m_Size, CalculateSize(), ());
+    return m_Size;
+  }
+
+  void Append(Covering<CellId> const & c)
+  {
+    AppendWithoutNormalize(c);
+    RemoveDuplicateChildren();
+    RemoveFullSquares();
+    m_Size = CalculateSize();
+  }
+
+  void OutputToVector(vector<CellId> & result) const
+  {
+    for (int level = 0; level < CellId::DEPTH_LEVELS; ++level)
+        result.insert(result.end(), m_Covering[level].begin(), m_Covering[level].end());
+  }
+
+  void OutputToVector(vector<int64_t> & result) const
+  {
+    for (int level = 0; level < CellId::DEPTH_LEVELS; ++level)
+      for (size_t i = 0; i < m_Covering[level].size(); ++i)
+        result.push_back(m_Covering[level][i].ToInt64());
+  }
+
+  void Simplify(int64_t minId = 0)
+  {
+    int cellsSimplified = 0;
+    int const initialSize = m_Size;
+    for (int level = CellId::DEPTH_LEVELS - 1; level > 1; --level)
+    {
+      if (m_Covering[level].size() >= 2)
+      {
+        int const initialLevelSize = static_cast<int>(m_Covering[level].size());
+        SimplifyLevel(level, minId);
+        cellsSimplified += initialLevelSize - static_cast<int>(m_Covering[level].size());
+        if (cellsSimplified > initialSize / 2)
+          break;
+      }
+    }
+    RemoveDuplicateChildren();
+    RemoveFullSquares();
+    m_Size = CalculateSize();
+  }
+
+private:
+
+  void SimplifyLevel(int level, int64_t minId)
+  {
+    map<CellId, uint32_t, LessQueueOrder> parentCellCounts;
+    typedef typename vector<CellId>::const_iterator ConstIteartor;
+    for (ConstIteartor it = m_Covering[level].begin(); it != m_Covering[level].end(); ++it)
+      if (it->Parent().ToInt64() >= minId)
+        ++parentCellCounts[it->Parent()];
+
+    vector<CellId> parentCells, childCells;
+    for (ConstIteartor it = m_Covering[level].begin(); it != m_Covering[level].end(); ++it)
+    {
+      if (parentCellCounts[it->Parent()] > 1)
+        parentCells.push_back(it->Parent());
+      else
+        childCells.push_back(*it);
+    }
+    ASSERT(IsSorted(parentCells.begin(), parentCells.end(), LessQueueOrder()), (parentCells));
+    ASSERT(IsSorted(childCells.begin(), childCells.end(), LessQueueOrder()), (childCells));
+    m_Covering[level].swap(childCells);
+    parentCells.erase(unique(parentCells.begin(), parentCells.end()), parentCells.end());
+    AppendToVector(m_Covering[level - 1], parentCells);
+  }
+
+  static void AppendToVector(vector<CellId> & a, vector<CellId> const & b)
+  {
+    ASSERT(IsSortedAndUnique(a.begin(), a.end(), LessQueueOrder()), (a));
+    ASSERT(IsSortedAndUnique(b.begin(), b.end(), LessQueueOrder()), (b));
+    vector<CellId> merged;
+    set_union(a.begin(), a.end(), b.begin(), b.end(), back_inserter(merged), LessQueueOrder());
+    a.swap(merged);
+  }
+
+  template <typename CompareT>
+  struct CompareCellsAtLevel
+  {
+    explicit CompareCellsAtLevel(int level) : m_Level(level) {}
+
+    bool operator() (CellId id1, CellId id2) const
+    {
+      return m_Comp(id1.AncestorAtLevel(m_Level), id2.AncestorAtLevel(m_Level));
+    }
+
+    CompareT m_Comp;
+    int m_Level;
+  };
+
+  void AppendWithoutNormalize(Covering const & c)
+  {
+    for (int level = CellId::DEPTH_LEVELS - 1; level >= 0; --level)
+      AppendToVector(m_Covering[level], c.m_Covering[level]);
+  }
+
+  void Sort()
+  {
+    for (int level = 0; level < CellId::DEPTH_LEVELS; ++level)
+      sort(m_Covering[level].begin(), m_Covering[level].end(), LessQueueOrder());
+  }
+
+  void Unique()
+  {
+    for (int level = 0; level < CellId::DEPTH_LEVELS; ++level)
+    {
+      vector<CellId> & covering = m_Covering[level];
+      ASSERT(IsSorted(covering.begin(), covering.end(), LessQueueOrder()), (covering));
+      covering.erase(unique(covering.begin(), covering.end()), covering.end());
+    }
+  }
+
+  void RemoveDuplicateChildren()
+  {
+    RemoveDuplicateChildrenImpl();
+#ifdef DEBUG
+    // Assert that all duplicate children were removed.
+    vector<int64_t> v1, v2;
+    OutputToVector(v1);
+    RemoveDuplicateChildrenImpl();
+    OutputToVector(v2);
+    ASSERT_EQUAL(v1, v2, ());
+#endif
+  }
+
+  void RemoveDuplicateChildrenImpl()
+  {
+    for (int parentLevel = 0; parentLevel < static_cast<int>(m_Covering.size()) - 1; ++parentLevel)
+    {
+      if (m_Covering[parentLevel].empty())
+        continue;
+      for (int childLevel = parentLevel + 1; childLevel < static_cast<int>(m_Covering.size()); ++childLevel)
+      {
+        vector<CellId> substracted;
+        CompareCellsAtLevel<LessQueueOrder> comparator(parentLevel);
+        ASSERT(IsSorted(m_Covering[childLevel].begin(), m_Covering[childLevel].end(), comparator),
+               (m_Covering[childLevel]));
+        ASSERT(IsSorted(m_Covering[parentLevel].begin(), m_Covering[parentLevel].end(), comparator),
+               (m_Covering[parentLevel]));
+        SetDifferenceUnlimited(m_Covering[childLevel].begin(), m_Covering[childLevel].end(),
+                               m_Covering[parentLevel].begin(), m_Covering[parentLevel].end(),
+                               back_inserter(substracted), comparator);
+        m_Covering[childLevel].swap(substracted);
+      }
+    }
+  }
+
+  void RemoveFullSquares()
+  {
+    vector<CellId> cellsToAppend;
+    for (int level = m_Covering.size() - 1; level >= 0; --level)
+    {
+      // a -> b + parents
+      vector<CellId> const & a = m_Covering[level];
+      vector<CellId> b;
+      vector<CellId> parents;
+      b.reserve(a.size());
+      for (size_t i = 0; i < a.size(); ++i)
+      {
+        if (i + 3 < a.size())
+        {
+          CellId const parent = a[i].Parent();
+          if (parent == a[i+1].Parent() && parent == a[i+2].Parent() && parent == a[i+3].Parent())
+          {
+            parents.push_back(parent);
+            i += 3;
+            continue;
+          }
+        }
+        b.push_back(a[i]);
+      }
+      m_Covering[level].swap(b);
+      if (level > 0)
+        AppendToVector(m_Covering[level - 1], parents);
+    }
+  }
+
+  size_t CalculateSize() const
+  {
+    size_t size = 0;
+    for (int level = 0; level < CellId::DEPTH_LEVELS; ++level)
+      size += m_Covering[level].size();
+    return size;
+  }
+
+  struct CoverTriangleInfo
+  {
+    m2::PointD m_A, m_B, m_C;
+    int m_Level;
+    Covering<CellId> * m_pCovering;
+  };
+
+  static void CoverTriangleImpl(CoverTriangleInfo const & info, CellId const cell)
+  {
+    ASSERT_LESS_OR_EQUAL(cell.Level(), info.m_Level, (info.m_A, info.m_B, info.m_C));
+    CellTriangleIntersection intersection =
+        IntersectCellWithTriangle(cell, info.m_A, info.m_B, info.m_C);
+
+    if (intersection == CELL_TRIANGLE_NO_INTERSECTION)
+      return;
+
+    if (cell.Level() == info.m_Level || intersection == CELL_INSIDE_TRIANGLE)
+    {
+      info.m_pCovering->m_Covering[cell.Level()].push_back(cell);
+      return;
+    }
+
+    for (uint8_t child = 0; child < 4; ++child)
+      CoverTriangleImpl(info, cell.Child(child));
+  }
+
+
+  array<vector<CellId>, CellId::DEPTH_LEVELS> m_Covering; // Covering by level.
+  size_t m_Size;
+};
+
+
+}