netgen/libsrc/geom2d/csg2d.hpp

#ifndef NETGEN_CSG2D_HPP_INCLUDED
#define NETGEN_CSG2D_HPP_INCLUDED

#include "geometry2d.hpp"

namespace netgen
{

using namespace ngcore;
using netgen::Point;
using netgen::Vec;

inline double Area(const Point<2>& P, const Point<2>& Q, const Point<2>& R)
{
  return (Q[0]-P[0]) * (R[1]-P[1]) - (Q[1]-P[1]) * (R[0]-P[0]);
}


enum IntersectionType
{                 // types of intersection (detected in the first phase)
  NO_INTERSECTION = 0,
  X_INTERSECTION,
  T_INTERSECTION_Q,
  T_INTERSECTION_P,
  V_INTERSECTION,
  X_OVERLAP,
  T_OVERLAP_Q,
  T_OVERLAP_P,
  V_OVERLAP
};

enum IntersectionLabel
{      // for the classification of intersection vertices in the second phase
  NONE,
  CROSSING,
  BOUNCING,
  LEFT_ON,
  RIGHT_ON,
  ON_ON,
  ON_LEFT,
  ON_RIGHT,
  DELAYED_CROSSING,
  DELAYED_BOUNCING
};

enum EntryExitLabel
{         // for marking intersection vertices as "entry" or "exit"
  EXIT,
  ENTRY,
  NEITHER
};

enum IteratorType
{
  SOURCE,
  INTERSECTION,
  CROSSING_INTERSECTION,
  ALL
};


using Spline = SplineSeg3<2>;

struct Vertex : Point<2>
{
  Vertex (Point<2> p) : Point<2>(p) {}

  Vertex * prev = nullptr;
  Vertex * next = nullptr;
  unique_ptr<Vertex> pnext = nullptr;
  Vertex * neighbour = nullptr; // same vertex in other polygon (at intersections)
  double lam = -1.0;
  bool is_intersection = false;
  bool is_source = false;

  IntersectionLabel label = NONE;    // type of intersection vertex
  EntryExitLabel enex = NEITHER;        // entry/exit "flag"

  string bc = "";

  // In case the edge this - next is curved, store the spline information here
  optional<Spline> spline = nullopt;

  Vertex * Insert(Point<2> p, double lam = -1.0);

  void Link( Vertex * v )
  {
    neighbour = v;
    v->neighbour = this;
    is_intersection = true;
    v->is_intersection = true;
  }
};

struct VertexIterator
{
  struct iterator
  {
    iterator(Vertex* root, IteratorType IterType) :
      root(root), V(NULL), iterType(IterType)
    {
      if (root == NULL)
        return;

      if (nextVertex() == NULL)         // no (source/intersection) vertex found
        root = V = NULL;                // -> mark iterator as "end"
    }

    const iterator& operator++()
    {
      nextVertex();
      return *this;
    }

    Vertex* operator*()
    {
      return V;
    }

    bool operator!=(const iterator& other) const
    {
      return (root != other.root) || (V != other.V);
    }

    private:
    Vertex* root;
    Vertex* V;
    IteratorType iterType;

    //
    // find the next vertex
    // if iterType is ALL, then it is just the next vertex
    // if iterType is SOURCE, then it is the next source vertex
    // if iterType is INTERSECTION, then it is the next intersection vertex
    // if iterType is CROSSING_INTERSECTION, then it is the next intersection vertex with CROSSING label
    //
    Vertex* nextVertex()
    {
      bool nextFound = false;

      if (V == NULL)
      {                  // find first (source/intersection) vertex
        V = root;
        switch(iterType)
        {
          case ALL:
            nextFound = true;
            break;
          case SOURCE:
            if (V->is_source)
              nextFound = true;
            break;
          case INTERSECTION:
            if (V->is_intersection)
              nextFound = true;
            break;
          case CROSSING_INTERSECTION:
            if (V->is_intersection && (V->label == CROSSING))
              nextFound = true;
            break;
        }
      }

      while (!nextFound)
      {              // find next (source/intersection) vertex
        switch(iterType)
        {
          case ALL:
            V = V->next;
            break;
          case SOURCE:
            do {
              V = V->next;
            } while (!V->is_source && V != root);
            break;
          case INTERSECTION:
            do {
              V = V->next;
            } while (!V->is_intersection && V != root);
            break;
          case CROSSING_INTERSECTION:
            do {
              V = V->next;
            } while ( ( !V->is_intersection || (V->label != CROSSING) ) && V != root);
            break;
        }

        if (V == root)
        {                // back at the root vertex?
          root = V = NULL;              // -> mark iterator as "end"
          return(V);
        }

        switch(iterType)
        {
          case ALL:
            nextFound = true;
            break;
          case SOURCE:
            if (V->is_source)
              nextFound = true;
            break;
          case INTERSECTION:
            if (V->is_intersection)
              nextFound = true;
            break;
          case CROSSING_INTERSECTION:
            if (V->is_intersection && (V->label == CROSSING))
              nextFound = true;
            break;
        }
      }
      return(V);
    }
  };

  public:
  VertexIterator() : root(NULL) {};

  iterator begin() { return iterator(root, iterType); }
  iterator end()   { return iterator(NULL, iterType); }

  Vertex* root;
  IteratorType iterType;
};


struct Edge
{
  Vertex * v0 = nullptr;
  Vertex * v1 = nullptr;

  Edge (Vertex* v, Vertex* w) : v0(v), v1(w) { };
};

struct EdgeIterator
{
  struct iterator
  {
    iterator(Vertex* root, IteratorType IterType) :
      root(root), one(NULL), two(NULL), iterType(IterType)
    {
      if (root == NULL)
        return;

      if (nextEdge() == NULL)           // no source edge found
        root = one = two = NULL;        // -> mark iterator as "end"
    }

    const iterator& operator++() { nextEdge(); return *this; }

    Edge operator*()
    {
      return Edge(one,two);
    }

    bool operator!=(const iterator& other) const
    {
      return (root != other.root) || (one != other.one) || (two != other.two);
    }

    private:
    Vertex* root;
    Vertex* one;
    Vertex* two;
    IteratorType iterType;

    //
    // find the next vertex, starting at curr
    // if iterType is ALL, then it is just the next vertex
    // if iterType is SOURCE, then it is the next source vertex
    //
    Vertex* nextVertex(Vertex* curr)
    {
      if (curr == NULL)
        return(NULL);

      switch(iterType)
      {
        case ALL:
          curr = curr->next;
          break;

        case SOURCE:
          do {
            curr = curr->next;
          } while (!curr->is_source);
          break;
        default:
          ;
      }

      return(curr);
    }

    //
    // find the next edge
    //
    Vertex* nextEdge()
    {
      if (root == NULL)                 // empty polygon?
        return (NULL);

      if (one == NULL)
      {                // find one (source) vertex
        one = root;                     // note: root is always a (source) vertex
        two = nextVertex(one);
        if (two == one)                 // just one (source) vertex
          return(NULL);                 // -> no (source) edges
        return(one);
      }

      if (two == root)
      {                // back at the root vertex?
        root = one = two = NULL;        // -> mark iterator as "end"
        return(NULL);
      }

      one = two;
      two = nextVertex(one);

      return (one);
    }
  };

  public:
  EdgeIterator() : root(NULL) {};

  iterator begin() { return iterator(root, iterType); }
  iterator end()   { return iterator(NULL, iterType); }

  Vertex* root;
  IteratorType iterType;
};


inline int CalcSide( const Point<2> & p0, const Point<2> & p1, const Point<2> & r )
{
  if ( (p0[1] < r[1]) != (p1[1] < r[1]) )
  {
    if (p0[0] >= r[0])
    {
      if (p1[0] > r[0])
        return 2 * (p1[1] > p0[1]) - 1;
      else
        if ( (Area(p0,p1,r) > 0) == (p1[1] > p0[1]) )
          return 2 * (p1[1] > p0[1]) - 1;
    }
    else
    {
      if (p1[0] > r[0])
        if ( (Area(p0,p1,r) > 0) == (p1[1] > p0[1]) )
          return 2 * (p1[1] > p0[1]) - 1;
    }
  }
  return 0;
}

struct Polygon2d
{
  unique_ptr<Vertex> first = nullptr;

  Polygon2d() = default;

  Polygon2d(const Polygon2d & p)
    : first(nullptr)
  {
    for(auto v : p.Vertices(ALL))
      AppendVertex(*v);
  }

  Polygon2d & operator=(const Polygon2d & p)
  {
    first = nullptr;
    if(p.first)
      for(const auto v : p.Vertices(ALL))
        AppendVertex(*v);
    return *this;
  }

  Vertex & AppendVertex(const Vertex & v)
  {
    auto & vnew = Append( static_cast<Point<2>>(v), true );
    vnew.bc = v.bc;
    if(v.spline)
      vnew.spline = *v.spline;
    return vnew;
  }

  Vertex & Append(Point<2> p, bool source = false)
  {
    Vertex * vnew;
    if(first==nullptr)
    {
      first = make_unique<Vertex>(p);
      first->next = first.get();
      first->prev = first.get();
      vnew = first.get();
    }
    else
    {
      vnew = first->prev->Insert(p);
    }

    vnew->is_source = source;
    //     cout << "size after " << Size() << endl;
    return *vnew;
  }

  void Remove (Vertex* v)
  {
    v->prev->next = v->next;
    v->next->prev = v->prev;
    if(first.get() == v)
      first = std::move(v->pnext);
    else
      v->prev->pnext = std::move(v->pnext);
  }

  bool IsInside( Point<2> r ) const
  {
    int w = 0;
    for(auto e : Edges(ALL))
      w += CalcSide(*e.v0, *e.v1, r);
    return ( (w % 2) != 0 );
  }

  EdgeIterator Edges(IteratorType iterType) const
  {
    EdgeIterator it;
    it.iterType = iterType;
    it.root = first.get();
    return it;
  }

  VertexIterator Vertices(IteratorType iterType, Vertex* first_ = nullptr) const
  {
    VertexIterator it;
    it.iterType = iterType;
    it.root = (first_ == nullptr) ? first.get() : first_;
    return it;
  }

  //
  // check, if all vertices have the ON_ON label
  //
  bool allOnOn()
  {
    for (Vertex* v : Vertices(ALL))
      if (v->label != ON_ON)
        return(false);
    return(true);
  }

  //
  // check, if the polygon does not contain any crossing intersection vertex
  // or crossing intersection chain or (if we want to compute the union instead
  // of the intersection) a bouncing vertex or a bouncing intersection chain
  //
  bool noCrossingVertex(bool union_case = false)
  {
    for (Vertex* v : Vertices(ALL))
      if (v->is_intersection)
      {
        if ( (v->label == CROSSING) || (v->label == DELAYED_CROSSING) )
          return(false);

        if (union_case && ( (v->label == BOUNCING) || (v->label == DELAYED_BOUNCING) ) )
          return(false);
      }
    return(true);
  }

  //
  // return a non-intersection point
  //
  Point<2> getNonIntersectionPoint()
  {
    for (Vertex* v : Vertices(ALL))
      if (!v->is_intersection)
        return *v;

    // no non-intersection vertex found -> find suitable edge midpoint
    for (Vertex* v : Vertices(ALL))
      // make sure that edge from V to V->next is not collinear with other polygon
      if ( (v->next->neighbour != v->neighbour->prev) && (v->next->neighbour != v->neighbour->next) )
        // return edge midpoint
        return Center(*v, *v->next);
    throw Exception("no point found");
  }

  //
  // return and insert a non-intersection vertex
  //
  Vertex* getNonIntersectionVertex()
  {
    for (Vertex* v : Vertices(ALL))
      if (!v->is_intersection)
        return(v);

    // no non-intersection vertex found -> generate and return temporary vertex
    for (Vertex* v : Vertices(ALL))
      // make sure that edge from V to V->next is not collinear with other polygon
      if ( (v->next->neighbour != v->neighbour->prev) && (v->next->neighbour != v->neighbour->next) )
      {
        // add edge midpoint as temporary vertex
        auto p = Center(*v, *v->next);
        return v->Insert(p);
      }
    return(NULL);
  }

  void SetBC(string bc)
  {
    for(auto v : Vertices(ALL))
      v->bc = bc;
  }

  size_t Size() const
  {
    if(first==nullptr) return 0;

    size_t cnt = 0;

    for(auto v : Vertices(ALL))
      cnt++;

    return cnt;
  }
};


struct Solid2d
{
  Array<Polygon2d> polys;

  string name = "";

  Solid2d() = default;
  Solid2d(string name_) : name(name_) {}

  Solid2d operator+(Solid2d & other);
  Solid2d operator*(Solid2d & other);
  Solid2d operator-(Solid2d other);

  void Append( const Polygon2d & poly )
  {
    polys.Append(poly);
  }

  bool IsInside( Point<2> r ) const;
  bool IsLeftInside( const Vertex & p0 );
  bool IsRightInside( const Vertex & p0 );

  void SetBC(string bc)
  {
    for(auto & p : polys)
      for(auto v : p.Vertices(ALL))
        v->bc = bc;
  }
};

class CSG2d
{
  public:
    Array<Solid2d> solids;

    void Add ( Solid2d s )
    {
      solids.Append(s);
    }

    shared_ptr<netgen::SplineGeometry2d> GenerateSplineGeometry();
};

Solid2d Circle(double x, double y, double r, string name="", string bc="");
Solid2d Rectangle(double x0, double x1, double y0, double y1, string name="", string bc="");

Solid2d AddIntersectionPoints ( Solid2d s1, Solid2d s2 );
Solid2d ClipSolids ( Solid2d s1, Solid2d s2, bool intersect=true );

}
#endif // NETGEN_CSG2D_HPP_INCLUDED