TGeoPolygon

    private:

        void ConvexCheck()
      Bool_t IsRightSided(Double_t* point, Int_t ind1, Int_t ind2) const
      Bool_t IsSegConvex(Int_t i1, Int_t i2 = -1) const
        void OutscribedConvex()

    public:

                      TGeoPolygon()
                      TGeoPolygon(Int_t nvert)
                      TGeoPolygon(const TGeoPolygon&)
              virtual ~TGeoPolygon()
             Double_t Area() const
       static TClass* Class()
               Bool_t Contains(Double_t* point) const
                 void FinishPolygon()
                Int_t GetNvert() const
            Double_t* GetX()
            Double_t* GetY()
      virtual TClass* IsA() const
               Bool_t IsClockwise() const
               Bool_t IsConvex() const
               Bool_t IsFinished() const
         TGeoPolygon& operator=(const TGeoPolygon&)
             Double_t Safety(Double_t* point, Int_t& isegment) const
                 void SetConvex(Bool_t flag = kTRUE)
                 void SetNextIndex(Int_t index = -1)
                 void SetXY(Double_t* x, Double_t* y)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)

    protected:

           Int_t fNvert      number of vertices (must be defined clockwise in XY plane)
           Int_t fNconvex    number of points of the outscribed convex polygon 
          Int_t* fInd        [fNvert] list of vertex indices
          Int_t* fIndc       [fNconvex] indices of vertices of the outscribed convex polygon
       Double_t* fX          ! pointer to list of current X coordinates of vertices
       Double_t* fY          ! pointer to list of current Y coordinates of vertices
      TObjArray* fDaughters  list of concave daughters

    public:

      static const enum TGeoPolygon:: kGeoConvex         
      static const enum TGeoPolygon:: kGeoFinishPolygon  
      static const enum TGeoPolygon:: kGeoACW            

Class Description

____________________________________________________________________________
 TGeoPolygon - Arbitrary polygon class
____________________________________________________________________________

 A polygon is a 2D shape defined by vertices in the XY plane. It is used by
 TGeoXtru class for computing Contains() and Safety(). Only the pointers to
 the actual lists of XY values are used - these are not owned by the class.

 To check if a point in XY plane is contained by a polygon, this is splitted
 into an outscribed convex polygon and the remaining polygons of its subtracton
 from the outscribed one. A point is INSIDE if it is
 contained by the outscribed polygon but NOT by the remaining ones. Since these
 can also be arbitrary polygons at their turn, a tree structure is formed:

  P = Pconvex - (Pconvex-P)           where (-) means 'subtraction'
  Pconvex-P = P1 + P2 + ...           where (+) means 'union'

  *Note that P1, P2, ... do not intersect each other and they are defined
   by subsets of the list of vertices of P. They can be splitted in the same
   way as P*

 Therefore, if C(P) represents the Boolean : 'does P contains a given point?',
 then:

 C(P) = C(Pconvex) .and. not(C(P1) | C(P2) | ...)

 For creating a polygon without TGeoXtru class, one has to call the constructor
 TGeoPolygon(nvert) and then SetXY(Double_t *x, Double_t *y) providing the
 arrays of X and Y vertex positions (defined clockwise) that have to 'live' longer
 than the polygon they will describe. This complication is due to efficiency reasons.
 At the end one has to call the FinishPolygon() method.

 Dummy constructor.

 Default constructor.

 Destructor

 Computes area of the polygon in [length^2].

 Check if a point given by X = point[0], Y = point[1] is inside the polygon.

 Check polygon convexity.

 Decompose polygon in a convex outscribed part and a list of daughter
 polygons that have to be substracted to get the actual one.

 Check if POINT is right-sided with respect to the segment defined by IND1 and IND2.

 Check if a segment [0..fNvert-1] belongs to the outscribed convex pgon.

 Compute indices for the outscribed convex polygon.

 Compute minimum distance from POINT to any segment. Returns segment index.

 Sets the next polygone index. If index<0 sets all indices consecutive
 in increasing order.

 Set X/Y array pointer for the polygon and daughters.

 constructors