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Shape.h

/*
 *  Digraph.h
 *  nlivarot
 *
 *  Created by fred on Thu Jun 12 2003.
 *
 */

#ifndef my_shape
#define my_shape

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <inttypes.h>
#include <cstring>
#include <vector>

#include "libnr/nr-point.h"
#include "livarot/livarot-forward.h"
#include "livarot/sweep-event.h"
#include "livarot/sweep-tree.h"
#include "livarot/LivarotDefs.h"

/*
 * the Shape class (was the Digraph class, as the header says) stores digraphs (no kidding!) of which 
 * a very interesting kind are polygons.
 * the main use of this class is the ConvertToShape() (or Booleen(), quite the same) function, which
 * removes all problems a polygon can present: duplicate points or edges, self-intersection. you end up with a
 * full-fledged polygon
 */

// possible values for the "type" field in the Shape class:
enum
{
  shape_graph = 0,            // it's just a graph; a bunch of edges, maybe intersections
  shape_polygon = 1,          // a polygon: intersection-free, edges oriented so that the inside is on their left
  shape_polypatch = 2         // a graph without intersection; each face is a polygon (not yet used)
};

class IntLigne;
class BitLigne;
class AlphaLigne;

class Shape
{
public:

    struct back_data
    {
      int pathID, pieceID;
      double tSt, tEn;
    };
    
    struct voronoi_point
    {                   // info for points treated as points of a voronoi diagram (obtained by MakeShape())
      double value;           // distance to source
      int winding;            // winding relatively to source
    };
    
    struct voronoi_edge
    {                   // info for edges, treated as approximation of edges of the voronoi diagram
      int leF, riF;           // left and right site
      double leStX, leStY, riStX, riStY;  // on the left side: (leStX,leStY) is the smallest vector from the source to st
      // etc...
      double leEnX, leEnY, riEnX, riEnY;
    };

    struct quick_raster_data
    {
      double x;                   // x-position on the sweepline
      int    bord;                  // index of the edge
      int    ind;       // index of qrsData elem for edge (ie inverse of the bord)
      int    next,prev; // dbl linkage
    };

    enum sTreeChangeType
    {
      EDGE_INSERTED = 0,
      EDGE_REMOVED = 1,
      INTERSECTION = 2
    };
  
    struct sTreeChange
    {
      sTreeChangeType type;         // type of modification to the sweepline:
      int ptNo;               // point at which the modification takes place
      
      Shape *src;             // left edge (or unique edge if not an intersection) involved in the event
      int bord;
      Shape *osrc;            // right edge (if intersection)
      int obord;
      Shape *lSrc;            // edge directly on the left in the sweepline at the moment of the event
      int lBrd;
      Shape *rSrc;            // edge directly on the right
      int rBrd;
    };
    
    struct incidenceData
    {
      int nextInc;            // next incidence in the linked list
      int pt;                 // point incident to the edge (there is one list per edge)
      double theta;           // coordinate of the incidence on the edge
    };
    
    Shape();
    ~Shape();

    void MakeBackData(bool nVal);
    void MakeVoronoiData(bool nVal);

    void Affiche();

    // insertion/deletion/movement of elements in the graph
    void Copy(Shape *a);
    // -reset the graph, and ensure there's room for n points and m edges
    void Reset(int n = 0, int m = 0);
    //  -points:
    int AddPoint(const NR::Point x);      // as the function name says
    // returns the index at which the point has been added in the array
    void SubPoint(int p);     // removes the point at index p
    // nota: this function relocates the last point to the index p
    // so don't trust point indices if you use SubPoint
    void SwapPoints(int a, int b);  // swaps 2 points at indices a and b
    void SwapPoints(int a, int b, int c); // swaps 3 points: c <- a <- b <- c
    void SortPoints();  // sorts the points if needed (checks the need_points_sorting flag)

    //  -edges:
    // add an edge between points of indices st and en    
    int AddEdge(int st, int en);
    // return the edge index in the array
    
    // add an edge between points of indices st and en    
    int AddEdge(int st, int en, int leF, int riF);
    // return the edge index in the array
    
    // version for the voronoi (with faces IDs)
    void SubEdge(int e);            // removes the edge at index e (same remarks as for SubPoint)
    void SwapEdges(int a, int b);   // swaps 2 edges
    void SwapEdges(int a, int b, int c);  // swaps 3 edges
    void SortEdges();   // sort the edges if needed (checks the need_edges_sorting falg)

    // primitives for topological manipulations
  
    // endpoint of edge at index b that is different from the point p      
    inline int Other(int p, int b) const
    {
      if (getEdge(b).st == p) {
          return getEdge(b).en;
      }
      return getEdge(b).st;
    }

    // next edge (after edge b) in the double-linked list at point p  
    inline int NextAt(int p, int b) const 
    {
      if (p == getEdge(b).st) {
          return getEdge(b).nextS;
      }
      else if (p == getEdge(b).en) {
          return getEdge(b).nextE;
      }
      
      return -1;
    }

    // previous edge
    inline int PrevAt(int p, int b) const
    {
      if (p == getEdge(b).st) {
          return getEdge(b).prevS;
      }
      else if (p == getEdge(b).en) {
          return getEdge(b).prevE;
      }
      
      return -1;
    }

    // same as NextAt, but the list is considered circular  
    inline int CycleNextAt(int p, int b) const  
    {
      if (p == getEdge(b).st) {
          if (getEdge(b).nextS < 0) {
            return getPoint(p).incidentEdge[FIRST];
          }
          return getEdge(b).nextS;
      } else if (p == getEdge(b).en) {
          if (getEdge(b).nextE < 0) {
            return getPoint(p).incidentEdge[FIRST];
          }
          
          return getEdge(b).nextE;
      }
      
      return -1;
    }

    // same as PrevAt, but the list is considered circular  
    inline int CyclePrevAt(int p, int b) const
    {
      if (p == getEdge(b).st) {
          if (getEdge(b).prevS < 0) {
            return getPoint(p).incidentEdge[LAST];
          }
          return getEdge(b).prevS;
      } else if (p == getEdge(b).en) {
          if (getEdge(b).prevE < 0) {
            return getPoint(p).incidentEdge[LAST];
          }
          return getEdge(b).prevE;
      }
      
      return -1;
    }
    
    void ConnectStart(int p, int b);      // set the point p as the start of edge b
    void ConnectEnd(int p, int b);  // set the point p as the end of edge b
    void DisconnectStart(int b);    // disconnect edge b from its start point
    void DisconnectEnd(int b);      // disconnect edge b from its end point

    // reverses edge b (start <-> end)    
    void Inverse(int b);            
    // calc bounding box and sets leftX,rightX,topY and bottomY to their values
    void CalcBBox(bool strict_degree = false);
    
    // debug function: plots the graph (mac only)
    void Plot(double ix, double iy, double ir, double mx, double my, bool doPoint,
            bool edgesNo, bool pointNo, bool doDir, char *fileName);

    // transforms a polygon in a "forme" structure, ie a set of contours, which can be holes (see ShapeUtils.h)
    // return NULL in case it's not possible
    void ConvertToForme(Path *dest);
    
    // version to use when conversion was done with ConvertWithBackData(): will attempt to merge segment belonging to 
    // the same curve
    // nota: apparently the function doesn't like very small segments of arc
    void ConvertToForme(Path *dest, int nbP, Path **orig, bool splitWhenForced = false);
    // version trying to recover the nesting of subpaths (ie: holes)
    void ConvertToFormeNested(Path *dest, int nbP, Path **orig, int wildPath, int &nbNest,
                        int *&nesting, int *&contStart, bool splitWhenForced = false);
  
    // sweeping a digraph to produce a intersection-free polygon
    // return 0 if everything is ok and a return code otherwise (see LivarotDefs.h)
    // the input is the Shape "a"
    // directed=true <=> non-zero fill rule    
    int ConvertToShape(Shape *a, FillRule directed = fill_nonZero, bool invert = false);
    // directed=false <=> even-odd fill rule
    // invert=true: make as if you inverted all edges in the source
    int Reoriente(Shape *a);  // subcase of ConvertToShape: the input a is already intersection-free
    // all that's missing are the correct directions of the edges
    // Reoriented is equivalent to ConvertToShape(a,false,false) , but faster sicne
    // it doesn't computes interections nor adjacencies
    void ForceToPolygon();    // force the Shape to believe it's a polygon (eulerian+intersection-free+no
    // duplicate edges+no duplicate points)
    // be careful when using this function

    // the coordinate rounding function
    inline static double Round(double x)
    {
      return ldexp(rint(ldexp(x, 5)), -5);
    }
    
    // 2 miscannellous variations on it, to scale to and back the rounding grid
    inline static double HalfRound(double x)
    {
      return ldexp(x, -5);
    }
    
    inline static double IHalfRound(double x)
    {
      return ldexp(x, 5);
    }

    // boolean operations on polygons (requests intersection-free poylygons)
    // boolean operation types are defined in LivarotDefs.h
    // same return code as ConvertToShape
    int Booleen(Shape *a, Shape *b, BooleanOp mod, int cutPathID = -1);

    // create a graph that is an offseted version of the graph "of"
    // the offset is dec, with joins between edges of type "join" (see LivarotDefs.h)
    // the result is NOT a polygon; you need a subsequent call to ConvertToShape to get a real polygon
    int MakeOffset(Shape *of, double dec, JoinType join, double miter);
  
    int PtWinding(const NR::Point px) const; // plus rapide
    int Winding(const NR::Point px) const;
  
    // rasterization
    void BeginRaster(float &pos, int &curPt);
    void EndRaster();
    void BeginQuickRaster(float &pos, int &curPt);
    void EndQuickRaster();
  
    void Scan(float &pos, int &curP, float to, float step);
    void QuickScan(float &pos, int &curP, float to, bool doSort, float step);
    void DirectScan(float &pos, int &curP, float to, float step);
    void DirectQuickScan(float &pos, int &curP, float to, bool doSort, float step);

    void Scan(float &pos, int &curP, float to, FloatLigne *line, bool exact, float step);
    void Scan(float &pos, int &curP, float to, FillRule directed, BitLigne *line, bool exact, float step);
    void Scan(float &pos, int &curP, float to, AlphaLigne *line, bool exact, float step);

    void QuickScan(float &pos, int &curP, float to, FloatLigne* line, float step);
    void QuickScan(float &pos, int &curP, float to, FillRule directed, BitLigne* line, float step);
    void QuickScan(float &pos, int &curP, float to, AlphaLigne* line, float step);

    void Transform(NR::Matrix const &tr)
        {for(std::vector<dg_point>::iterator it=_pts.begin();it!=_pts.end();it++) it->x*=tr;}

    std::vector<back_data> ebData;
    std::vector<voronoi_point> vorpData;
    std::vector<voronoi_edge> voreData;

    int nbQRas;
    int firstQRas;
    int lastQRas;
    std::vector<quick_raster_data> qrsData;

    std::vector<sTreeChange> chgts;
    int nbInc;
    int maxInc;

    incidenceData *iData;
    // these ones are allocated at the beginning of each sweep and freed at the end of the sweep
    SweepTreeList *sTree;
    SweepEventQueue *sEvts;
    
    // bounding box stuff
    double leftX, topY, rightX, bottomY;

    // topological information: who links who?
    struct dg_point
    {
      NR::Point x;            // position
      int dI, dO;       // indegree and outdegree
        int incidentEdge[2];    // first and last incident edge
      int oldDegree;
      
      int totalDegree() const { return dI + dO; }
    };
    
    struct dg_arete
    {
      NR::Point dx;           // edge vector
      int st, en;       // start and end points of the edge
      int nextS, prevS; // next and previous edge in the double-linked list at the start point
      int nextE, prevE; // next and previous edge in the double-linked list at the end point
    };

    // lists of the nodes and edges
    int maxPt; // [FIXME: remove this]
    int maxAr; // [FIXME: remove this]
    
    // flags
    int type;
    
    inline int numberOfPoints() const { return _pts.size(); }
    inline bool hasPoints() const { return (_pts.empty() == false); }
    inline int numberOfEdges() const { return _aretes.size(); }
    inline bool hasEdges() const { return (_aretes.empty() == false); }

    inline void needPointsSorting() { _need_points_sorting = true; }
    inline void needEdgesSorting()  { _need_edges_sorting = true; }
    
    inline bool hasBackData() const { return _has_back_data; }
    
    inline dg_point const &getPoint(int n) const { return _pts[n]; }
    inline dg_arete const &getEdge(int n) const { return _aretes[n]; }

private:

    friend class SweepTree;
    friend class SweepEvent;
    friend class SweepEventQueue;
  
    // temporary data for the various algorithms
    struct edge_data
    {
      int weight;             // weight of the edge (to handle multiple edges)
      NR::Point rdx;          // rounded edge vector
      double length, sqlength, ilength, isqlength;    // length^2, length, 1/length^2, 1/length
      double siEd, coEd;            // siEd=abs(rdy/length) and coEd=rdx/length
      edge_data() : weight(0), length(0.0), sqlength(0.0), ilength(0.0), isqlength(0.0), siEd(0.0), coEd(0.0) {}
      // used to determine the "most horizontal" edge between 2 edges
    };
    
    struct sweep_src_data
    {
      void *misc;             // pointer to the SweepTree* in the sweepline
      int firstLinkedPoint;   // not used
      int stPt, enPt;         // start- end end- points for this edge in the resulting polygon
      int ind;                // for the GetAdjacencies function: index in the sliceSegs array (for quick deletions)
      int leftRnd, rightRnd;  // leftmost and rightmost points (in the result polygon) that are incident to
      // the edge, for the current sweep position
      // not set if the edge doesn't start/end or intersect at the current sweep position
      Shape *nextSh;          // nextSh and nextBo identify the next edge in the list
      int nextBo;             // they are used to maintain a linked list of edge that start/end or intersect at
      // the current sweep position
      int curPoint, doneTo;
      double curT;
    };
    
    struct sweep_dest_data
    {
      void *misc;             // used to check if an edge has already been seen during the depth-first search
      int suivParc, precParc; // previous and current next edge in the depth-first search
      int leW, riW;           // left and right winding numbers for this edge
      int ind;                // order of the edges during the depth-first search
    };
    
    struct raster_data
    {
      SweepTree *misc;        // pointer to the associated SweepTree* in the sweepline
      double lastX, lastY, curX, curY;    // curX;curY is the current intersection of the edge with the sweepline
      // lastX;lastY is the intersection with the previous sweepline
      bool sens;              // true if the edge goes down, false otherwise
      double calcX;           // horizontal position of the intersection of the edge with the
      // previous sweepline
      double dxdy, dydx;            // horizontal change per unit vertical move of the intersection with the sweepline
      int guess;
    };
    
    struct point_data
    {
      int oldInd, newInd;           // back and forth indices used when sorting the points, to know where they have
      // been relocated in the array
      int pending;            // number of intersection attached to this edge, and also used when sorting arrays
      int edgeOnLeft;         // not used (should help speeding up winding calculations)
      int nextLinkedPoint;    // not used
      Shape *askForWindingS;
      int askForWindingB;
      NR::Point  rx;          // rounded coordinates of the point
    };
    
    
    struct edge_list
    {                   // temporary array of edges for easier sorting
      int no;
      bool starting;
      NR::Point x;
    };

    void initialisePointData();
    void initialiseEdgeData();
    void clearIncidenceData();

    void _countUpDown(int P, int *numberUp, int *numberDown, int *upEdge, int *downEdge) const;
    void _countUpDownTotalDegree2(int P, int *numberUp, int *numberDown, int *upEdge, int *downEdge) const;
    void _updateIntersection(int e, int p);
  
    // activation/deactivation of the temporary data arrays
    void MakePointData(bool nVal);
    void MakeEdgeData(bool nVal);
    void MakeSweepSrcData(bool nVal);
    void MakeSweepDestData(bool nVal);
    void MakeRasterData(bool nVal);
    void MakeQuickRasterData(bool nVal);

    void SortPoints(int s, int e);
    void SortPointsByOldInd(int s, int e);

    // fonctions annexes pour ConvertToShape et Booleen
    void ResetSweep();  // allocates sweep structures
    void CleanupSweep();      // deallocates them

    // edge sorting function    
    void SortEdgesList(edge_list *edges, int s, int e);
  
    void TesteIntersection(SweepTree *t, Side s, bool onlyDiff);  // test if there is an intersection
    bool TesteIntersection(SweepTree *iL, SweepTree *iR, NR::Point &atx, double &atL, double &atR, bool onlyDiff);
    bool TesteIntersection(Shape *iL, Shape *iR, int ilb, int irb,
                     NR::Point &atx, double &atL, double &atR,
                     bool onlyDiff);
    bool TesteAdjacency(Shape *iL, int ilb, const NR::Point atx, int nPt,
                  bool push);
    int PushIncidence(Shape *a, int cb, int pt, double theta);
    int CreateIncidence(Shape *a, int cb, int pt);
    void AssemblePoints(Shape *a);
    int AssemblePoints(int st, int en);
    void AssembleAretes(FillRule directed = fill_nonZero);
    void AddChgt(int lastPointNo, int lastChgtPt, Shape *&shapeHead,
             int &edgeHead, sTreeChangeType type, Shape *lS, int lB, Shape *rS,
             int rB);
    void CheckAdjacencies(int lastPointNo, int lastChgtPt, Shape *shapeHead, int edgeHead);
    void CheckEdges(int lastPointNo, int lastChgtPt, Shape *a, Shape *b, BooleanOp mod);
    void Avance(int lastPointNo, int lastChgtPt, Shape *iS, int iB, Shape *a, Shape *b, BooleanOp mod);
    void DoEdgeTo(Shape *iS, int iB, int iTo, bool direct, bool sens);
    void GetWindings(Shape *a, Shape *b = NULL, BooleanOp mod = bool_op_union, bool brutal = false);

    void Validate();

    int Winding(int nPt) const;
    void SortPointsRounded();
    void SortPointsRounded(int s, int e);
    
    void CreateEdge(int no, float to, float step);
    void AvanceEdge(int no, float to, bool exact, float step);
    void DestroyEdge(int no, float to, FloatLigne *line);
    void AvanceEdge(int no, float to, FloatLigne *line, bool exact, float step);
    void DestroyEdge(int no, BitLigne *line);
    void AvanceEdge(int no, float to, BitLigne *line, bool exact, float step);
    void DestroyEdge(int no, AlphaLigne *line);
    void AvanceEdge(int no, float to, AlphaLigne *line, bool exact, float step);
  
    void AddContour(Path * dest, int nbP, Path **orig, int startBord,
               int curBord, bool splitWhenForced);
    int ReFormeLineTo(int bord, int curBord, Path *dest, Path *orig);
    int ReFormeArcTo(int bord, int curBord, Path *dest, Path *orig);
    int ReFormeCubicTo(int bord, int curBord, Path *dest, Path *orig);
    int ReFormeBezierTo(int bord, int curBord, Path *dest, Path *orig);
    void ReFormeBezierChunk(const NR::Point px, const NR::Point nx,
                      Path *dest, int inBezier, int nbInterm,
                      Path *from, int p, double ts, double te);

    int QuickRasterChgEdge(int oBord, int nbord, double x);
    int QuickRasterAddEdge(int bord, double x, int guess);
    void QuickRasterSubEdge(int bord);
    void QuickRasterSwapEdge(int a, int b);
    void QuickRasterSort();

    bool _need_points_sorting;  ///< points have been added or removed: we need to sort the points again
    bool _need_edges_sorting;   ///< edges have been added: maybe they are not ordered clockwise
    ///< nota: if you remove an edge, the clockwise order still holds
    bool _has_points_data;      ///< the pData array is allocated
    bool _has_edges_data;       ///< the eData array is allocated
    bool _has_sweep_src_data;   ///< the swsData array is allocated
    bool _has_sweep_dest_data;  ///< the swdData array is allocated
    bool _has_raster_data;      ///< the swrData array is allocated
    bool _has_quick_raster_data;///< the swrData array is allocated
    bool _has_back_data;        //< the ebData array is allocated
    bool _has_voronoi_data;

    std::vector<dg_point> _pts;
    std::vector<dg_arete> _aretes;
  
    // the arrays of temporary data
    // these ones are dynamically kept at a length of maxPt or maxAr
    std::vector<edge_data> eData;
    std::vector<sweep_src_data> swsData;
    std::vector<sweep_dest_data> swdData;
    std::vector<raster_data> swrData;
    std::vector<point_data> pData;
    
    static int CmpQRs(const quick_raster_data &p1, const quick_raster_data &p2) {
      if ( fabs(p1.x - p2.x) < 0.00001 ) {
          return 0;
      }
      
      return ( ( p1.x < p2.x ) ? -1 : 1 );
    };

    // edge direction comparison function    
    static int CmpToVert(const NR::Point ax, const NR::Point bx, bool as, bool bs);
};

bool directedEulerian(Shape const *s);
double distance(Shape const *s, NR::Point const &p);
bool distanceLessThanOrEqual(Shape const *s, NR::Point const &p, double const max_l2);

#endif

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