TASPolyUtils.c

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// @(#)root/asimage:$Id: TASPolyUtils.c 20882 2007-11-19 11:31:26Z rdm $
// Author: Valeriy Onuchin  20/04/2005

/*************************************************************************
 * Copyright (C) 1995-2001, Rene Brun, Fons Rademakers and Reiner Rohlfs *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

/************************************************************************

Copyright 1987, 1998  The Open Group

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Copyright 1987 by Digital Equipment Corporation, Maynard, Massachusetts.

                        All Rights Reserved

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************************************************************************/

#include "TPoint.h"

/*
 *     This file contains a few macros to help track
 *     the edge of a filled object.  The object is assumed
 *     to be filled in scanline order, and thus the
 *     algorithm used is an extension of Bresenham's line
 *     drawing algorithm which assumes that y is always the
 *     major axis.
 *     Since these pieces of code are the same for any filled shape,
 *     it is more convenient to gather the library in one
 *     place, but since these pieces of code are also in
 *     the inner loops of output primitives, procedure call
 *     overhead is out of the question.
 *     See the author for a derivation if needed.
 */


/*
 *  In scan converting polygons, we want to choose those pixels
 *  which are inside the polygon.  Thus, we add .5 to the starting
 *  x coordinate for both left and right edges.  Now we choose the
 *  first pixel which is inside the pgon for the left edge and the
 *  first pixel which is outside the pgon for the right edge.
 *  Draw the left pixel, but not the right.
 *
 *  How to add .5 to the starting x coordinate:
 *      If the edge is moving to the right, then subtract dy from the
 *  error term from the general form of the algorithm.
 *      If the edge is moving to the left, then add dy to the error term.
 *
 *  The reason for the difference between edges moving to the left
 *  and edges moving to the right is simple:  If an edge is moving
 *  to the right, then we want the algorithm to flip immediately.
 *  If it is moving to the left, then we don't want it to flip until
 *  we traverse an entire pixel.
 */

#define BRESINITPGON(dy, x1, x2, xStart, d, m, m1, incr1, incr2) { \
    int dx;\
\
    if ((dy) != 0) { \
        xStart = (x1); \
        dx = (x2) - xStart; \
        if (dx < 0) { \
            m = dx / (dy); \
            m1 = m - 1; \
            incr1 = -2 * dx + 2 * (dy) * m1; \
            incr2 = -2 * dx + 2 * (dy) * m; \
            d = 2 * m * (dy) - 2 * dx - 2 * (dy); \
        } else { \
            m = dx / (dy); \
            m1 = m + 1; \
            incr1 = 2 * dx - 2 * (dy) * m1; \
            incr2 = 2 * dx - 2 * (dy) * m; \
            d = -2 * m * (dy) + 2 * dx; \
        } \
    } \
}

#define BRESINCRPGON(d, minval, m, m1, incr1, incr2) { \
    if (m1 > 0) { \
        if (d > 0) { \
            minval += m1; \
            d += incr1; \
        } \
        else { \
            minval += m; \
            d += incr2; \
        } \
    } else {\
        if (d >= 0) { \
            minval += m1; \
            d += incr1; \
        } \
        else { \
            minval += m; \
            d += incr2; \
        } \
    } \
}


/*
 *     This structure contains all of the information needed
 *     to run the bresenham algorithm.
 *     The variables may be hardcoded into the declarations
 *     instead of using this structure to make use of
 *     register declarations.
 */
typedef struct {
    int minor_axis;     /* minor axis        */
    int d;              /* decision variable */
    int m, m1;          /* slope and slope+1 */
    int incr1, incr2;   /* error increments */
} BRESINFO;


#define BRESINITPGONSTRUCT(dmaj, min1, min2, bres) \
        BRESINITPGON(dmaj, min1, min2, bres.minor_axis, bres.d, \
                     bres.m, bres.m1, bres.incr1, bres.incr2)

#define BRESINCRPGONSTRUCT(bres) \
        BRESINCRPGON(bres.d, bres.minor_axis, bres.m, bres.m1, bres.incr1, bres.incr2)


/*
 *     These are the data structures needed to scan
 *     convert regions.  Two different scan conversion
 *     methods are available -- the even-odd method, and
 *     the winding number method.
 *     The even-odd rule states that a point is inside
 *     the polygon if a ray drawn from that point in any
 *     direction will pass through an odd number of
 *     path segments.
 *     By the winding number rule, a point is decided
 *     to be inside the polygon if a ray drawn from that
 *     point in any direction passes through a different
 *     number of clockwise and counter-clockwise path
 *     segments.
 *
 *     These data structures are adapted somewhat from
 *     the algorithm in (Foley/Van Dam) for scan converting
 *     polygons.
 *     The basic algorithm is to start at the top (smallest y)
 *     of the polygon, stepping down to the bottom of
 *     the polygon by incrementing the y coordinate.  We
 *     keep a list of edges which the current scanline crosses,
 *     sorted by x.  This list is called the Active Edge Table (AET)
 *     As we change the y-coordinate, we update each entry in 
 *     in the active edge table to reflect the edges new xcoord.
 *     This list must be sorted at each scanline in case
 *     two edges intersect.
 *     We also keep a data structure known as the Edge Table (ET),
 *     which keeps track of all the edges which the current
 *     scanline has not yet reached.  The ET is basically a
 *     list of ScanLineList structures containing a list of
 *     edges which are entered at a given scanline.  There is one
 *     ScanLineList per scanline at which an edge is entered.
 *     When we enter a new edge, we move it from the ET to the AET.
 *
 *     From the AET, we can implement the even-odd rule as in
 *     (Foley/Van Dam).
 *     The winding number rule is a little trickier.  We also
 *     keep the EdgeTableEntries in the AET linked by the
 *     nextWETE (winding EdgeTableEntry) link.  This allows
 *     the edges to be linked just as before for updating
 *     purposes, but only uses the edges linked by the nextWETE
 *     link as edges representing spans of the polygon to
 *     drawn (as with the even-odd rule).
 */

/*
 * for the winding number rule
 */
#define CLOCKWISE          1
#define COUNTERCLOCKWISE  -1 

typedef struct _EdgeTableEntry {
     int ymax;             /* ycoord at which we exit this edge. */
     BRESINFO bres;        /* Bresenham info to run the edge     */
     struct _EdgeTableEntry *next;       /* next in the list     */
     struct _EdgeTableEntry *back;       /* for insertion sort   */
     struct _EdgeTableEntry *nextWETE;   /* for winding num rule */
     int ClockWise;        /* flag for winding number rule       */
} EdgeTableEntry;


typedef struct _ScanLineList{
     int scanline;              /* the scanline represented */
     EdgeTableEntry *edgelist;  /* header node              */
     struct _ScanLineList *next;  /* next in the list       */
} ScanLineList;


typedef struct {
     int ymax;                 /* ymax for the polygon     */
     int ymin;                 /* ymin for the polygon     */
     ScanLineList scanlines;   /* header node              */
} EdgeTable;


/*
 * Here is a struct to help with storage allocation
 * so we can allocate a big chunk at a time, and then take
 * pieces from this heap when we need to.
 */
#define SLLSPERBLOCK 25

typedef struct _ScanLineListBlock {
     ScanLineList SLLs[SLLSPERBLOCK];
     struct _ScanLineListBlock *next;
} ScanLineListBlock;



/*
 *
 *     a few macros for the inner loops of the fill code where
 *     performance considerations don't allow a procedure call.
 *
 *     Evaluate the given edge at the given scanline.
 *     If the edge has expired, then we leave it and fix up
 *     the active edge table; otherwise, we increment the
 *     x value to be ready for the next scanline.
 *     The winding number rule is in effect, so we must notify
 *     the caller when the edge has been removed so he
 *     can reorder the Winding Active Edge Table.
 */
#define EVALUATEEDGEWINDING(pAET, pPrevAET, y, fixWAET) { \
   if (pAET->ymax == y) {          /* leaving this edge */ \
      pPrevAET->next = pAET->next; \
      pAET = pPrevAET->next; \
      fixWAET = 1; \
      if (pAET) \
         pAET->back = pPrevAET; \
   } \
   else { \
      BRESINCRPGONSTRUCT(pAET->bres); \
      pPrevAET = pAET; \
      pAET = pAET->next; \
   } \
}


/*
 *     Evaluate the given edge at the given scanline.
 *     If the edge has expired, then we leave it and fix up
 *     the active edge table; otherwise, we increment the
 *     x value to be ready for the next scanline.
 *     The even-odd rule is in effect.
 */
#define EVALUATEEDGEEVENODD(pAET, pPrevAET, y) { \
   if (pAET->ymax == y) {          /* leaving this edge */ \
      pPrevAET->next = pAET->next; \
      pAET = pPrevAET->next; \
      if (pAET) \
         pAET->back = pPrevAET; \
   } \
   else { \
      BRESINCRPGONSTRUCT(pAET->bres); \
      pPrevAET = pAET; \
      pAET = pAET->next; \
   } \
}

#define LARGE_COORDINATE 1000000
#define SMALL_COORDINATE -LARGE_COORDINATE

//______________________________________________________________________________
static void InsertEdgeInET(EdgeTable *ET, EdgeTableEntry *ETE, int scanline,
                           ScanLineListBlock **SLLBlock, int *iSLLBlock)
{
   //     Insert the given edge into the edge table.
   //    First we must find the correct bucket in the
   //    Edge table, then find the right slot in the
   //    bucket.  Finally, we can insert it.

   EdgeTableEntry *start, *prev;
   ScanLineList *pSLL, *pPrevSLL;
   ScanLineListBlock *tmpSLLBlock;

   /*
    * find the right bucket to put the edge into
    */
   pPrevSLL = &ET->scanlines;
   pSLL = pPrevSLL->next;
   while (pSLL && (pSLL->scanline < scanline)) {
      pPrevSLL = pSLL;
      pSLL = pSLL->next;
   }

    /*
     * reassign pSLL (pointer to ScanLineList) if necessary
     */
   if ((!pSLL) || (pSLL->scanline > scanline)) {
      if (*iSLLBlock > SLLSPERBLOCK-1) {
         tmpSLLBlock = new ScanLineListBlock;
         (*SLLBlock)->next = tmpSLLBlock;
         tmpSLLBlock->next = (ScanLineListBlock *)0;
         *SLLBlock = tmpSLLBlock;
         *iSLLBlock = 0;
      }
      pSLL = &((*SLLBlock)->SLLs[(*iSLLBlock)++]);

      pSLL->next = pPrevSLL->next;
      pSLL->edgelist = (EdgeTableEntry *)0;
      pPrevSLL->next = pSLL;
   }
   pSLL->scanline = scanline;

    /*
     * now insert the edge in the right bucket
     */
   prev = (EdgeTableEntry *)0;
   start = pSLL->edgelist;
   while (start && (start->bres.minor_axis < ETE->bres.minor_axis)) {
      prev = start;
      start = start->next;
   }
   ETE->next = start;

   if (prev) {
      prev->next = ETE;
   } else {
      pSLL->edgelist = ETE;
   }
}

//______________________________________________________________________________
static void CreateETandAET(int count, TPoint *pts, EdgeTable *ET, EdgeTableEntry *AET,
                           EdgeTableEntry *pETEs, ScanLineListBlock *pSLLBlock)
{
   //     This routine creates the edge table for
   //     scan converting polygons. 
   //     The Edge Table (ET) looks like:
   //
   //    EdgeTable
   //     --------
   //    |  ymax  |        ScanLineLists
   //    |scanline|-->------------>-------------->...
   //     --------   |scanline|   |scanline|
   //                |edgelist|   |edgelist|
   //                ---------    ---------
   //                    |             |
   //                    |             |
   //                    V             V
   //              list of ETEs   list of ETEs
   //
   //     where ETE is an EdgeTableEntry data structure,
   //     and there is one ScanLineList per scanline at
   //     which an edge is initially entered.

   TPoint *top, *bottom;
   TPoint *PrevPt, *CurrPt;
   int iSLLBlock = 0;
   int dy;

   if (count < 2)  return;

    /*
     *  initialize the Active Edge Table
     */
   AET->next = (EdgeTableEntry *)0;
   AET->back = (EdgeTableEntry *)0;
   AET->nextWETE = (EdgeTableEntry *)0;
   AET->bres.minor_axis = SMALL_COORDINATE;

    /*
     *  initialize the Edge Table.
     */
   ET->scanlines.next = (ScanLineList *)0;
   ET->ymax = SMALL_COORDINATE;
   ET->ymin = LARGE_COORDINATE;
   pSLLBlock->next = (ScanLineListBlock *)0;

   PrevPt = &pts[count-1];

    /*
     *  for each vertex in the array of points.
     *  In this loop we are dealing with two vertices at
     *  a time -- these make up one edge of the polygon.
     */
   while (count--) {
      CurrPt = pts++;

        /*
         *  find out which point is above and which is below.
         */
      if (PrevPt->fY > CurrPt->fY) {
         bottom = PrevPt, top = CurrPt;
         pETEs->ClockWise = 0;
      } else {
         bottom = CurrPt, top = PrevPt;
         pETEs->ClockWise = 1;
      }

        /*
         * don't add horizontal edges to the Edge table.
         */
      if (bottom->fY != top->fY) {
         pETEs->ymax = bottom->fY-1;  /* -1 so we don't get last scanline */

            /*
             *  initialize integer edge algorithm
             */
         dy = bottom->fY - top->fY;
         BRESINITPGONSTRUCT(dy, top->fX, bottom->fX, pETEs->bres);

         InsertEdgeInET(ET, pETEs, top->fY, &pSLLBlock, &iSLLBlock);

              if (PrevPt->fY > ET->ymax) ET->ymax = PrevPt->fY;
              if (PrevPt->fY < ET->ymin) ET->ymin = PrevPt->fY;
         pETEs++;
      }
      PrevPt = CurrPt;
   }
}

//______________________________________________________________________________
static void loadAET(EdgeTableEntry *AET, EdgeTableEntry *ETEs)
{
   //    This routine moves EdgeTableEntries from the
   //     EdgeTable into the Active Edge Table,
   //     leaving them sorted by smaller x coordinate.

   EdgeTableEntry *pPrevAET;
   EdgeTableEntry *tmp;

   pPrevAET = AET;
   AET = AET->next;
   while (ETEs) {
      while (AET && (AET->bres.minor_axis < ETEs->bres.minor_axis))  {
         pPrevAET = AET;
         AET = AET->next;
      }
      tmp = ETEs->next;
      ETEs->next = AET;
      if (AET) {
         AET->back = ETEs;
      }
      ETEs->back = pPrevAET;
      pPrevAET->next = ETEs;
      pPrevAET = ETEs;

      ETEs = tmp;
   }
}

//______________________________________________________________________________
static int InsertionSort(EdgeTableEntry * AET)
{
   // InsertionSort
   //
   //    Just a simple insertion sort using
   //     pointers and back pointers to sort the Active
   //     Edge Table.

   EdgeTableEntry *pETEchase;
   EdgeTableEntry *pETEinsert;
   EdgeTableEntry *pETEchaseBackTMP;
   int changed = 0;

   AET = AET->next;
   while (AET) {
      pETEinsert = AET;
      pETEchase = AET;
      while (pETEchase->back->bres.minor_axis > AET->bres.minor_axis) {
         pETEchase = pETEchase->back;
      }

      AET = AET->next;
      if (pETEchase != pETEinsert) {
         pETEchaseBackTMP = pETEchase->back;
         pETEinsert->back->next = AET;
         if (AET) {
            AET->back = pETEinsert->back;
         }
         pETEinsert->next = pETEchase;
         pETEchase->back->next = pETEinsert;
         pETEchase->back = pETEinsert;
         pETEinsert->back = pETEchaseBackTMP;
         changed = 1;
      }
   }
   return (changed);
}

//______________________________________________________________________________
static void FreeStorage(ScanLineListBlock *pSLLBlock)
{
   // Clean up our act.

   ScanLineListBlock *tmpSLLBlock;

   while (pSLLBlock) {
      tmpSLLBlock = pSLLBlock->next;
      delete pSLLBlock;
      pSLLBlock = tmpSLLBlock;
   }
}

---