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poly.h

/* $XConsortium: poly.h,v 1.4 94/04/17 20:22:19 rws Exp $ */
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Copyright (c) 1987  X Consortium

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Copyright 1987 by Digital Equipment Corporation, Maynard, Massachusetts.

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/*
 *     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;      /* local storage */ \
\
    /* \
     *  if the edge is horizontal, then it is ignored \
     *  and assumed not to be processed.  Otherwise, do this stuff. \
     */ \
    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; \
   } \
}

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