_GRAPHICS PROGRAMMING COLUMN_
by Michael Abrash



[LISTING ONE]

/* Color-fills an arbitrarily-shaped polygon described by VertexList.
If the first and last points in VertexList are not the same, the path
around the polygon is automatically closed. All vertices are offset
by (XOffset, YOffset). Returns 1 for success, 0 if memory allocation
failed. All C code tested with Turbo C++.
If the polygon shape is known in advance, speedier processing may be
enabled by specifying the shape as follows: "convex" - a rubber band
stretched around the polygon would touch every vertex in order;
"nonconvex" - the polygon is not self-intersecting, but need not be
convex; "complex" - the polygon may be self-intersecting, or, indeed,
any sort of polygon at all. Complex will work for all polygons; convex
is fastest. Undefined results will occur if convex is specified for a
nonconvex or complex polygon.
Define CONVEX_CODE_LINKED if the fast convex polygon filling code from
the February 1991 column is linked in. Otherwise, convex polygons are
handled by the complex polygon filling code.
Nonconvex is handled as complex in this implementation. See text for a
discussion of faster nonconvex handling */

#include <stdio.h>
#include <math.h>
#ifdef __TURBOC__
#include <alloc.h>
#else    /* MSC */
#include <malloc.h>
#endif
#include "polygon.h"

#define SWAP(a,b) {temp = a; a = b; b = temp;}

struct EdgeState {
   struct EdgeState *NextEdge;
   int X;
   int StartY;
   int WholePixelXMove;
   int XDirection;
   int ErrorTerm;
   int ErrorTermAdjUp;
   int ErrorTermAdjDown;
   int Count;
};

extern void DrawHorizontalLineSeg(int, int, int, int);
extern int FillConvexPolygon(struct PointListHeader *, int, int, int);
static void BuildGET(struct PointListHeader *, struct EdgeState *,
   int, int);
static void MoveXSortedToAET(int);
static void ScanOutAET(int, int);
static void AdvanceAET(void);
static void XSortAET(void);

/* Pointers to global edge table (GET) and active edge table (AET) */
static struct EdgeState *GETPtr, *AETPtr;

int FillPolygon(struct PointListHeader * VertexList, int Color,
      int PolygonShape, int XOffset, int YOffset)
{
   struct EdgeState *EdgeTableBuffer;
   int CurrentY;

#ifdef CONVEX_CODE_LINKED
   /* Pass convex polygons through to fast convex polygon filler */
   if (PolygonShape == CONVEX)
      return(FillConvexPolygon(VertexList, Color, XOffset, YOffset));
#endif

   /* It takes a minimum of 3 vertices to cause any pixels to be
      drawn; reject polygons that are guaranteed to be invisible */
   if (VertexList->Length < 3)
      return(1);
   /* Get enough memory to store the entire edge table */
   if ((EdgeTableBuffer =
         (struct EdgeState *) (malloc(sizeof(struct EdgeState) *
         VertexList->Length))) == NULL)
      return(0);  /* couldn't get memory for the edge table */
   /* Build the global edge table */
   BuildGET(VertexList, EdgeTableBuffer, XOffset, YOffset);
   /* Scan down through the polygon edges, one scan line at a time,
      so long as at least one edge remains in either the GET or AET */
   AETPtr = NULL;    /* initialize the active edge table to empty */
   CurrentY = GETPtr->StartY; /* start at the top polygon vertex */
   while ((GETPtr != NULL) || (AETPtr != NULL)) {
      MoveXSortedToAET(CurrentY);  /* update AET for this scan line */
      ScanOutAET(CurrentY, Color); /* draw this scan line from AET */
      AdvanceAET();                /* advance AET edges 1 scan line */
      XSortAET();                  /* resort on X */
      CurrentY++;                  /* advance to the next scan line */
   }
   /* Release the memory we've allocated and we're done */
   free(EdgeTableBuffer);
   return(1);
}

/* Creates a GET in the buffer pointed to by NextFreeEdgeStruc from
   the vertex list. Edge endpoints are flipped, if necessary, to
   guarantee all edges go top to bottom. The GET is sorted primarily
   by ascending Y start coordinate, and secondarily by ascending X
   start coordinate within edges with common Y coordinates */
static void BuildGET(struct PointListHeader * VertexList,
      struct EdgeState * NextFreeEdgeStruc, int XOffset, int YOffset)
{
   int i, StartX, StartY, EndX, EndY, DeltaY, DeltaX, Width, temp;
   struct EdgeState *NewEdgePtr;
   struct EdgeState *FollowingEdge, **FollowingEdgeLink;
   struct Point *VertexPtr;

   /* Scan through the vertex list and put all non-0-height edges into
      the GET, sorted by increasing Y start coordinate */
   VertexPtr = VertexList->PointPtr;   /* point to the vertex list */
   GETPtr = NULL;    /* initialize the global edge table to empty */
   for (i = 0; i < VertexList->Length; i++) {
      /* Calculate the edge height and width */
      StartX = VertexPtr[i].X + XOffset;
      StartY = VertexPtr[i].Y + YOffset;
      /* The edge runs from the current point to the previous one */
      if (i == 0) {
         /* Wrap back around to the end of the list */
         EndX = VertexPtr[VertexList->Length-1].X + XOffset;
         EndY = VertexPtr[VertexList->Length-1].Y + YOffset;
      } else {
         EndX = VertexPtr[i-1].X + XOffset;
         EndY = VertexPtr[i-1].Y + YOffset;
      }
      /* Make sure the edge runs top to bottom */
      if (StartY > EndY) {
         SWAP(StartX, EndX);
         SWAP(StartY, EndY);
      }
      /* Skip if this can't ever be an active edge (has 0 height) */
      if ((DeltaY = EndY - StartY) != 0) {
         /* Allocate space for this edge's info, and fill in the
            structure */
         NewEdgePtr = NextFreeEdgeStruc++;
         NewEdgePtr->XDirection =   /* direction in which X moves */
               ((DeltaX = EndX - StartX) > 0) ? 1 : -1;
         Width = abs(DeltaX);
         NewEdgePtr->X = StartX;
         NewEdgePtr->StartY = StartY;
         NewEdgePtr->Count = DeltaY;
         NewEdgePtr->ErrorTermAdjDown = DeltaY;
         if (DeltaX >= 0)  /* initial error term going L->R */
            NewEdgePtr->ErrorTerm = 0;
         else              /* initial error term going R->L */
            NewEdgePtr->ErrorTerm = -DeltaY + 1;
         if (DeltaY >= Width) {     /* Y-major edge */
            NewEdgePtr->WholePixelXMove = 0;
            NewEdgePtr->ErrorTermAdjUp = Width;
         } else {                   /* X-major edge */
            NewEdgePtr->WholePixelXMove =
                  (Width / DeltaY) * NewEdgePtr->XDirection;
            NewEdgePtr->ErrorTermAdjUp = Width % DeltaY;
         }
         /* Link the new edge into the GET so that the edge list is
            still sorted by Y coordinate, and by X coordinate for all
            edges with the same Y coordinate */
         FollowingEdgeLink = &GETPtr;
         for (;;) {
            FollowingEdge = *FollowingEdgeLink;
            if ((FollowingEdge == NULL) ||
                  (FollowingEdge->StartY > StartY) ||
                  ((FollowingEdge->StartY == StartY) &&
                  (FollowingEdge->X >= StartX))) {
               NewEdgePtr->NextEdge = FollowingEdge;
               *FollowingEdgeLink = NewEdgePtr;
               break;
            }
            FollowingEdgeLink = &FollowingEdge->NextEdge;
         }
      }
   }
}

/* Sorts all edges currently in the active edge table into ascending
   order of current X coordinates */
static void XSortAET() {
   struct EdgeState *CurrentEdge, **CurrentEdgePtr, *TempEdge;
   int SwapOccurred;

   /* Scan through the AET and swap any adjacent edges for which the
      second edge is at a lower current X coord than the first edge.
      Repeat until no further swapping is needed */
   if (AETPtr != NULL) {
      do {
         SwapOccurred = 0;
         CurrentEdgePtr = &AETPtr;
         while ((CurrentEdge = *CurrentEdgePtr)->NextEdge != NULL) {
            if (CurrentEdge->X > CurrentEdge->NextEdge->X) {
               /* The second edge has a lower X than the first;
                  swap them in the AET */
               TempEdge = CurrentEdge->NextEdge->NextEdge;
               *CurrentEdgePtr = CurrentEdge->NextEdge;
               CurrentEdge->NextEdge->NextEdge = CurrentEdge;
               CurrentEdge->NextEdge = TempEdge;
               SwapOccurred = 1;
            }
            CurrentEdgePtr = &(*CurrentEdgePtr)->NextEdge;
         }
      } while (SwapOccurred != 0);
   }
}

/* Advances each edge in the AET by one scan line.
   Removes edges that have been fully scanned. */
static void AdvanceAET() {
   struct EdgeState *CurrentEdge, **CurrentEdgePtr;

   /* Count down and remove or advance each edge in the AET */
   CurrentEdgePtr = &AETPtr;
   while ((CurrentEdge = *CurrentEdgePtr) != NULL) {
      /* Count off one scan line for this edge */
      if ((--(CurrentEdge->Count)) == 0) {
         /* This edge is finished, so remove it from the AET */
         *CurrentEdgePtr = CurrentEdge->NextEdge;
      } else {
         /* Advance the edge's X coordinate by minimum move */
         CurrentEdge->X += CurrentEdge->WholePixelXMove;
         /* Determine whether it's time for X to advance one extra */
         if ((CurrentEdge->ErrorTerm +=
               CurrentEdge->ErrorTermAdjUp) > 0) {
            CurrentEdge->X += CurrentEdge->XDirection;
            CurrentEdge->ErrorTerm -= CurrentEdge->ErrorTermAdjDown;
         }
         CurrentEdgePtr = &CurrentEdge->NextEdge;
      }
   }
}

/* Moves all edges that start at the specified Y coordinate from the
   GET to the AET, maintaining the X sorting of the AET. */
static void MoveXSortedToAET(int YToMove) {
   struct EdgeState *AETEdge, **AETEdgePtr, *TempEdge;
   int CurrentX;

   /* The GET is Y sorted. Any edges that start at the desired Y
      coordinate will be first in the GET, so we'll move edges from
      the GET to AET until the first edge left in the GET is no longer
      at the desired Y coordinate. Also, the GET is X sorted within
      each Y coordinate, so each successive edge we add to the AET is
      guaranteed to belong later in the AET than the one just added */
   AETEdgePtr = &AETPtr;
   while ((GETPtr != NULL) && (GETPtr->StartY == YToMove)) {
      CurrentX = GETPtr->X;
      /* Link the new edge into the AET so that the AET is still
         sorted by X coordinate */
      for (;;) {
         AETEdge = *AETEdgePtr;
         if ((AETEdge == NULL) || (AETEdge->X >= CurrentX)) {
            TempEdge = GETPtr->NextEdge;
            *AETEdgePtr = GETPtr;  /* link the edge into the AET */
            GETPtr->NextEdge = AETEdge;
            AETEdgePtr = &GETPtr->NextEdge;
            GETPtr = TempEdge;   /* unlink the edge from the GET */
            break;
         } else {
            AETEdgePtr = &AETEdge->NextEdge;
         }
      }
   }
}

/* Fills the scan line described by the current AET at the specified Y
   coordinate in the specified color, using the odd/even fill rule */
static void ScanOutAET(int YToScan, int Color) {
   int LeftX;
   struct EdgeState *CurrentEdge;

   /* Scan through the AET, drawing line segments as each pair of edge
      crossings is encountered. The nearest pixel on or to the right
      of left edges is drawn, and the nearest pixel to the left of but
      not on right edges is drawn */
   CurrentEdge = AETPtr;
   while (CurrentEdge != NULL) {
      LeftX = CurrentEdge->X;
      CurrentEdge = CurrentEdge->NextEdge;
      DrawHorizontalLineSeg(YToScan, LeftX, CurrentEdge->X-1, Color);
      CurrentEdge = CurrentEdge->NextEdge;
   }
}


[LISTING TWO]

/* Draws all pixels in the horizontal line segment passed in, from
   (LeftX,Y) to (RightX,Y), in the specified color in mode 13h, the
   VGA's 320x200 256-color mode. Both LeftX and RightX are drawn. No
   drawing will take place if LeftX > RightX. */

#include <dos.h>
#include "polygon.h"

#define SCREEN_WIDTH    320
#define SCREEN_SEGMENT  0xA000

static void DrawPixel(int, int, int);

void DrawHorizontalLineSeg(Y, LeftX, RightX, Color) {
   int X;

   /* Draw each pixel in the horizontal line segment, starting with
      the leftmost one */
   for (X = LeftX; X <= RightX; X++)
      DrawPixel(X, Y, Color);
}

/* Draws the pixel at (X, Y) in color Color in VGA mode 13h */
static void DrawPixel(int X, int Y, int Color) {
   unsigned char far *ScreenPtr;

#ifdef __TURBOC__
   ScreenPtr = MK_FP(SCREEN_SEGMENT, Y * SCREEN_WIDTH + X);
#else    /* MSC 5.0 */
   FP_SEG(ScreenPtr) = SCREEN_SEGMENT;
   FP_OFF(ScreenPtr) = Y * SCREEN_WIDTH + X;
#endif
   *ScreenPtr = (unsigned char) Color;
}


[LISTING THREE]

/* POLYGON.H: Header file for polygon-filling code */

#define CONVEX    0
#define NONCONVEX 1
#define COMPLEX   2

/* Describes a single point (used for a single vertex) */
struct Point {
   int X;   /* X coordinate */
   int Y;   /* Y coordinate */
};
/* Describes a series of points (used to store a list of vertices that
   describe a polygon; each vertex connects to the two adjacent
   vertices; the last vertex is assumed to connect to the first) */
struct PointListHeader {
   int Length;                /* # of points */
   struct Point * PointPtr;   /* pointer to list of points */
};
/* Describes the beginning and ending X coordinates of a single
   horizontal line (used only by fast polygon fill code) */
struct HLine {
   int XStart; /* X coordinate of leftmost pixel in line */
   int XEnd;   /* X coordinate of rightmost pixel in line */
};
/* Describes a Length-long series of horizontal lines, all assumed to
   be on contiguous scan lines starting at YStart and proceeding
   downward (used to describe a scan-converted polygon to the
   low-level hardware-dependent drawing code) (used only by fast
   polygon fill code) */
struct HLineList {
   int Length;                /* # of horizontal lines */
   int YStart;                /* Y coordinate of topmost line */
   struct HLine * HLinePtr;   /* pointer to list of horz lines */
};



[LISTING FOUR]

/* Sample program to exercise the polygon-filling routines */

#include <conio.h>
#include <dos.h>
#include "polygon.h"

#define DRAW_POLYGON(PointList,Color,Shape,X,Y)             \
   Polygon.Length = sizeof(PointList)/sizeof(struct Point); \
   Polygon.PointPtr = PointList;                            \
   FillPolygon(&Polygon, Color, Shape, X, Y);
   
void main(void);
extern int FillPolygon(struct PointListHeader *, int, int, int, int);

void main() {
   int i, j;
   struct PointListHeader Polygon;
   static struct Point Polygon1[] =
         {{0,0},{100,150},{320,0},{0,200},{220,50},{320,200}};
   static struct Point Polygon2[] =
         {{0,0},{320,0},{320,200},{0,200},{0,0},{50,50},
          {270,50},{270,150},{50,150},{50,50}};
   static struct Point Polygon3[] =
         {{0,0},{10,0},{105,185},{260,30},{15,150},{5,150},{5,140},
          {260,5},{300,5},{300,15},{110,200},{100,200},{0,10}};
   static struct Point Polygon4[] =
         {{0,0},{30,-20},{30,0},{0,20},{-30,0},{-30,-20}};
   static struct Point Triangle1[] = {{30,0},{15,20},{0,0}};
   static struct Point Triangle2[] = {{30,20},{15,0},{0,20}};
   static struct Point Triangle3[] = {{0,20},{20,10},{0,0}};
   static struct Point Triangle4[] = {{20,20},{20,0},{0,10}};
   union REGS regset;

   /* Set the display to VGA mode 13h, 320x200 256-color mode */
   regset.x.ax = 0x0013;
   int86(0x10, &regset, &regset);

   /* Draw three complex polygons */
   DRAW_POLYGON(Polygon1, 15, COMPLEX, 0, 0);
   getch();    /* wait for a keypress */
   DRAW_POLYGON(Polygon2, 5, COMPLEX, 0, 0);
   getch();    /* wait for a keypress */
   DRAW_POLYGON(Polygon3, 3, COMPLEX, 0, 0);
   getch();    /* wait for a keypress */

   /* Draw some adjacent nonconvex polygons */
   for (i=0; i<5; i++) {
      for (j=0; j<8; j++) {
         DRAW_POLYGON(Polygon4, 16+i*8+j, NONCONVEX, 40+(i*60),
               30+(j*20));
      }
   }
   getch();    /* wait for a keypress */

   /* Draw adjacent triangles across the screen */
   for (j=0; j<=80; j+=20) {
      for (i=0; i<290; i += 30) {
         DRAW_POLYGON(Triangle1, 2, CONVEX, i, j);
         DRAW_POLYGON(Triangle2, 4, CONVEX, i+15, j);
      }
   }
   for (j=100; j<=170; j+=20) {
      /* Do a row of pointing-right triangles */
      for (i=0; i<290; i += 20) {
         DRAW_POLYGON(Triangle3, 40, CONVEX, i, j);
      }
      /* Do a row of pointing-left triangles halfway between one row
         of pointing-right triangles and the next, to fit between */
      for (i=0; i<290; i += 20) {
         DRAW_POLYGON(Triangle4, 1, CONVEX, i, j+10);
      }
   }
   getch();    /* wait for a keypress */

   /* Return to text mode and exit */
   regset.x.ax = 0x0003;
   int86(0x10, &regset, &regset);
}



[LISTING FIVE]


; Draws all pixels in the horizontal line segment passed in, from
;  (LeftX,Y) to (RightX,Y), in the specified color in mode 13h, the
;  VGA's 320x200 256-color mode. No drawing will take place if
;  LeftX > RightX. Tested with TASM 2.0
; C near-callable as:
;       void DrawHorizontalLineSeg(Y, LeftX, RightX, Color);

SCREEN_WIDTH    equ     320
SCREEN_SEGMENT  equ     0a000h

Parms   struc
        dw      2 dup(?) ;return address & pushed BP
Y       dw      ?       ;Y coordinate of line segment to draw
LeftX   dw      ?       ;left endpoint of the line segment
RightX  dw      ?       ;right endpoint of the line segment
Color   dw      ?       ;color in which to draw the line segment
Parms   ends

        .model small
        .code
        public _DrawHorizontalLineSeg
        align   2
_DrawHorizontalLineSeg  proc
        push    bp              ;preserve caller's stack frame
        mov     bp,sp           ;point to our stack frame
        push    di              ;preserve caller's register variable
        cld                     ;make string instructions inc pointers
        mov     ax,SCREEN_SEGMENT
        mov     es,ax           ;point ES to display memory
        mov     di,[bp+LeftX]
        mov     cx,[bp+RightX]
        sub     cx,di           ;width of line
        jl      DrawDone        ;RightX < LeftX; no drawing to do
        inc     cx              ;include both endpoints
        mov     ax,SCREEN_WIDTH
        mul     [bp+Y]          ;offset of scan line on which to draw
        add     di,ax           ;ES:DI points to start of line seg
        mov     al,byte ptr [bp+Color] ;color in which to draw
        mov     ah,al           ;put color in AH for STOSW
        shr     cx,1            ;# of words to fill
        rep     stosw           ;fill a word at a time
        adc     cx,cx
        rep     stosb           ;draw the odd byte, if any
DrawDone:
        pop     di              ;restore caller's register variable
        pop     bp              ;restore caller's stack frame
        ret
_DrawHorizontalLineSeg  endp
        end