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LISTING 41.4 L41-4.C

    /* 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 Borland 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 FillMonotoneVerticalPolygon(struct PointListHeader *,
       int, int, int);
    extern int PolygonIsMonotoneVertical(struct PointListHeader *);
    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) ||
             PolygonIsMonotoneVertical(VertexList))
          return(FillMonotoneVerticalPolygon(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 41.5 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 series of points (used to store a list of vertices that describe
    a polygon; each vertex is assumed to connect to the two adjacent vertices, and
    last vertex is assumed to connect to the first) */
    struct PointListHeader {
       int Length;                /* # of points */
       struct Point * PointPtr;   /* pointer to list of points */
    };

    /* Describes beginning and ending X coordinates of a single horizontal line */
    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 scan-converted polygon to low-level hardware-dependent drawing code) */
    struct HLineList {
       int Length;                /* # of horizontal lines */
       int YStart;                /* Y coordinate of topmost line */
       struct HLine * HLinePtr;   /* pointer to list of horz lines */
    };

    /* Describes a color as an RGB triple, plus one byte for other info */
    struct RGB { unsigned char Red, Green, Blue, Spare; };

Is monotone-vertical polygon detection worth all this trouble? Under the right circumstances, you bet. In a situation where a great many polygons are being drawn, and the application either doesn’t know whether they’re monotone-vertical or has no way to tell the polygon filler that they are, performance can be increased considerably if most polygons are, in fact, monotone-vertical. This potential performance advantage is helped along by the surprising fact that Jim’s test for monotone-vertical status is simpler and faster than my original, nonfunctional test for convexity.

See what accurate terminology and effective communication can do?

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Graphics Programming Black Book © 2001 Michael Abrash