/* $TOG: poly.h /main/5 1998/02/06 17:47:27 kaleb $ */
/************************************************************************
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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; \
} \
}