ptinpoly.c

[Game.Programming].Academic - Graphics Gems (6 books source code)

    /* first, is point inside bounding rectangle? */
    if ( ( ty = point[Y] ) < p_trap_set->miny ||
	 ty >= p_trap_set->maxy ||
	 ( tx = point[X] ) < p_trap_set->minx ||
	 tx >= p_trap_set->maxx ) {

	/* outside of box */
	return( 0 ) ;
    }

    /* what bin are we in? */
    b = ( ty - p_trap_set->miny ) * p_trap_set->inv_ydelta ;

    /* find if we're inside this bin's bounds */
    if ( tx < (p_trap = &p_trap_set->trapz[b])->minx ||
	 tx > p_trap->maxx ) {

	/* outside of box */
	return( 0 ) ;
    }

    /* now search bin for crossings */
    pp_bin = p_trap->edge_set ;
    count = p_trap->count ;
    for ( j = 0 ; j < count ; j++, pp_bin++ ) {
	if ( tx < (*pp_bin)->minx ) {

	    /* all remaining edges are to right of point, so test them */
	    do {
		if ( (*pp_bin)->full_cross ) {
		    inside_flag = !inside_flag ;
		} else {
		    id = (*pp_bin)->id ;
		    if ( ( ty <= pgon[id][Y] ) !=
			    ( ty <= pgon[(id+1)%numverts][Y] ) ) {

			/* point crosses edge in Y, so must cross */
			inside_flag = !inside_flag ;
		    }
		}
		pp_bin++ ;
	    } while ( ++j < count ) ;
	    goto Exit;

	} else if ( tx < (*pp_bin)->maxx ) {
	    /* edge is overlapping point in X, check it */
	    id = (*pp_bin)->id ;
	    vtx0 = pgon[id] ;
	    vtx1 = pgon[(id+1)%numverts] ;

	    if ( (*pp_bin)->full_cross ||
		 ( ty <= vtx0[Y] ) != ( ty <= vtx1[Y] ) ) {

		/* edge crosses in Y, so have to do full crossings test */
		if ( (vtx0[X] -
		    (vtx0[Y] - ty )*
			( vtx1[X]-vtx0[X])/(vtx1[Y]-vtx0[Y])) >= tx ) {
		    inside_flag = !inside_flag ;
		}
	    }

	} /* else edge is to left of point, ignore it */
    }

    Exit:
    return( inside_flag ) ;
}

void TrapezoidCleanup( p_trap_set )
pTrapezoidSet	p_trap_set ;
{
int	i, j, count ;

    for ( i = 0 ; i < p_trap_set->bins ; i++ ) {
	/* all of these should have bin sets, but check just in case */
	if ( p_trap_set->trapz[i].edge_set ) {
	    count = p_trap_set->trapz[i].count ;
	    for ( j = 0 ; j < count ; j++ ) {
		if ( p_trap_set->trapz[i].edge_set[j] ) {
		    free( p_trap_set->trapz[i].edge_set[j] ) ;
		}
	    }
	    free( p_trap_set->trapz[i].edge_set ) ;
	}
    }
    free( p_trap_set->trapz ) ;
}

/* ======= Grid algorithm ================================================= */

/* Impose a grid upon the polygon and test only the local edges against the
 * point.
 *
 * Call setup with 2D polygon _pgon_ with _numverts_ number of vertices,
 * grid resolution _resolution_ and a pointer to a grid structure _p_gs_.
 * Call testing procedure with a pointer to this array and test point _point_,
 * returns 1 if inside, 0 if outside.
 * Call cleanup with pointer to grid structure to free space.
 */

/* Strategy for setup:
 *   Get bounds of polygon, allocate grid.
 *   "Walk" each edge of the polygon and note which edges have been crossed
 *     and what cells are entered (points on a grid edge are always considered
 *     to be above that edge).	Keep a record of the edges overlapping a cell.
 *     For cells with edges, determine if any cell border has no edges passing
 *     through it and so can be used for shooting a test ray.
 *     Keep track of the parity of the x (horizontal) grid cell borders for
 *     use in determining whether the grid corners are inside or outside.
 */
void GridSetup( pgon, numverts, resolution, p_gs )
double	pgon[][2] ;
int	numverts ;
int	resolution ;
pGridSet	p_gs ;
{
double	*vtx0, *vtx1, *vtxa, *vtxb, *p_gl ;
int	i, j, gc_clear_flags ;
double	vx0, vx1, vy0, vy1, gxdiff, gydiff, eps ;
pGridCell	p_gc, p_ngc ;
double	xdiff, ydiff, tmax, inv_x, inv_y, xdir, ydir, t_near, tx, ty ;
double	tgcx, tgcy ;
int	gcx, gcy, sign_x ;
int	y_flag, io_state ;

    p_gs->xres = p_gs->yres = resolution ;
    p_gs->tot_cells = p_gs->xres * p_gs->yres ;
    p_gs->glx = (double *)malloc( (p_gs->xres+1) * sizeof(double));
    MALLOC_CHECK( p_gs->glx ) ;
    p_gs->gly = (double *)malloc( (p_gs->yres+1) * sizeof(double));
    MALLOC_CHECK( p_gs->gly ) ;
    p_gs->gc = (pGridCell)malloc( p_gs->tot_cells * sizeof(GridCell));
    MALLOC_CHECK( p_gs->gc ) ;

    p_gs->minx =
    p_gs->maxx = pgon[0][X] ;
    p_gs->miny =
    p_gs->maxy = pgon[0][Y] ;

    /* find bounds of polygon */
    for ( i = 1 ; i < numverts ; i++ ) {
	vx0 = pgon[i][X] ;
	if ( p_gs->minx > vx0 ) {
	    p_gs->minx = vx0 ;
	} else if ( p_gs->maxx < vx0 ) {
	    p_gs->maxx = vx0 ;
	}

	vy0 = pgon[i][Y] ;
	if ( p_gs->miny > vy0 ) {
	    p_gs->miny = vy0 ;
	} else if ( p_gs->maxy < vy0 ) {
	    p_gs->maxy = vy0 ;
	}
    }

    /* add a little to the bounds to ensure everything falls inside area */
    gxdiff = p_gs->maxx - p_gs->minx ;
    gydiff = p_gs->maxy - p_gs->miny ;
    p_gs->minx -= EPSILON * gxdiff ;
    p_gs->maxx += EPSILON * gxdiff ;
    p_gs->miny -= EPSILON * gydiff ;
    p_gs->maxy += EPSILON * gydiff ;

    /* avoid roundoff problems near corners by not getting too close to them */
    eps = 1e-9 * ( gxdiff + gydiff ) ;

    /* use the new bounds to compute cell widths */
    TryAgain:
    p_gs->xdelta =
	    (p_gs->maxx-p_gs->minx) / (double)p_gs->xres ;
    p_gs->inv_xdelta = 1.0 / p_gs->xdelta ;

    p_gs->ydelta =
	    (p_gs->maxy-p_gs->miny) / (double)p_gs->yres ;
    p_gs->inv_ydelta = 1.0 / p_gs->ydelta ;

    for ( i = 0, p_gl = p_gs->glx ; i < p_gs->xres ; i++ ) {
	*p_gl++ = p_gs->minx + i * p_gs->xdelta ;
    }
    /* make last grid corner precisely correct */
    *p_gl = p_gs->maxx ;

    for ( i = 0, p_gl = p_gs->gly ; i < p_gs->yres ; i++ ) {
	*p_gl++ = p_gs->miny + i * p_gs->ydelta ;
    }
    *p_gl = p_gs->maxy ;

    for ( i = 0, p_gc = p_gs->gc ; i < p_gs->tot_cells ; i++, p_gc++ ) {
	p_gc->tot_edges = 0 ;
	p_gc->gc_flags = 0x0 ;
	p_gc->gr = NULL ;
    }

    /* loop through edges and insert into grid structure */
    vtx0 = pgon[numverts-1] ;
    for ( i = 0 ; i < numverts ; i++ ) {
	vtx1 = pgon[i] ;

	if ( vtx0[Y] < vtx1[Y] ) {
	    vtxa = vtx0 ;
	    vtxb = vtx1 ;
	} else {
	    vtxa = vtx1 ;
	    vtxb = vtx0 ;
	}

	/* Set x variable for the direction of the ray */
	xdiff = vtxb[X] - vtxa[X] ;
	ydiff = vtxb[Y] - vtxa[Y] ;
	tmax = sqrt( xdiff * xdiff + ydiff * ydiff ) ;

	/* if edge is of 0 length, ignore it (useless edge) */
	if ( tmax == 0.0 ) goto NextEdge ;

	xdir = xdiff / tmax ;
	ydir = ydiff / tmax ;

	gcx = (int)(( vtxa[X] - p_gs->minx ) * p_gs->inv_xdelta) ;
	gcy = (int)(( vtxa[Y] - p_gs->miny ) * p_gs->inv_ydelta) ;

	/* get information about slopes of edge, etc */
	if ( vtxa[X] == vtxb[X] ) {
	    sign_x = 0 ;
	    tx = HUGE ;
	} else {
	    inv_x = tmax / xdiff ;
	    tx = p_gs->xdelta * (double)gcx + p_gs->minx - vtxa[X] ;
	    if ( vtxa[X] < vtxb[X] ) {
		sign_x = 1 ;
		tx += p_gs->xdelta ;
		tgcx = p_gs->xdelta * inv_x ;
	    } else {
		sign_x = -1 ;
		tgcx = -p_gs->xdelta * inv_x ;
	    }
	    tx *= inv_x ;
	}

	if ( vtxa[Y] == vtxb[Y] ) {
	    ty = HUGE ;
	} else {
	    inv_y = tmax / ydiff ;
	    ty = (p_gs->ydelta * (double)(gcy+1) + p_gs->miny - vtxa[Y])
		* inv_y ;
	    tgcy = p_gs->ydelta * inv_y ;
	}

	p_gc = &p_gs->gc[gcy*p_gs->xres+gcx] ;

	vx0 = vtxa[X] ;
	vy0 = vtxa[Y] ;

	t_near = 0.0 ;

	do {
	    /* choose the next boundary, but don't move yet */
	    if ( tx <= ty ) {
		gcx += sign_x ;

		ty -= tx ;
		t_near += tx ;
		tx = tgcx ;

		/* note which edge is hit when leaving this cell */
		if ( t_near < tmax ) {
		    if ( sign_x > 0 ) {
			p_gc->gc_flags |= GC_R_EDGE_HIT ;
			vx1 = p_gs->glx[gcx] ;
		    } else {
			p_gc->gc_flags |= GC_L_EDGE_HIT ;
			vx1 = p_gs->glx[gcx+1] ;
		    }

		    /* get new location */
		    vy1 = t_near * ydir + vtxa[Y] ;
		} else {
		    /* end of edge, so get exact value */
		    vx1 = vtxb[X] ;
		    vy1 = vtxb[Y] ;
		}

		y_flag = FALSE ;

	    } else {

		gcy++ ;

		tx -= ty ;
		t_near += ty ;
		ty = tgcy ;

		/* note top edge is hit when leaving this cell */
		if ( t_near < tmax ) {
		    p_gc->gc_flags |= GC_T_EDGE_HIT ;
		    /* this toggles the parity bit */
		    p_gc->gc_flags ^= GC_T_EDGE_PARITY ;

		    /* get new location */
		    vx1 = t_near * xdir + vtxa[X] ;
		    vy1 = p_gs->gly[gcy] ;
		} else {
		    /* end of edge, so get exact value */
		    vx1 = vtxb[X] ;
		    vy1 = vtxb[Y] ;
		}

		y_flag = TRUE ;
	    }

	    /* check for corner crossing, then mark the cell we're in */
	    if ( !AddGridRecAlloc( p_gc, vx0, vy0, vx1, vy1, eps ) ) {
		/* warning, danger - we have just crossed a corner.
		 * There are all kinds of topological messiness we could
		 * do to get around this case, but they're a headache.
		 * The simplest recovery is just to change the extents a bit
		 * and redo the meshing, so that hopefully no edges will
		 * perfectly cross a corner.  Since it's a preprocess, we
		 * don't care too much about the time to do it.
		 */

		/* clean out all grid records */
		for ( i = 0, p_gc = p_gs->gc
		    ; i < p_gs->tot_cells
		    ; i++, p_gc++ ) {

		    if ( p_gc->gr ) {
			free( p_gc->gr ) ;
		    }
		}

		/* make the bounding box ever so slightly larger, hopefully
		 * changing the alignment of the corners.
		 */
		p_gs->minx -= EPSILON * gxdiff * 0.24 ;
		p_gs->miny -= EPSILON * gydiff * 0.10 ;

		/* yes, it's the dreaded goto - run in fear for your lives! */
		goto TryAgain ;
	    }

	    if ( t_near < tmax ) {
		/* note how we're entering the next cell */
		/* TBD: could be done faster by incrementing index in the
		 * incrementing code, above */
		p_gc = &p_gs->gc[gcy*p_gs->xres+gcx] ;

		if ( y_flag ) {
		    p_gc->gc_flags |= GC_B_EDGE_HIT ;
		    /* this toggles the parity bit */
		    p_gc->gc_flags ^= GC_B_EDGE_PARITY ;
		} else {
		    p_gc->gc_flags |=
			( sign_x > 0 ) ? GC_L_EDGE_HIT : GC_R_EDGE_HIT ;
		}
	    }

	    vx0 = vx1 ;
	    vy0 = vy1 ;
	}
	/* have we gone further than the end of the edge? */
	while ( t_near < tmax ) ;

	NextEdge:
	vtx0 = vtx1 ;
    }

    /* the grid is all set up, now set up the inside/outside value of each
     * corner.
     */
    p_gc = p_gs->gc ;
    p_ngc = &p_gs->gc[p_gs->xres] ;

    /* we know the bottom and top rows are all outside, so no flag is set */
    for ( i = 1; i < p_gs->yres ; i++ ) {
	/* start outside */
	io_state = 0x0 ;

	for ( j = 0; j < p_gs->xres ; j++ ) {

	    if ( io_state ) {
		/* change cell left corners to inside */
		p_gc->gc_flags |= GC_TL_IN ;
		p_ngc->gc_flags |= GC_BL_IN ;
	    }

	    if ( p_gc->gc_flags & GC_T_EDGE_PARITY ) {
		io_state = !io_state ;
	    }

	    if ( io_state ) {
		/* change cell right corners to inside */
		p_gc->gc_flags |= GC_TR_IN ;
		p_ngc->gc_flags |= GC_BR_IN ;
	    }

	    p_gc++ ;
	    p_ngc++ ;
	}
    }

    p_gc = p_gs->gc ;
    for ( i = 0; i < p_gs->tot_cells ; i++ ) {

	/* reverse parity of edge clear (1==edge clear) */
	gc_clear_flags = p_gc->gc_flags ^ GC_ALL_EDGE_CLEAR ;
	if ( gc_clear_flags & GC_L_EDGE_CLEAR ) {
	    p_gc->gc_flags |= GC_AIM_L ;
	} else
	if ( gc_clear_flags & GC_B_EDGE_CLEAR ) {
	    p_gc->gc_flags |= GC_AIM_B ;
	} else
	if ( gc_clear_flags & GC_R_EDGE_CLEAR ) {
	    p_gc->gc_flags |= GC_AIM_R ;
	} else
	if ( gc_clear_flags & GC_T_EDGE_CLEAR ) {
	    p_gc->gc_flags |= GC_AIM_T ;
	} else {
	    /* all edges have something on them, do full test */
	    p_gc->gc_flags |= GC_AIM_C ;
	}
	p_gc++ ;
    }
}

int AddGridRecAlloc( p_gc, xa, ya, xb, yb, eps )
pGridCell	p_gc ;
double	xa,ya,xb,yb,eps ;
{
pGridRec	p_gr ;
double		slope, inv_slope ;

    if ( Near(ya, yb, eps) ) {
	if ( Near(xa, xb, eps) ) {
	    /* edge is 0 length, so get rid of it */
	    return( FALSE ) ;
	} else {
	    /* horizontal line */
	    slope = HUGE ;
	    inv_slope = 0.0 ;
	}
    } else {
	if ( Near(xa, xb, eps) ) {
	    /* vertical line */
	    slope = 0.0 ;
	    inv_slope = HUGE ;
	} else {
	    slope = (xb-xa)/(yb-ya) ;
	    inv_slope = (yb-ya)/(xb-xa) ;
	}
    }

    p_gc->tot_edges++ ;
    if ( p_gc->tot_edges <= 1 ) {
	p_gc->gr = (pGridRec)malloc( sizeof(GridRec) ) ;
    } else {
	p_gc->gr = (pGridRec)realloc( p_gc->gr,
		p_gc->tot_edges * sizeof(GridRec) ) ;
    }
    MALLOC_CHECK( p_gc->gr ) ;
    p_gr = &p_gc->gr[p_gc->tot_edges-1] ;

    p_gr->slope = slope ;
    p_gr->inv_slope = inv_slope ;

    p_gr->xa = xa ;
    p_gr->ya = ya ;
    if ( xa <= xb ) {
	p_gr->minx = xa ;
	p_gr->maxx = xb ;
    } else {
	p_gr->minx = xb ;
	p_gr->maxx = xa ;
    }
    if ( ya <= yb ) {
	p_gr->miny = ya ;
	p_gr->maxy = yb ;
    } else {
	p_gr->miny = yb ;
	p_gr->maxy = ya ;
    }

    /* P2 - P1 */
    p_gr->ax = xb - xa ;
    p_gr->ay = yb - ya ;

    return( TRUE ) ;
}

/* Test point against grid and edges in the cell (if any).  Algorithm:
 *    Check bounding box; if outside then return.
 *    Check cell point is inside; if simple inside or outside then return.
 *    Find which edge or corner is considered to be the best for testing and
 *	  send a test ray towards it, counting the crossings.  Add in the
 *	  state of the edge or corner the ray went to and so determine the
 *	  state of the point (inside or outside).
 */
int GridTest( p_gs, point )
register pGridSet	p_gs ;
double	point[2] ;
{
int	j, count, init_flag ;
pGridCell	p_gc ;
pGridRec	p_gr ;
double	tx, ty, xcell, ycell, bx,by,cx,cy, cornerx, cornery ;
double	alpha, beta, denom ;
unsigned short	gc_flags ;
int	inside_flag ;

    /* first, is point inside bounding rectangle? */
    if ( ( ty = point[Y] ) < p_gs->miny ||
	 ty >= p_gs->maxy ||
	 ( tx = point[X] ) < p_gs->minx ||
	 tx >= p_gs->maxx ) {

	/* outside of box */
	inside_flag = FALSE ;
    } else {

	/* what cell are we in? */
	ycell = ( ty - p_gs->miny ) * p_gs->inv_ydelta ;
	xcell = ( tx - p_gs->minx ) * p_gs->inv_xdelta ;
	p_gc = &p_gs->gc[((int)ycell)*p_gs->xres + (int)xcell] ;

	/* is cell simple? */
	count = p_gc->tot_edges ;
	if ( count ) {
	    /* no, so find an edge which is free. */
	    gc_flags = p_gc->gc_flags ;
	    p_gr = p_gc->gr ;
	    switch( gc_flags & GC_AIM ) {
	    case GC_AIM_L:
		/* left edge is clear, shoot X- ray */
		/* note - this next statement requires that GC_BL_IN is 1 */
		inside_flag = gc_flags & GC_BL_IN ;