concscan.c

Graphics Gems 源码 a collection of algorithms, programs, and mathematical techniques for the computer

/*
 * Concave Polygon Scan Conversion
 * by Paul Heckbert
 * from "Graphics Gems", Academic Press, 1990
 */

/*
 * concave: scan convert nvert-sided concave non-simple polygon with vertices at
 * (point[i].x, point[i].y) for i in [0..nvert-1] within the window win by
 * calling spanproc for each visible span of pixels.
 * Polygon can be clockwise or counterclockwise.
 * Algorithm does uniform point sampling at pixel centers.
 * Inside-outside test done by Jordan's rule: a point is considered inside if
 * an emanating ray intersects the polygon an odd number of times.
 * drawproc should fill in pixels from xl to xr inclusive on scanline y,
 * e.g:
 *	drawproc(y, xl, xr)
 *	int y, xl, xr;
 *	{
 *	    int x;
 *	    for (x=xl; x<=xr; x++)
 *		pixel_write(x, y, pixelvalue);
 *	}
 *
 *  Paul Heckbert	30 June 81, 18 Dec 89
 */

#include <stdio.h>
#include <math.h>
#include "GGems.h"

#define ALLOC(ptr, type, n)  ASSERT(ptr = (type *)malloc((n)*sizeof(type)))

typedef struct {		/* window: a discrete 2-D rectangle */
    int x0, y0;			/* xmin and ymin */
    int x1, y1;			/* xmax and ymax (inclusive) */
} Window;

typedef struct {		/* a polygon edge */
    double x;	/* x coordinate of edge's intersection with current scanline */
    double dx;	/* change in x with respect to y */
    int i;	/* edge number: edge i goes from pt[i] to pt[i+1] */
} Edge;

static int n;			/* number of vertices */
static Point2 *pt;		/* vertices */

static int nact;		/* number of active edges */
static Edge *active;		/* active edge list:edges crossing scanline y */

int compare_ind(), compare_active();

concave(nvert, point, win, spanproc)
int nvert;			/* number of vertices */
Point2 *point;			/* vertices of polygon */
Window *win;			/* screen clipping window */
void (*spanproc)();		/* called for each span of pixels */
{
    int k, y0, y1, y, i, j, xl, xr;
    int *ind;		/* list of vertex indices, sorted by pt[ind[j]].y */

    n = nvert;
    pt = point;
    if (n<=0) return;
    ALLOC(ind, int, n);
    ALLOC(active, Edge, n);

    /* create y-sorted array of indices ind[k] into vertex list */
    for (k=0; k<n; k++)
	ind[k] = k;
    qsort(ind, n, sizeof ind[0], compare_ind);	/* sort ind by pt[ind[k]].y */

    nact = 0;				/* start with empty active list */
    k = 0;				/* ind[k] is next vertex to process */
    y0 = MAX(win->y0, ceil(pt[ind[0]].y-.5));		/* ymin of polygon */
    y1 = MIN(win->y1, floor(pt[ind[n-1]].y-.5));	/* ymax of polygon */

    for (y=y0; y<=y1; y++) {		/* step through scanlines */
	/* scanline y is at y+.5 in continuous coordinates */

	/* check vertices between previous scanline and current one, if any */
	for (; k<n && pt[ind[k]].y<=y+.5; k++) {
	    /* to simplify, if pt.y=y+.5, pretend it's above */
	    /* invariant: y-.5 < pt[i].y <= y+.5 */
	    i = ind[k];	
	    /*
	     * insert or delete edges before and after vertex i (i-1 to i,
	     * and i to i+1) from active list if they cross scanline y
	     */
	    j = i>0 ? i-1 : n-1;	/* vertex previous to i */
	    if (pt[j].y <= y-.5)	/* old edge, remove from active list */
		cdelete(j);
	    else if (pt[j].y > y+.5)	/* new edge, add to active list */
		cinsert(j, y);
	    j = i<n-1 ? i+1 : 0;	/* vertex next after i */
	    if (pt[j].y <= y-.5)	/* old edge, remove from active list */
		cdelete(i);
	    else if (pt[j].y > y+.5)	/* new edge, add to active list */
		cinsert(i, y);
	}

	/* sort active edge list by active[j].x */
	qsort(active, nact, sizeof active[0], compare_active);

	/* draw horizontal segments for scanline y */
	for (j=0; j<nact; j+=2) {	/* draw horizontal segments */
	    /* span 'tween j & j+1 is inside, span tween j+1 & j+2 is outside */
	    xl = ceil(active[j].x-.5);		/* left end of span */
	    if (xl<win->x0) xl = win->x0;
	    xr = floor(active[j+1].x-.5);	/* right end of span */
	    if (xr>win->x1) xr = win->x1;
	    if (xl<=xr)
		(*spanproc)(y, xl, xr);		/* draw pixels in span */
	    active[j].x += active[j].dx;	/* increment edge coords */
	    active[j+1].x += active[j+1].dx;
	}
    }
}

static cdelete(i)		/* remove edge i from active list */
int i;
{
    int j;

    for (j=0; j<nact && active[j].i!=i; j++);
    if (j>=nact) return;	/* edge not in active list; happens at win->y0*/
    nact--;
    bcopy(&active[j+1], &active[j], (nact-j)*sizeof active[0]);
}

static cinsert(i, y)		/* append edge i to end of active list */
int i, y;
{
    int j;
    double dx;
    Point2 *p, *q;

    j = i<n-1 ? i+1 : 0;
    if (pt[i].y < pt[j].y) {p = &pt[i]; q = &pt[j];}
    else		   {p = &pt[j]; q = &pt[i];}
    /* initialize x position at intersection of edge with scanline y */
    active[nact].dx = dx = (q->x-p->x)/(q->y-p->y);
    active[nact].x = dx*(y+.5-p->y)+p->x;
    active[nact].i = i;
    nact++;
}

/* comparison routines for qsort */
compare_ind(u, v) int *u, *v; {return pt[*u].y <= pt[*v].y ? -1 : 1;}
compare_active(u, v) Edge *u, *v; {return u->x <= v->x ? -1 : 1;}