/*------------------------------------------------------------------------- * * geo-ops.c-- * 2D geometric operations * * Copyright (c) 1994, Regents of the University of California * * * IDENTIFICATION * /usr/local/devel/pglite/cvs/src/backend/utils/adt/geo-ops.c,v 1.5 1994/12/23 17:30:42 andrew Exp * *------------------------------------------------------------------------- */ #include #include /* faked on sunos */ #include /* for sprintf proto, etc. */ #include #include "utils/geo-decls.h" #include "utils/elog.h" #include "utils/palloc.h" #define LDELIM '(' #define RDELIM ')' #define DELIM ',' #define BOXNARGS 4 #define LSEGNARGS 4 #define POINTNARGS 2 /*********************************************************************** ** ** Routines for two-dimensional boxes. ** ***********************************************************************/ /*---------------------------------------------------------- * Formatting and conversion routines. *---------------------------------------------------------*/ /* box_in - convert a string to internal form. * * str: input string "(f8, f8, f8, f8)" */ BOX *box_in(char *str) { double tmp; char *p, *coord[BOXNARGS]; int i; BOX *result; if (str == NULL) elog (WARN," Bad (null) box external representation"); if ((p = (char *)strchr(str, LDELIM)) == (char *)NULL) elog (WARN, "Bad box external representation '%s'",str); for (i = 0, p = str; *p && i < BOXNARGS && *p != RDELIM; p++) if (*p == DELIM || (*p == LDELIM && !i)) coord[i++] = p + 1; if (i < BOXNARGS - 1) elog (WARN, "Bad box external representation '%s'", str); result = PALLOCTYPE(BOX); result->xh = atof(coord[0]); result->yh = atof(coord[1]); result->xl = atof(coord[2]); result->yl = atof(coord[3]); if (result->xh < result->xl) { tmp = result->xh; result->xh = result->xl; result->xl = tmp; } if (result->yh < result->yl) { tmp = result->yh; result->yh = result->yl; result->yl = tmp; } return(result); } /* box_out - convert a box to external form. */ char *box_out(BOX *box) { char *result; if (box == NULL) return(NULL); result = (char *)PALLOC(80); (void) sprintf(result, "(%lg,%lg,%lg,%lg)", box->xh, box->yh, box->xl, box->yl); return(result); } /* box_construct - fill in a new box. */ BOX *box_construct(double x1, double x2, double y1, double y2) { BOX *result; result = PALLOCTYPE(BOX); return( box_fill(result, x1, x2, y1, y2) ); } /* box_fill - fill in a static box */ BOX *box_fill(BOX *result, double x1, double x2, double y1, double y2) { double tmp; result->xh = x1; result->xl = x2; result->yh = y1; result->yl = y2; if (result->xh < result->xl) { tmp = result->xh; result->xh = result->xl; result->xl = tmp; } if (result->yh < result->yl) { tmp = result->yh; result->yh = result->yl; result->yl = tmp; } return(result); } /* box_copy - copy a box */ BOX *box_copy(BOX *box) { BOX *result; result = PALLOCTYPE(BOX); memmove((char *) result, (char *) box, sizeof(BOX)); return(result); } /*---------------------------------------------------------- * Relational operators for BOXes. * <, >, <=, >=, and == are based on box area. *---------------------------------------------------------*/ /* box_same - are two boxes identical? */ long box_same(BOX *box1, BOX *box2) { return((box1->xh == box2->xh && box1->xl == box2->xl) && (box1->yh == box2->yh && box1->yl == box2->yl)); } /* box_overlap - does box1 overlap box2? */ long box_overlap(BOX *box1, BOX *box2) { return(((box1->xh >= box2->xh && box1->xl <= box2->xh) || (box2->xh >= box1->xh && box2->xl <= box1->xh)) && ((box1->yh >= box2->yh && box1->yl <= box2->yh) || (box2->yh >= box1->yh && box2->yl <= box1->yh)) ); } /* box_overleft - is the right edge of box1 to the left of * the right edge of box2? * * This is "less than or equal" for the end of a time range, * when time ranges are stored as rectangles. */ long box_overleft(BOX *box1, BOX *box2) { return(box1->xh <= box2->xh); } /* box_left - is box1 strictly left of box2? */ long box_left(BOX *box1, BOX *box2) { return(box1->xh < box2->xl); } /* box_right - is box1 strictly right of box2? */ long box_right(BOX *box1, BOX *box2) { return(box1->xl > box2->xh); } /* box_overright - is the left edge of box1 to the right of * the left edge of box2? * * This is "greater than or equal" for time ranges, when time ranges * are stored as rectangles. */ long box_overright(BOX *box1, BOX *box2) { return(box1->xl >= box2->xl); } /* box_contained - is box1 contained by box2? */ long box_contained(BOX *box1, BOX *box2) { return((box1->xh <= box2->xh && box1->xl >= box2->xl && box1->yh <= box2->yh && box1->yl >= box2->yl)); } /* box_contain - does box1 contain box2? */ long box_contain(BOX *box1, BOX *box2) { return((box1->xh >= box2->xh && box1->xl <= box2->xl && box1->yh >= box2->yh && box1->yl <= box2->yl)); } /* box_positionop - * is box1 entirely {above, below } box2? */ long box_below(BOX *box1, BOX *box2) { return( box1->yh <= box2->yl ); } long box_above(BOX *box1, BOX *box2) { return( box1->yl >= box2->yh ); } /* box_relop - is area(box1) relop area(box2), within * our accuracy constraint? */ long box_lt(BOX *box1, BOX *box2) { return( FPlt(box_ar(box1), box_ar(box2)) ); } long box_gt(BOX *box1, BOX *box2) { return( FPgt(box_ar(box1), box_ar(box2)) ); } long box_eq(BOX *box1, BOX *box2) { return( FPeq(box_ar(box1), box_ar(box2)) ); } long box_le(BOX *box1, BOX *box2) { return( FPle(box_ar(box1), box_ar(box2)) ); } long box_ge(BOX *box1, BOX *box2) { return( FPge(box_ar(box1), box_ar(box2)) ); } /*---------------------------------------------------------- * "Arithmetic" operators on boxes. * box_foo returns foo as an object (pointer) that can be passed between languages. * box_xx is an internal routine which returns the * actual value (and cannot be handed back to * LISP). *---------------------------------------------------------*/ /* box_area - returns the area of the box. */ double *box_area(BOX *box) { double *result; result = PALLOCTYPE(double); *result = box_ln(box) * box_ht(box); return(result); } /* box_length - returns the length of the box * (horizontal magnitude). */ double *box_length(BOX *box) { double *result; result = PALLOCTYPE(double); *result = box->xh - box->xl; return(result); } /* box_height - returns the height of the box * (vertical magnitude). */ double *box_height(BOX *box) { double *result; result = PALLOCTYPE(double); *result = box->yh - box->yl; return(result); } /* box_distance - returns the distance between the * center points of two boxes. */ double *box_distance(BOX *box1, BOX *box2) { double *result; Point *box_center(), *a, *b; result = PALLOCTYPE(double); a = box_center(box1); b = box_center(box2); *result = HYPOT(a->x - b->x, a->y - b->y); PFREE(a); PFREE(b); return(result); } /* box_center - returns the center point of the box. */ Point *box_center(BOX *box) { Point *result; result = PALLOCTYPE(Point); result->x = (box->xh + box->xl) / 2.0; result->y = (box->yh + box->yl) / 2.0; return(result); } /* box_ar - returns the area of the box. */ double box_ar(BOX *box) { return( box_ln(box) * box_ht(box) ); } /* box_ln - returns the length of the box * (horizontal magnitude). */ double box_ln(BOX *box) { return( box->xh - box->xl ); } /* box_ht - returns the height of the box * (vertical magnitude). */ double box_ht(BOX *box) { return( box->yh - box->yl ); } /* box_dt - returns the distance between the * center points of two boxes. */ double box_dt(BOX *box1, BOX *box2) { double result; Point *box_center(), *a, *b; a = box_center(box1); b = box_center(box2); result = HYPOT(a->x - b->x, a->y - b->y); PFREE(a); PFREE(b); return(result); } /*---------------------------------------------------------- * Funky operations. *---------------------------------------------------------*/ /* box_intersect - * returns the overlapping portion of two boxes, * or NULL if they do not intersect. */ BOX *box_intersect(BOX *box1, BOX *box2) { BOX *result; long box_overlap(); if (! box_overlap(box1,box2)) return(NULL); result = PALLOCTYPE(BOX); result->xh = Min(box1->xh, box2->xh); result->xl = Max(box1->xl, box2->xl); result->yh = Min(box1->yh, box2->yh); result->yl = Max(box1->yl, box2->yl); return(result); } /* box_diagonal - * returns a line segment which happens to be the * positive-slope diagonal of "box". * provided, of course, we have LSEGs. */ LSEG *box_diagonal(BOX *box) { Point p1, p2; p1.x = box->xh; p1.y = box->yh; p2.x = box->xl; p2.y = box->yl; return( lseg_construct( &p1, &p2 ) ); } /*********************************************************************** ** ** Routines for 2D lines. ** Lines are not intended to be used as ADTs per se, ** but their ops are useful tools for other ADT ops. Thus, ** there are few relops. ** ***********************************************************************/ /*---------------------------------------------------------- * Conversion routines from one line formula to internal. * Internal form: Ax+By+C=0 *---------------------------------------------------------*/ LINE * /* point-slope */ line_construct_pm(Point *pt, double m) { LINE *result; result = PALLOCTYPE(LINE); /* use "mx - y + yinter = 0" */ result->A = m; result->B = -1.0; result->C = pt->y - m * pt->x; return(result); } LINE * /* two points */ line_construct_pp(Point *pt1, Point *pt2) { LINE *result; result = PALLOCTYPE(LINE); if (FPeq(pt1->x, pt2->x)) { /* vertical */ /* use "x = C" */ result->m = 0.0; result->A = -1.0; result->B = 0.0; result->C = pt1->x; } else { /* use "mx - y + yinter = 0" */ result->m = (pt1->y - pt2->y) / (pt1->x - pt2->x); result->A = result->m; result->B = -1.0; result->C = pt1->y - result->m * pt1->x; } return(result); } /*---------------------------------------------------------- * Relative position routines. *---------------------------------------------------------*/ long line_intersect(LINE *l1, LINE *l2) { return( ! line_parallel(l1, l2) ); } long line_parallel(LINE *l1, LINE *l2) { return( FPeq(l1->m, l2->m) ); } long line_perp(LINE *l1, LINE *l2) { if (l1->m) return( FPeq(l2->m / l1->m, -1.0) ); else if (l2->m) return( FPeq(l1->m / l2->m, -1.0) ); return(1); /* both 0.0 */ } long line_vertical(LINE *line) { return( FPeq(line->A, -1.0) && FPzero(line->B) ); } long line_horizontal(LINE *line) { return( FPzero(line->m) ); } long line_eq(LINE *l1, LINE *l2) { double k; if (! FPzero(l2->A)) k = l1->A / l2->A; else if (! FPzero(l2->B)) k = l1->B / l2->B; else if (! FPzero(l2->C)) k = l1->C / l2->C; else k = 1.0; return( FPeq(l1->A, k * l2->A) && FPeq(l1->B, k * l2->B) && FPeq(l1->C, k * l2->C) ); } /*---------------------------------------------------------- * Line arithmetic routines. *---------------------------------------------------------*/ double * /* distance between l1, l2 */ line_distance(LINE *l1, LINE *l2) { double *result; Point *tmp; result = PALLOCTYPE(double); if (line_intersect(l1, l2)) { *result = 0.0; return(result); } if (line_vertical(l1)) *result = fabs(l1->C - l2->C); else { tmp = point_construct(0.0, l1->C); result = dist_pl(tmp, l2); PFREE(tmp); } return(result); } Point * /* point where l1, l2 intersect (if any) */ line_interpt(LINE *l1, LINE *l2) { Point *result; double x; if (line_parallel(l1, l2)) return(NULL); if (line_vertical(l1)) result = point_construct(l2->m * l1->C + l2->C, l1->C); else if (line_vertical(l2)) result = point_construct(l1->m * l2->C + l1->C, l2->C); else { x = (l1->C - l2->C) / (l2->A - l1->A); result = point_construct(x, l1->m * x + l1->C); } return(result); } /*********************************************************************** ** ** Routines for 2D paths (sequences of line segments, also ** called `polylines'). ** ** This is not a general package for geometric paths, ** which of course include polygons; the emphasis here ** is on (for example) usefulness in wire layout. ** ***********************************************************************/ #define PATHALLOCSIZE(N) \ (long) ((unsigned) (sizeof(PATH) + \ (((N)-1) > 0 ? ((N)-1) : 0) \ * sizeof(Point))) /*---------------------------------------------------------- * String to path / path to string conversion. * External format: * "(closed, npts, xcoord, ycoord,... )" *---------------------------------------------------------*/ PATH *path_in(char *str) { double coord; long field[2]; char *s; int ct, i; PATH *result; long pathsize; if (str == NULL) elog(WARN, "Bad (null) path external representation"); /* read the path header information */ for (i = 0, s = str; *s && i < 2 && *s != RDELIM; ++s) if (*s == DELIM || (*s == LDELIM && !i)) field[i++] = atol(s + 1); if (i < 1) elog(WARN, "Bad path external representation '%s'", str); pathsize = PATHALLOCSIZE(field[1]); result = (PATH *)palloc(pathsize); result->length = pathsize; result->closed = field[0]; result->npts = field[1]; /* read the path points */ ct = result->npts * 2; /* two coords for every point */ for (i = 0; *s && i < ct && *s != RDELIM; ++s) { if (*s == ',') { coord = atof(s + 1); if (i % 2) (result->p[i/2]).y = coord; else (result->p[i/2]).x = coord; ++i; } } if (i % 2 || i < --ct) { PFREE(result); elog(WARN, "Bad path external representation '%s'", str); } return(result); } char *path_out(PATH *path) { char buf[BUFSIZ + 20000], *result, *s; int i; char tmp[64]; if (path == NULL) return(NULL); (void) sprintf(buf,"%c%d,%d\0", LDELIM, path->closed, path->npts); s = buf + strlen(buf); for (i = 0; i < path->npts; ++i) { (void) sprintf(tmp, ",%lg,%lg", path->p[i].x, path->p[i].y); (void) strcpy(s, tmp); s += strlen(tmp); } *s++ = RDELIM; *s = '\0'; result = (char *)PALLOC(strlen(buf) + 1); (void) strcpy(result, buf); return(result); } /*---------------------------------------------------------- * Relational operators. * These are based on the path cardinality, * as stupid as that sounds. * * Better relops and access methods coming soon. *---------------------------------------------------------*/ long path_n_lt(PATH *p1, PATH *p2) { return( (p1->npts < p2->npts ) ); } long path_n_gt(PATH *p1, PATH *p2) { return( (p1->npts > p2->npts ) ); } long path_n_eq(PATH *p1, PATH *p2) { return( (p1->npts == p2->npts) ); } long path_n_le(PATH *p1, PATH *p2) { return( (p1->npts <= p2->npts ) ); } long path_n_ge(PATH *p1, PATH *p2) { return( (p1->npts >= p2->npts ) ); } /* path_inter - * Does p1 intersect p2 at any point? * Use bounding boxes for a quick (O(n)) check, then do a * O(n^2) iterative edge check. */ long path_inter(PATH *p1, PATH *p2) { BOX b1, b2; int i, j; LSEG seg1, seg2; b1.xh = b1.yh = b2.xh = b2.yh = DBL_MAX; b1.xl = b1.yl = b2.xl = b2.yl = -DBL_MAX; for (i = 0; i < p1->npts; ++i) { b1.xh = Max(p1->p[i].x, b1.xh); b1.yh = Max(p1->p[i].y, b1.yh); b1.xl = Min(p1->p[i].x, b1.xl); b1.yl = Min(p1->p[i].y, b1.yl); } for (i = 0; i < p2->npts; ++i) { b2.xh = Max(p2->p[i].x, b2.xh); b2.yh = Max(p2->p[i].y, b2.yh); b2.xl = Min(p2->p[i].x, b2.xl); b2.yl = Min(p2->p[i].y, b2.yl); } if (! box_overlap(&b1, &b2)) return(0); /* pairwise check lseg intersections */ for (i = 0; i < p1->npts - 1; i++) { for (j = 0; j < p2->npts - 1; j++) { statlseg_construct(&seg1, &p1->p[i], &p1->p[i+1]); statlseg_construct(&seg2, &p2->p[j], &p2->p[j+1]); if (lseg_intersect(&seg1, &seg2)) return(1); } } /* if we dropped through, no two segs intersected */ return(0); } /* this essentially does a cartesian product of the lsegs in the two paths, and finds the min distance between any two lsegs */ double *path_distance(PATH *p1, PATH *p2) { double *min, *tmp; int i,j; LSEG seg1, seg2; statlseg_construct(&seg1, &p1->p[0], &p1->p[1]); statlseg_construct(&seg2, &p2->p[0], &p2->p[1]); min = lseg_distance(&seg1, &seg2); for (i = 0; i < p1->npts - 1; i++) for (j = 0; j < p2->npts - 1; j++) { statlseg_construct(&seg1, &p1->p[i], &p1->p[i+1]); statlseg_construct(&seg2, &p2->p[j], &p2->p[j+1]); if (*min < *(tmp = lseg_distance(&seg1, &seg2))) *min = *tmp; PFREE(tmp); } return(min); } /*---------------------------------------------------------- * "Arithmetic" operations. *---------------------------------------------------------*/ double *path_length(PATH *path) { double *result; int ct, i; result = PALLOCTYPE(double); ct = path->npts - 1; for (i = 0; i < ct; ++i) *result += point_dt(&path->p[i], &path->p[i+1]); return(result); } double path_ln(PATH *path) { double result; int ct, i; ct = path->npts - 1; for (result = i = 0; i < ct; ++i) result += point_dt(&path->p[i], &path->p[i+1]); return(result); } /*********************************************************************** ** ** Routines for 2D points. ** ***********************************************************************/ /*---------------------------------------------------------- * String to point, point to string conversion. * External form: "(x, y)" *---------------------------------------------------------*/ Point *point_in(char *str) { char *coord[POINTNARGS], *p, *r; int i; Point *result; if (str == NULL) elog(WARN, "Bad (null) point external representation"); if ((p = (char *)strchr(str, LDELIM)) == (char *)NULL) elog (WARN, "Bad point external representation '%s'",str); for (i = 0, p++; *p && i < POINTNARGS-1 && *p != RDELIM; p = r+1) if ((r = (char *)strchr(p, DELIM)) == (char *)NULL) elog (WARN, "Bad point external representation '%s'",str); else coord[i++] = p; if ((r = (char *)strchr(p, RDELIM)) == (char *)NULL) elog (WARN, "Bad point external representation '%s'",str); coord[i++] = p; if (i < POINTNARGS - 1) elog(WARN, "Bad point external representation '%s'",str); result = PALLOCTYPE(Point); result->x = atof(coord[0]); result->y = atof(coord[1]); return(result); } char *point_out(Point *pt) { char *result; if (pt == NULL) return(NULL); result = (char *)PALLOC(40); (void) sprintf(result, "(%lg,%lg)", pt->x, pt->y); return(result); } Point *point_construct(double x, double y) { Point *result; result = PALLOCTYPE(Point); result->x = x; result->y = y; return(result); } Point *point_copy(Point *pt) { Point *result; result = PALLOCTYPE(Point); result->x = pt->x; result->y = pt->y; return(result); } /*---------------------------------------------------------- * Relational operators for Points. * Since we do have a sense of coordinates being * "equal" to a given accuracy (point_vert, point_horiz), * the other ops must preserve that sense. This means * that results may, strictly speaking, be a lie (unless * EPSILON = 0.0). *---------------------------------------------------------*/ long point_left(Point *pt1, Point *pt2) { return( FPlt(pt1->x, pt2->x) ); } long point_right(Point *pt1, Point *pt2) { return( FPgt(pt1->x, pt2->x) ); } long point_above(Point *pt1, Point *pt2) { return( FPgt(pt1->y, pt2->y) ); } long point_below(Point *pt1, Point *pt2) { return( FPlt(pt1->y, pt2->y) ); } long point_vert(Point *pt1, Point *pt2) { return( FPeq( pt1->x, pt2->x ) ); } long point_horiz(Point *pt1, Point *pt2) { return( FPeq( pt1->y, pt2->y ) ); } long point_eq(Point *pt1, Point *pt2) { return( point_horiz(pt1, pt2) && point_vert(pt1, pt2) ); } /*---------------------------------------------------------- * "Arithmetic" operators on points. *---------------------------------------------------------*/ long pointdist(Point *p1, Point *p2) { long result; result = point_dt(p1, p2); return(result); } double *point_distance(Point *pt1, Point *pt2) { double *result; result = PALLOCTYPE(double); *result = HYPOT( pt1->x - pt2->x, pt1->y - pt2->y ); return(result); } double point_dt(Point *pt1, Point *pt2) { return( HYPOT( pt1->x - pt2->x, pt1->y - pt2->y ) ); } double *point_slope(Point *pt1, Point *pt2) { double *result; result = PALLOCTYPE(double); if (point_vert(pt1, pt2)) *result = DBL_MAX; else *result = (pt1->y - pt2->y) / (pt1->x - pt1->x); return(result); } double point_sl(Point *pt1, Point *pt2) { return( point_vert(pt1, pt2) ? DBL_MAX : (pt1->y - pt2->y) / (pt1->x - pt2->x) ); } /*********************************************************************** ** ** Routines for 2D line segments. ** ***********************************************************************/ /*---------------------------------------------------------- * String to lseg, lseg to string conversion. * External form: "(id, info, x1, y1, x2, y2)" *---------------------------------------------------------*/ LSEG *lseg_in(char *str) { char *coord[LSEGNARGS], *p; int i; LSEG *result; if (str == NULL) elog (WARN," Bad (null) box external representation"); if ((p = (char *)strchr(str, LDELIM)) == (char *)NULL) elog (WARN, "Bad lseg external representation '%s'",str); for (i = 0, p = str; *p && i < LSEGNARGS && *p != RDELIM; p++) if (*p == DELIM || (*p == LDELIM && !i)) coord[i++] = p + 1; if (i < LSEGNARGS - 1) elog (WARN, "Bad lseg external representation '%s'", str); result = PALLOCTYPE(LSEG); result->p[0].x = atof(coord[0]); result->p[0].y = atof(coord[1]); result->p[1].x = atof(coord[2]); result->p[1].y = atof(coord[3]); result->m = point_sl(&result->p[0], &result->p[1]); return(result); } char *lseg_out(LSEG *ls) { char *result; if (ls == NULL) return(NULL); result = (char *)PALLOC(80); (void) sprintf(result, "(%lg,%lg,%lg,%lg)", ls->p[0].x, ls->p[0].y, ls->p[1].x, ls->p[1].y); return(result); } /* lseg_construct - * form a LSEG from two Points. */ LSEG *lseg_construct(Point *pt1, Point *pt2) { LSEG *result; result = PALLOCTYPE(LSEG); result->p[0].x = pt1->x; result->p[0].y = pt1->y; result->p[1].x = pt2->x; result->p[1].y = pt2->y; result->m = point_sl(pt1, pt2); return(result); } /* like lseg_construct, but assume space already allocated */ void statlseg_construct(LSEG *lseg, Point *pt1, Point *pt2) { lseg->p[0].x = pt1->x; lseg->p[0].y = pt1->y; lseg->p[1].x = pt2->x; lseg->p[1].y = pt2->y; lseg->m = point_sl(pt1, pt2); } /*---------------------------------------------------------- * Relative position routines. *---------------------------------------------------------*/ /* ** find intersection of the two lines, and see if it falls on ** both segments. */ long lseg_intersect(LSEG *l1, LSEG *l2) { LINE *ln; Point *interpt; long retval; ln = line_construct_pp(&l2->p[0], &l2->p[1]); interpt = interpt_sl(l1, ln); if (interpt != NULL && on_ps(interpt, l2)) /* interpt on l1 and l2 */ retval = 1; else retval = 0; if (interpt != NULL) PFREE(interpt); PFREE(ln); return(retval); } long lseg_parallel(LSEG *l1, LSEG *l2) { return( FPeq(l1->m, l2->m) ); } long lseg_perp(LSEG *l1, LSEG *l2) { if (! FPzero(l1->m)) return( FPeq(l2->m / l1->m, -1.0) ); else if (! FPzero(l2->m)) return( FPeq(l1->m / l2->m, -1.0) ); return(0); /* both 0.0 */ } long lseg_vertical(LSEG *lseg) { return( FPeq(lseg->p[0].x, lseg->p[1].x) ); } long lseg_horizontal(LSEG *lseg) { return( FPeq(lseg->p[0].y, lseg->p[1].y) ); } long lseg_eq(LSEG *l1, LSEG *l2) { return( FPeq(l1->p[0].x, l2->p[0].x) && FPeq(l1->p[1].y, l2->p[1].y) && FPeq(l1->p[0].x, l2->p[0].x) && FPeq(l1->p[1].y, l2->p[1].y) ); } /*---------------------------------------------------------- * Line arithmetic routines. *---------------------------------------------------------*/ /* lseg_distance - * If two segments don't intersect, then the closest * point will be from one of the endpoints to the other * segment. */ double *lseg_distance(LSEG *l1, LSEG *l2) { double *d, *result; result = PALLOCTYPE(double); if (lseg_intersect(l1, l2)) { *result = 0.0; return(result); } *result = DBL_MAX; d = dist_ps(&l1->p[0], l2); *result = Min(*result, *d); PFREE(d); d = dist_ps(&l1->p[1], l2); *result = Min(*result, *d); PFREE(d); d = dist_ps(&l2->p[0], l1); *result = Min(*result, *d); PFREE(d); d = dist_ps(&l2->p[1], l1); *result = Min(*result, *d); PFREE(d); return(result); } /* distance between l1, l2 */ double lseg_dt(LSEG *l1, LSEG *l2) { double *d, result; if (lseg_intersect(l1, l2)) return(0.0); result = DBL_MAX; d = dist_ps(&l1->p[0], l2); result = Min(result, *d); PFREE(d); d = dist_ps(&l1->p[1], l2); result = Min(result, *d); PFREE(d); d = dist_ps(&l2->p[0], l1); result = Min(result, *d); PFREE(d); d = dist_ps(&l2->p[1], l1); result = Min(result, *d); PFREE(d); return(result); } /* lseg_interpt - * Find the intersection point of two segments (if any). * Find the intersection of the appropriate lines; if the * point is not on a given segment, there is no valid segment * intersection point at all. */ Point *lseg_interpt(LSEG *l1, LSEG *l2) { Point *result; LINE *tmp1, *tmp2; tmp1 = line_construct_pp(&l1->p[0], &l1->p[1]); tmp2 = line_construct_pp(&l2->p[0], &l2->p[1]); result = line_interpt(tmp1, tmp2); if (result) if (! on_ps(result, l1)) { PFREE(result); result = NULL; } PFREE(tmp1); PFREE(tmp2); return(result); } /*********************************************************************** ** ** Routines for position comparisons of differently-typed ** 2D objects. ** ***********************************************************************/ #define ABOVE 1 #define BELOW 0 #define UNDEF -1 /*--------------------------------------------------------------------- * dist_ * Minimum distance from one object to another. *-------------------------------------------------------------------*/ double *dist_pl(Point *pt, LINE *line) { double *result; result = PALLOCTYPE(double); *result = (line->A * pt->x + line->B * pt->y + line->C) / HYPOT(line->A, line->B); return(result); } double *dist_ps(Point *pt, LSEG *lseg) { double m; /* slope of perp. */ LINE *ln; double *result, *tmpdist; Point *ip; /* construct a line that's perpendicular. See if the intersection of the two lines is on the line segment. */ if (lseg->p[1].x == lseg->p[0].x) m = 0; else if (lseg->p[1].y == lseg->p[0].y) /* slope is infinite */ m = DBL_MAX; else m = (-1) * (lseg->p[1].y - lseg->p[0].y) / (lseg->p[1].x - lseg->p[0].x); ln = line_construct_pm(pt, m); if ((ip = interpt_sl(lseg, ln)) != NULL) result = point_distance(pt, ip); else /* intersection is not on line segment, so distance is min of distance from point to an endpoint */ { result = point_distance(pt, &lseg->p[0]); tmpdist = point_distance(pt, &lseg->p[1]); if (*tmpdist < *result) *result = *tmpdist; PFREE (tmpdist); } if (ip != NULL) PFREE(ip); PFREE(ln); return (result); } /* ** Distance from a point to a path */ double *dist_ppth(Point *pt, PATH *path) { double *result; double *tmp; int i; LSEG lseg; switch (path->npts) { case 0: result = PALLOCTYPE(double); *result = Abs((double) DBL_MAX); /* +infinity */ break; case 1: result = point_distance(pt, &path->p[0]); break; default: /* * the distance from a point to a path is the smallest distance * from the point to any of its constituent segments. */ Assert(path->npts > 1); result = PALLOCTYPE(double); for (i = 0; i < path->npts - 1; ++i) { statlseg_construct(&lseg, &path->p[i], &path->p[i+1]); tmp = dist_ps(pt, &lseg); if (i == 0 || *tmp < *result) *result = *tmp; PFREE(tmp); } break; } return(result); } double *dist_pb(Point *pt, BOX *box) { Point *tmp; double *result; tmp = close_pb(pt, box); result = point_distance(tmp, pt); PFREE(tmp); return(result); } double *dist_sl(LSEG *lseg, LINE *line) { double *result; if (inter_sl(lseg, line)) { result = PALLOCTYPE(double); *result = 0.0; } else /* parallel */ result = dist_pl(&lseg->p[0], line); return(result); } double *dist_sb(LSEG *lseg, BOX *box) { Point *tmp; double *result; tmp = close_sb(lseg, box); if (tmp == NULL) { result = PALLOCTYPE(double); *result = 0.0; } else { result = dist_pb(tmp, box); PFREE(tmp); } return(result); } double *dist_lb(LINE *line, BOX *box) { Point *tmp; double *result; tmp = close_lb(line, box); if (tmp == NULL) { result = PALLOCTYPE(double); *result = 0.0; } else { result = dist_pb(tmp, box); PFREE(tmp); } return(result); } /*--------------------------------------------------------------------- * interpt_ * Intersection point of objects. * We choose to ignore the "point" of intersection between * lines and boxes, since there are typically two. *-------------------------------------------------------------------*/ Point *interpt_sl(LSEG *lseg, LINE *line) { LINE *tmp; Point *p; tmp = line_construct_pp(&lseg->p[0], &lseg->p[1]); p = line_interpt(tmp, line); if (p) if (! on_ps(p, lseg)) { PFREE(p); p = NULL; } PFREE(tmp); return(p); } /*--------------------------------------------------------------------- * close_ * Point of closest proximity between objects. *-------------------------------------------------------------------*/ /* close_pl - * The intersection point of a perpendicular of the line * through the point. */ Point *close_pl(Point *pt, LINE *line) { Point *result; LINE *tmp; double invm; result = PALLOCTYPE(Point); if (FPeq(line->A, -1.0) && FPzero(line->B)) { /* vertical */ result->x = line->C; result->y = pt->y; return(result); } else if (FPzero(line->m)) { /* horizontal */ result->x = pt->x; result->y = line->C; return(result); } /* drop a perpendicular and find the intersection point */ invm = -1.0 / line->m; tmp = line_construct_pm(pt, invm); result = line_interpt(tmp, line); return(result); } /* close_ps - * Take the closest endpoint if the point is left, right, * above, or below the segment, otherwise find the intersection * point of the segment and its perpendicular through the point. */ Point *close_ps(Point *pt, LSEG *lseg) { Point *result; LINE *tmp; double invm; int xh, yh; result = NULL; xh = lseg->p[0].x < lseg->p[1].x; yh = lseg->p[0].y < lseg->p[1].y; if (pt->x < lseg->p[!xh].x) result = point_copy(&lseg->p[!xh]); else if (pt->x > lseg->p[xh].x) result = point_copy(&lseg->p[xh]); else if (pt->y < lseg->p[!yh].y) result = point_copy(&lseg->p[!yh]); else if (pt->y > lseg->p[yh].y) result = point_copy(&lseg->p[yh]); if (result) return(result); if (FPeq(lseg->p[0].x, lseg->p[1].x)) { /* vertical */ result->x = lseg->p[0].x; result->y = pt->y; return(result); } else if (FPzero(lseg->m)) { /* horizontal */ result->x = pt->x; result->y = lseg->p[0].y; return(result); } invm = -1.0 / lseg->m; tmp = line_construct_pm(pt, invm); result = interpt_sl(lseg, tmp); return(result); } Point *close_pb(Point *pt, BOX *box) { /* think about this one for a while */ return(NULL); } Point *close_sl(LSEG *lseg, LINE *line) { Point *result; double *d1, *d2; result = interpt_sl(lseg, line); if (result) return(result); d1 = dist_pl(&lseg->p[0], line); d2 = dist_pl(&lseg->p[1], line); if (d1 < d2) result = point_copy(&lseg->p[0]); else result = point_copy(&lseg->p[1]); PFREE(d1); PFREE(d2); return(result); } Point *close_sb(LSEG *lseg, BOX *box) { /* think about this one for a while */ return(NULL); } Point *close_lb(LINE *line, BOX *box) { /* think about this one for a while */ return(NULL); } /*--------------------------------------------------------------------- * on_ * Whether one object lies completely within another. *-------------------------------------------------------------------*/ /* on_pl - * Does the point satisfy the equation? */ long on_pl(Point *pt, LINE *line) { return( FPzero(line->A * pt->x + line->B * pt->y + line->C) ); } /* on_ps - * Determine colinearity by detecting a triangle inequality. */ long on_ps(Point *pt, LSEG *lseg) { return( point_dt(pt, &lseg->p[0]) + point_dt(pt, &lseg->p[1]) == point_dt(&lseg->p[0], &lseg->p[1]) ); } long on_pb(Point *pt, BOX *box) { return( pt->x <= box->xh && pt->x >= box->xl && pt->y <= box->yh && pt->y >= box->yl ); } /* on_ppath - * Whether a point lies within (on) a polyline. * If open, we have to (groan) check each segment. * If closed, we use the old O(n) ray method for point-in-polygon. * The ray is horizontal, from pt out to the right. * Each segment that crosses the ray counts as an * intersection; note that an endpoint or edge may touch * but not cross. * (we can do p-in-p in lg(n), but it takes preprocessing) */ #define NEXT(A) ((A+1) % path->npts) /* cyclic "i+1" */ long on_ppath(Point *pt, PATH *path) { int above, next, /* is the seg above the ray? */ inter, /* # of times path crosses ray */ hi, /* index inc of higher seg (0,1) */ i, n; double a, b, x, yh, yl, xh, xl; if (! path->closed) { /*-- OPEN --*/ n = path->npts - 1; a = point_dt(pt, &path->p[0]); for (i = 0; i < n; i++) { b = point_dt(pt, &path->p[i+1]); if (FPeq(a+b, point_dt(&path->p[i], &path->p[i+1]))) return(1); a = b; } return(0); } inter = 0; /*-- CLOSED --*/ above = FPgt(path->p[0].y, pt->y) ? ABOVE : FPlt(path->p[0].y, pt->y) ? BELOW : UNDEF; for (i = 0; i < path->npts; i++) { hi = path->p[i].y < path->p[NEXT(i)].y; /* must take care of wrap around to original vertex for closed paths */ yh = (i+hi < path->npts) ? path->p[i+hi].y : path->p[0].y; yl = (i+!hi < path->npts) ? path->p[i+!hi].y : path->p[0].y; hi = path->p[i].x < path->p[NEXT(i)].x; xh = (i+hi < path->npts) ? path->p[i+hi].x : path->p[0].x; xl = (i+!hi < path->npts) ? path->p[i+!hi].x : path->p[0].x; /* skip seg if it doesn't touch the ray */ if (FPeq(yh, yl)) /* horizontal seg? */ if (FPge(pt->x, xl) && FPle(pt->x, xh) && FPeq(pt->y, yh)) return(1); /* pt lies on seg */ else continue; /* skip other hz segs */ if (FPlt(yh, pt->y) || /* pt is strictly below seg */ FPgt(yl, pt->y)) /* strictly above */ continue; /* seg touches the ray, find out where */ x = FPeq(xh, xl) /* vertical seg? */ ? path->p[i].x : (pt->y - path->p[i].y) / point_sl(&path->p[i], &path->p[NEXT(i)]) + path->p[i].x; if (FPeq(x, pt->x)) /* pt lies on this seg */ return(1); /* does the seg actually cross the ray? */ next = FPgt(path->p[NEXT(i)].y, pt->y) ? ABOVE : FPlt(path->p[NEXT(i)].y, pt->y) ? BELOW : above; inter += FPge(x, pt->x) && next != above; above = next; } return( above == UNDEF || /* path is horizontal */ inter % 2); /* odd # of intersections */ } long on_sl(LSEG *lseg, LINE *line) { return( on_pl(&lseg->p[0], line) && on_pl(&lseg->p[1], line) ); } long on_sb(LSEG *lseg, BOX *box) { return( on_pb(&lseg->p[0], box) && on_pb(&lseg->p[1], box) ); } /*--------------------------------------------------------------------- * inter_ * Whether one object intersects another. *-------------------------------------------------------------------*/ long inter_sl(LSEG *lseg, LINE *line) { Point *tmp; tmp = interpt_sl(lseg, line); if (tmp) { PFREE(tmp); return(1); } return(0); } long inter_sb(LSEG *lseg, BOX *box) { return(0); } long inter_lb(LINE *line, BOX *box) { return(0); } /*------------------------------------------------------------------ * The following routines define a data type and operator class for * POLYGONS .... Part of which (the polygon's bounding box is built on * top of the BOX data type. * * make_bound_box - create the bounding box for the input polygon *------------------------------------------------------------------*/ /* Maximum number of output digits printed */ #define P_MAXDIG 12 /*--------------------------------------------------------------------- * Make the smallest bounding box for the given polygon. *---------------------------------------------------------------------*/ void make_bound_box(POLYGON *poly) { double x1,y1,x2,y2; int npts = poly->npts; if (npts > 0) { x1 = poly_min((double *)poly->pts, npts); x2 = poly_max((double *)poly->pts, npts); y1 = poly_min(((double *)poly->pts)+npts, npts), y2 = poly_max(((double *)poly->pts)+npts, npts); box_fill(&(poly->boundbox), x1, x2, y1, y2); } } /*------------------------------------------------------------------ * polygon_in - read in the polygon from a string specification * the string is of the form "(f8,f8,f8,f8,...,f8)" *------------------------------------------------------------------*/ POLYGON *poly_in(char *s) { POLYGON *poly; long points; double *xp, *yp, strtod(); int i, size; if((points = poly_pt_count(s, ',')) < 0) elog(WARN, "Bad polygon external representation '%s'", s); size = offsetof(POLYGON, pts[0]) + 2 * sizeof(double) * points; poly = (POLYGON *) PALLOC(size); memset((char *) poly, 0, size); /* zero any holes */ if (!PointerIsValid(poly)) elog(WARN, "Memory allocation failed, can't input polygon"); poly->npts = points; poly->size = size; /* Store all x coords followed by all y coords */ xp = (double *) &(poly->pts[0]); yp = (double *) (poly->pts + points*sizeof(double)); s++; /* skip LDELIM */ for (i=0; inpts + 3); outptr = output; if (!output) elog(WARN, "Memory allocation failed, can't output polygon"); *outptr++ = LDELIM; xp = (double *) poly->pts; yp = (double *) (poly->pts + (poly->npts * sizeof(double))); sprintf(outptr, "%*g,%*g", P_MAXDIG, *xp++, P_MAXDIG, *yp++); outptr += (2*P_MAXDIG + 1); for (i=1; inpts; i++,xp++,yp++) { sprintf(outptr, ",%*g,%*g", P_MAXDIG, *xp, P_MAXDIG, *yp); outptr += 2*(P_MAXDIG + 1); } *outptr++ = RDELIM; *outptr = '\0'; return (output); } /*------------------------------------------------------- * Find the largest coordinate out of n coordinates *-------------------------------------------------------*/ double poly_max(double *coords, int ncoords) { double max; max = *coords++; ncoords--; while (ncoords--) { if (*coords > max) max = *coords; coords++; } return max; } /*------------------------------------------------------- * Find the smallest coordinate out of n coordinates *-------------------------------------------------------*/ double poly_min(double *coords, int ncoords) { double min; min = *coords++; ncoords--; while (ncoords--) { if (*coords < min) min = *coords; coords++; } return min; } /*------------------------------------------------------- * Is polygon A strictly left of polygon B? i.e. is * the right most point of A left of the left most point * of B? *-------------------------------------------------------*/ long poly_left(POLYGON *polya, POLYGON *polyb) { double right, left; if (polya->npts > 0) right = poly_max((double *)polya->pts, polya->npts); else right = polya->boundbox.xh; if (polyb->npts > 0) left = poly_min((double *)polyb->pts, polyb->npts); else left = polyb->boundbox.xl; return (right < left); } /*------------------------------------------------------- * Is polygon A overlapping or left of polygon B? i.e. is * the left most point of A left of the right most point * of B? *-------------------------------------------------------*/ long poly_overleft(POLYGON *polya, POLYGON *polyb) { double left, right; if (polya->npts > 0) left = poly_min((double *)polya->pts, polya->npts); else left = polya->boundbox.xl; if (polyb->npts > 0) right = poly_max((double *)polyb->pts, polyb->npts); else right = polyb->boundbox.xh; return (left <= right); } /*------------------------------------------------------- * Is polygon A strictly right of polygon B? i.e. is * the left most point of A right of the right most point * of B? *-------------------------------------------------------*/ long poly_right(POLYGON *polya, POLYGON *polyb) { double right, left; if (polya->npts > 0) left = poly_min((double *)polya->pts, polya->npts); else left = polya->boundbox.xl; if (polyb->npts > 0) right = poly_max((double *)polyb->pts, polyb->npts); else right = polyb->boundbox.xh; return (left > right); } /*------------------------------------------------------- * Is polygon A overlapping or right of polygon B? i.e. is * the right most point of A right of the left most point * of B? *-------------------------------------------------------*/ long poly_overright(POLYGON *polya, POLYGON *polyb) { double right, left; if (polya->npts > 0) right = poly_max((double *)polya->pts, polya->npts); else right = polya->boundbox.xh; if (polyb->npts > 0) left = poly_min((double *)polyb->pts, polyb->npts); else left = polyb->boundbox.xl; return (right > left); } /*------------------------------------------------------- * Is polygon A the same as polygon B? i.e. are all the * points the same? *-------------------------------------------------------*/ long poly_same(POLYGON *polya, POLYGON *polyb) { int i; double *axp, *bxp; /* point to x coordinates for a and b */ if (polya->npts != polyb->npts) return 0; axp = (double *)polya->pts; bxp = (double *)polyb->pts; for (i=0; inpts; axp++, bxp++, i++) { if (*axp != *bxp) return 0; } return 1; } /*----------------------------------------------------------------- * Determine if polygon A overlaps polygon B by determining if * their bounding boxes overlap. *-----------------------------------------------------------------*/ long poly_overlap(POLYGON *polya, POLYGON *polyb) { return box_overlap(&(polya->boundbox), &(polyb->boundbox)); } /*----------------------------------------------------------------- * Determine if polygon A contains polygon B by determining if A's * bounding box contains B's bounding box. *-----------------------------------------------------------------*/ long poly_contain(POLYGON *polya, POLYGON *polyb) { return box_contain(&(polya->boundbox), &(polyb->boundbox)); } /*----------------------------------------------------------------- * Determine if polygon A is contained by polygon B by determining * if A's bounding box is contained by B's bounding box. *-----------------------------------------------------------------*/ long poly_contained(POLYGON *polya, POLYGON *polyb) { return box_contained(&(polya->boundbox), &(polyb->boundbox)); }