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postgresql/src/backend/utils/adt/geo-ops.c

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/*-------------------------------------------------------------------------
*
* geo-ops.c--
* 2D geometric operations
*
* Copyright (c) 1994, Regents of the University of California
*
*
* IDENTIFICATION
* $Header: /cvsroot/pgsql/src/backend/utils/adt/Attic/geo-ops.c,v 1.2 1996/07/22 21:56:01 scrappy Exp $
*
*-------------------------------------------------------------------------
*/
#include <math.h>
#include <float.h> /* faked on sunos */
#include <stdio.h> /* for sprintf proto, etc. */
#include <string.h>
#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, "(%G,%G,%G,%G)",
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", LDELIM,
path->closed, path->npts);
s = buf + strlen(buf);
for (i = 0; i < path->npts; ++i) {
(void) sprintf(tmp, ",%G,%G",
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 = (double)DBL_MAX;
b1.xl = b1.yl = b2.xl = b2.yl = -(double)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, "(%G,%G)", 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 = (double)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)
? (double)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, "(%G,%G,%G,%G)",
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 = (double)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 = (double)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 = (double)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( FPeq (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; i<points; i++,xp++,yp++)
{
*xp = strtod(s, &s);
s++; /* skip delimiter */
*yp = strtod(s, &s);
s++; /* skip delimiter */
}
make_bound_box(poly);
return (poly);
}
/*-------------------------------------------------------------
* poly_pt_count - count the number of points specified in the
* polygon.
*-------------------------------------------------------------*/
long poly_pt_count(char *s, char delim)
{
long total = 0;
if (*s++ != LDELIM) /* no left delimeter */
return (long) -1;
while (*s && (*s != RDELIM))
{
while (*s && (*s != delim))
s++;
total++; /* found one */
if (*s)
s++; /* bump s past the delimiter */
}
/* if there was no right delimiter OR an odd number of points */
if ((*(s-1) != RDELIM) || ((total%2) != 0))
return (long) -1;
return (total/2);
}
/*---------------------------------------------------------------
* poly_out - convert internal POLYGON representation to the
* character string format "(f8,f8,f8,f8,...f8)"
*---------------------------------------------------------------*/
char *poly_out(POLYGON *poly)
{
int i;
double *xp, *yp;
char *output, *outptr;
/*-----------------------------------------------------
* Get enough space for "(f8,f8,f8,f8,...,f8)"
* which P_MAXDIG+1 for each coordinate plus 2
* for parens and 1 for the null
*-----------------------------------------------------*/
output = (char *)PALLOC(2*(P_MAXDIG+1)*poly->npts + 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; i<poly->npts; 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; i<polya->npts; 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));
}
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