/*------------------------------------------------------------------------- * * geo_ops.c-- * 2D geometric operations * * Copyright (c) 1994, Regents of the University of California * * * IDENTIFICATION * $Header: /cvsroot/pgsql/src/backend/utils/adt/geo_ops.c,v 1.4 1997/04/25 18:40:25 scrappy Exp $ * *------------------------------------------------------------------------- */ #include #include #include /* for sprintf proto, etc. */ #include /* for strtod, etc. */ #include #include #include "postgres.h" #include "utils/geo_decls.h" #include "utils/palloc.h" #define OLD_FORMAT_IN 1 #define OLD_FORMAT_OUT 0 /* * Delimiters for input and output strings. * LDELIM, RDELIM, and DELIM are left, right, and separator delimiters, respectively. * LDELIM_EP, RDELIM_EP are left and right delimiters for paths with endpoints. */ #define LDELIM '(' #define RDELIM ')' #define DELIM ',' #define LDELIM_EP '[' #define RDELIM_EP ']' #define LDELIM_C '<' #define RDELIM_C '>' /* Maximum number of output digits printed */ #define P_MAXDIG DBL_DIG #define P_MAXLEN (2*(P_MAXDIG+7)+1) static int digits8 = P_MAXDIG; int geo_precision(int digits); int geo_precision(int digits) { if (digits > P_MAXDIG) { digits8 = P_MAXDIG; } else if (digits > 0) { digits8 = digits; }; return digits8; } /* * Geometric data types are composed of points. * This code tries to support a common format throughout the data types, * to allow for more predictable usage and data type conversion. * The fundamental unit is the point. Other units are line segments, * open paths, boxes, closed paths, and polygons (which should be considered * non-intersecting closed paths). * * Data representation is as follows: * point: (x,y) * line segment: [(x1,y1),(x2,y2)] * box: (x1,y1),(x2,y2) * open path: [(x1,y1),...,(xn,yn)] * closed path: ((x1,y1),...,(xn,yn)) * polygon: ((x1,y1),...,(xn,yn)) * * For boxes, the points are opposite corners with the first point at the top right. * For closed paths and polygons, the points should be reordered to allow * fast and correct equality comparisons. * * XXX perhaps points in complex shapes should be reordered internally * to allow faster internal operations, but should keep track of input order * and restore that order for text output - tgl 97/01/16 */ int pair_decode(char *str, float8 *x, float8 *y, char **s); int pair_encode(float8 x, float8 y, char *str); int pair_count(char *s, char delim); int path_decode(int opentype, int npts, char *str, int *isopen, char **ss, Point *p); char *path_encode( bool closed, int npts, Point *pt); int pair_decode(char *str, float8 *x, float8 *y, char **s) { int has_delim; char *cp; if (!PointerIsValid((char *)str)) return(FALSE); while (isspace( *str)) str++; if ((has_delim = (*str == LDELIM))) str++; while (isspace( *str)) str++; *x = strtod( str, &cp); if (cp <= str) return(FALSE); while (isspace( *cp)) cp++; if (*cp++ != DELIM) return(FALSE); while (isspace( *cp)) cp++; *y = strtod( cp, &str); if (str <= cp) return(FALSE); while (isspace( *str)) str++; if (has_delim) { if (*str != RDELIM) return(FALSE); str++; while (isspace( *str)) str++; }; if (s != NULL) *s = str; return(TRUE); } int pair_encode(float8 x, float8 y, char *str) { (void) sprintf(str, "%.*g,%.*g", digits8, x, digits8, y); return(TRUE); } int path_decode(int opentype, int npts, char *str, int *isopen, char **ss, Point *p) { int depth = 0; char *s, *cp; int i; s = str; while (isspace( *s)) s++; if ((*isopen = (*s == LDELIM_EP))) { /* no open delimiter allowed? */ if (! opentype) return(FALSE); depth++; s++; while (isspace( *s)) s++; } else if (*s == LDELIM) { cp = (s+1); while (isspace( *cp)) cp++; if (*cp == LDELIM) { /* nested delimiters with only one point? */ if (npts <= 1) return(FALSE); depth++; s = cp; } else if (strrchr( s, LDELIM) == s) { depth++; s = cp; }; }; for (i = 0; i < npts; i++) { if (! pair_decode( s, &(p->x), &(p->y), &s)) return(FALSE); if (*s == DELIM) s++; p++; }; while (depth > 0) { if ((*s == RDELIM) || ((*s == RDELIM_EP) && (*isopen) && (depth == 1))) { depth--; s++; while (isspace( *s)) s++; } else { return(FALSE); }; }; *ss = s; return(TRUE); } /* path_decode() */ char *path_encode( bool closed, int npts, Point *pt) { char *result; char *cp; int i; if (!PointerIsValid(result = (char *)PALLOC(npts*(P_MAXLEN+3)+2))) elog(WARN, "Memory allocation failed, can't output path", NULL); cp = result; switch (closed) { case TRUE: *cp++ = LDELIM; break; case FALSE: *cp++ = LDELIM_EP; break; default: break; }; for (i = 0; i < npts; i++) { *cp++ = LDELIM; if (! pair_encode( pt->x, pt->y, cp)) elog (WARN, "Unable to format path", NULL); cp += strlen(cp); *cp++ = RDELIM; *cp++ = DELIM; pt++; }; cp--; switch (closed) { case TRUE: *cp++ = RDELIM; break; case FALSE: *cp++ = RDELIM_EP; break; default: break; }; *cp = '\0'; return(result); } /* path_encode() */ /*------------------------------------------------------------- * pair_count - count the number of points * allow the following notation: * '((1,2),(3,4))' * '(1,3,2,4)' * require an odd number of delim characters in the string *-------------------------------------------------------------*/ int pair_count(char *s, char delim) { int ndelim = 0; while ((s = strchr( s, delim)) != NULL) { ndelim++; s++; }; return((ndelim % 2)? ((ndelim+1)/2): -1); } /*********************************************************************** ** ** Routines for two-dimensional boxes. ** ***********************************************************************/ /*---------------------------------------------------------- * Formatting and conversion routines. *---------------------------------------------------------*/ /* box_in - convert a string to internal form. * * External format: (two corners of box) * "(f8, f8), (f8, f8)" * also supports the older style "(f8, f8, f8, f8)" */ BOX *box_in(char *str) { BOX *box; int isopen; char *s; double x, y; if (!PointerIsValid((char *)str)) elog (WARN," Bad (null) box external representation",NULL); if (!PointerIsValid(box = PALLOCTYPE(BOX))) elog(WARN, "Memory allocation failed, can't input box '%s'",str); if ((! path_decode(FALSE, 2, str, &isopen, &s, &(box->high))) || (*s != '\0')) elog (WARN, "Bad box external representation '%s'",str); /* reorder corners if necessary... */ if (box->high.x < box->low.x) { x = box->high.x; box->high.x = box->low.x; box->low.x = x; }; if (box->high.y < box->low.y) { y = box->high.y; box->high.y = box->low.y; box->low.y = y; }; return(box); } /* box_out - convert a box to external form. */ char *box_out(BOX *box) { #if OLD_FORMAT_OUT char *result; char *cp; #endif if (!PointerIsValid((char *)box)) return(NULL); #if OLD_FORMAT_OUT if (!PointerIsValid(result = (char *)PALLOC(2*(P_MAXLEN+1)+2))) elog(WARN, "Memory allocation failed, can't output box", NULL); cp = result; *cp++ = LDELIM; if (! pair_encode( box->high.x, box->high.y, cp)) elog (WARN, "Unable to format box", NULL); cp += strlen(cp); *cp++ = DELIM; if (! pair_encode( box->low.x, box->low.y, cp)) elog (WARN, "Unable to format box", NULL); cp += strlen(cp); *cp++ = RDELIM; *cp = '\0'; return( result); #else return( path_encode( -1, 2, (Point *) &(box->high))); #endif } /* 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) { if (x1 > x2) { result->high.x = x1; result->low.x = x2; } else { result->high.x = x2; result->low.x = x1; }; if (y1 > y2) { result->high.y = y1; result->low.y = y2; } else { result->high.y = y2; result->low.y = y1; }; 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? */ bool box_same(BOX *box1, BOX *box2) { return((FPeq(box1->high.x,box2->high.x) && FPeq(box1->low.x,box2->low.x)) && (FPeq(box1->high.y,box2->high.y) && FPeq(box1->low.y,box2->low.y))); } /* box_overlap - does box1 overlap box2? */ bool box_overlap(BOX *box1, BOX *box2) { return(((FPge(box1->high.x,box2->high.x) && FPle(box1->low.x,box2->high.x)) || (FPge(box2->high.x,box1->high.x) && FPle(box2->low.x,box1->high.x))) && ((FPge(box1->high.y,box2->high.y) && FPle(box1->low.y,box2->high.y)) || (FPge(box2->high.y,box1->high.y) && FPle(box2->low.y,box1->high.y))) ); } /* 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. */ bool box_overleft(BOX *box1, BOX *box2) { return(FPle(box1->high.x,box2->high.x)); } /* box_left - is box1 strictly left of box2? */ bool box_left(BOX *box1, BOX *box2) { return(FPlt(box1->high.x,box2->low.x)); } /* box_right - is box1 strictly right of box2? */ bool box_right(BOX *box1, BOX *box2) { return(FPgt(box1->low.x,box2->high.x)); } /* 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. */ bool box_overright(BOX *box1, BOX *box2) { return(box1->low.x >= box2->low.x); } /* box_contained - is box1 contained by box2? */ bool box_contained(BOX *box1, BOX *box2) { return((FPle(box1->high.x,box2->high.x) && FPge(box1->low.x,box2->low.x)) && (FPle(box1->high.y,box2->high.y) && FPge(box1->low.y,box2->low.y))); } /* box_contain - does box1 contain box2? */ bool box_contain(BOX *box1, BOX *box2) { return((FPge(box1->high.x,box2->high.x) && FPle(box1->low.x,box2->low.x) && FPge(box1->high.y,box2->high.y) && FPle(box1->low.y,box2->low.y))); } /* box_positionop - * is box1 entirely {above,below} box2? */ bool box_below(BOX *box1, BOX *box2) { return( FPle(box1->high.y,box2->low.y) ); } bool box_above(BOX *box1, BOX *box2) { return( FPge(box1->low.y,box2->high.y) ); } /* box_relop - is area(box1) relop area(box2), within * our accuracy constraint? */ bool box_lt(BOX *box1, BOX *box2) { return( FPlt(box_ar(box1), box_ar(box2)) ); } bool box_gt(BOX *box1, BOX *box2) { return( FPgt(box_ar(box1), box_ar(box2)) ); } bool box_eq(BOX *box1, BOX *box2) { return( FPeq(box_ar(box1), box_ar(box2)) ); } bool box_le(BOX *box1, BOX *box2) { return( FPle(box_ar(box1), box_ar(box2)) ); } bool 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->high.x - box->low.x; return(result); } /* box_height - returns the height of the box * (vertical magnitude). */ double *box_height(BOX *box) { double *result; result = PALLOCTYPE(double); *result = box->high.y - box->low.y; return(result); } /* box_distance - returns the distance between the * center points of two boxes. */ double *box_distance(BOX *box1, BOX *box2) { double *result; Point *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->high.x + box->low.x) / 2.0; result->y = (box->high.y + box->low.y) / 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->high.x - box->low.x ); } /* box_ht - returns the height of the box * (vertical magnitude). */ double box_ht(BOX *box) { return( box->high.y - box->low.y ); } /* box_dt - returns the distance between the * center points of two boxes. */ double box_dt(BOX *box1, BOX *box2) { double result; Point *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; if (! box_overlap(box1,box2)) return(NULL); result = PALLOCTYPE(BOX); result->high.x = Min(box1->high.x, box2->high.x); result->low.x = Max(box1->low.x, box2->low.x); result->high.y = Min(box1->high.y, box2->high.y); result->low.y = Max(box1->low.y, box2->low.y); 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->high.x; p1.y = box->high.y; p2.x = box->low.x; p2.y = box->low.y; 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. *---------------------------------------------------------*/ bool line_intersect(LINE *l1, LINE *l2) { return( ! line_parallel(l1, l2) ); } bool line_parallel(LINE *l1, LINE *l2) { return( FPeq(l1->m, l2->m) ); } bool 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 */ } bool line_vertical(LINE *line) { return( FPeq(line->A, -1.0) && FPzero(line->B) ); } bool line_horizontal(LINE *line) { return( FPzero(line->m) ); } bool 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. ** ***********************************************************************/ /*---------------------------------------------------------- * String to path / path to string conversion. * External format: * "((xcoord, ycoord),... )" * "[(xcoord, ycoord),... ]" * "(xcoord, ycoord),... " * "[xcoord, ycoord,... ]" * Also support older format: * "(closed, npts, xcoord, ycoord,... )" *---------------------------------------------------------*/ PATH *path_in(char *str) { PATH *path; int isopen; char *s; int npts; int size; #if OLD_FORMAT_IN int oldstyle = FALSE; double x, y; #endif if (!PointerIsValid((char *)str)) elog(WARN, "Bad (null) path external representation"); if ((npts = pair_count(str, ',')) <= 0) elog(WARN, "Bad path external representation '%s'", str); #if OLD_FORMAT_IN s = str; while (isspace( *s)) s++; /* identify old style format as having only one left delimiter in string... */ oldstyle = ((*s == LDELIM) && (strrchr( s, LDELIM) == s)); /* old-style format? then first two fields are closed flag and point count... */ if (oldstyle) { s++; if ((! pair_decode( s, &x, &y, &s)) || (*s++ != DELIM) || ((x != 0) && (x != 1)) || (y <= 0)) elog (WARN, "Bad path external representation '%s'",str); isopen = (x == 0); npts = y; }; #endif size = offsetof(PATH, p[0]) + (sizeof(path->p[0]) * npts); if (!PointerIsValid(path = PALLOC(size))) elog(WARN, "Memory allocation failed, can't input path '%s'",str); path->size = size; path->npts = npts; if (oldstyle) path->closed = (! isopen); #if OLD_FORMAT_IN if ((! path_decode(TRUE, npts, s, &isopen, &s, &(path->p[0]))) || ! (oldstyle? (*s++ == RDELIM): (*s == '\0'))) #else if ((! path_decode(TRUE, npts, s, &isopen, &s, &(path->p[0]))) || (*s != '\0')) #endif elog (WARN, "Bad path external representation '%s'",str); #if OLD_FORMAT_IN if (oldstyle) { while (isspace( *s)) s++; if (*s != '\0') elog (WARN, "Bad path external representation '%s'",str); }; #endif if (! oldstyle) path->closed = (! isopen); return(path); } char *path_out(PATH *path) { #if OLD_FORMAT_OUT int i; char *result, *cp; #endif if (!PointerIsValid((char *)path)) return NULL; #if OLD_FORMAT_OUT if (!PointerIsValid(result = (char *)PALLOC(path->npts*(P_MAXLEN+3)+2))) elog(WARN, "Memory allocation failed, can't output path", NULL); cp = result; *cp++ = LDELIM; if (! pair_encode( path->closed, path->npts, cp)) elog (WARN, "Unable to format path", NULL); cp += strlen(cp); for (i=0; inpts; i++) { *cp++ = DELIM; if (! pair_encode( path->p[i].x, path->p[i].y, cp)) elog (WARN, "Unable to format path", NULL); cp += strlen(cp); }; *cp++ = RDELIM; *cp = '\0'; return(result); #else return( path_encode( path->closed, path->npts, (Point *) &(path->p[0]))); #endif } /*---------------------------------------------------------- * Relational operators. * These are based on the path cardinality, * as stupid as that sounds. * * Better relops and access methods coming soon. *---------------------------------------------------------*/ bool path_n_lt(PATH *p1, PATH *p2) { return( (p1->npts < p2->npts ) ); } bool path_n_gt(PATH *p1, PATH *p2) { return( (p1->npts > p2->npts ) ); } bool path_n_eq(PATH *p1, PATH *p2) { return( (p1->npts == p2->npts) ); } bool path_n_le(PATH *p1, PATH *p2) { return( (p1->npts <= p2->npts ) ); } bool path_n_ge(PATH *p1, PATH *p2) { return( (p1->npts >= p2->npts ) ); } /*---------------------------------------------------------- * Conversion operators. *---------------------------------------------------------*/ PATH *path_copy(PATH *path); bool path_isclosed( PATH *path) { if (!PointerIsValid((char *)path)) return FALSE; return(path->closed); } /* path_isclosed() */ bool path_isopen( PATH *path) { if (!PointerIsValid((char *)path)) return FALSE; return(! path->closed); } /* path_isopen() */ int4 path_npoints( PATH *path) { if (!PointerIsValid((char *)path)) return 0; return(path->npts); } /* path_npoints() */ PATH * path_close(PATH *path) { PATH *result; if (PointerIsValid((char *)result = path_copy(path))) result->closed = TRUE; return(result); } /* path_close() */ PATH * path_open(PATH *path) { PATH *result; if (PointerIsValid((char *)result = path_copy(path))) result->closed = FALSE; return(result); } /* path_open() */ PATH * path_copy(PATH *path) { PATH *result; int size; if (!PointerIsValid((char *)path)) return NULL; size = offsetof(PATH, p[0]) + (sizeof(path->p[0]) * path->npts); if (!PointerIsValid(result = PALLOC(size))) elog(WARN, "Memory allocation failed, can't copy path",NULL); memmove((char *) result, (char *) path, size); return(result); } /* path_copy() */ /* 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. */ bool path_inter(PATH *p1, PATH *p2) { BOX b1, b2; int i, j; LSEG seg1, seg2; b1.high.x = b1.low.x = p1->p[0].x; b1.high.y = b1.low.y = p1->p[0].y; for (i = 1; i < p1->npts; i++) { b1.high.x = Max(p1->p[i].x, b1.high.x); b1.high.y = Max(p1->p[i].y, b1.high.y); b1.low.x = Min(p1->p[i].x, b1.low.x); b1.low.y = Min(p1->p[i].y, b1.low.y); } b2.high.x = b2.low.x = p2->p[0].x; b2.high.y = b2.low.y = p2->p[0].y; for (i = 1; i < p2->npts; i++) { b2.high.x = Max(p2->p[i].x, b2.high.x); b2.high.y = Max(p2->p[i].y, b2.high.y); b2.low.x = Min(p2->p[i].x, b2.low.x); b2.low.y = Min(p2->p[i].y, b2.low.y); } 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 = NULL, *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]); tmp = lseg_distance(&seg1, &seg2); if ((min == NULL) || (*min < *tmp)) { if (min != NULL) PFREE(min); min = tmp; } else { 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 format: * "(x,y)" * "x,y" *---------------------------------------------------------*/ Point * point_in(char *str) { Point *point; double x, y; char *s; if (str == NULL) { elog(WARN, "Bad (null) point external representation"); return NULL; } if (! pair_decode( str, &x, &y, &s) || (strlen(s) > 0)) elog (WARN, "Bad point external representation '%s'",str); if (!PointerIsValid(point = PALLOCTYPE(Point))) elog (WARN, "Unable to allocate point storage for '%s'",str); point->x = x; point->y = y; return(point); } /* point_in() */ char * point_out(Point *pt) { if (!PointerIsValid((char *)pt)) return(NULL); return( path_encode( -1, 1, pt)); } /* point_out() */ 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). *---------------------------------------------------------*/ bool point_left(Point *pt1, Point *pt2) { return( FPlt(pt1->x, pt2->x) ); } bool point_right(Point *pt1, Point *pt2) { return( FPgt(pt1->x, pt2->x) ); } bool point_above(Point *pt1, Point *pt2) { return( FPgt(pt1->y, pt2->y) ); } bool point_below(Point *pt1, Point *pt2) { return( FPlt(pt1->y, pt2->y) ); } bool point_vert(Point *pt1, Point *pt2) { return( FPeq( pt1->x, pt2->x ) ); } bool point_horiz(Point *pt1, Point *pt2) { return( FPeq( pt1->y, pt2->y ) ); } bool point_eq(Point *pt1, Point *pt2) { return( point_horiz(pt1, pt2) && point_vert(pt1, pt2) ); } /*---------------------------------------------------------- * "Arithmetic" operators on points. *---------------------------------------------------------*/ int32 pointdist(Point *p1, Point *p2) { int32 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 forms: "[(x1, y1), (x2, y2)]" * "(x1, y1), (x2, y2)" * "x1, y1, x2, y2" * closed form ok "((x1, y1), (x2, y2))" * (old form) "(x1, y1, x2, y2)" *---------------------------------------------------------*/ LSEG *lseg_in(char *str) { LSEG *lseg; int isopen; char *s; if (!PointerIsValid((char *)str)) elog (WARN," Bad (null) lseg external representation",NULL); if (!PointerIsValid(lseg = PALLOCTYPE(LSEG))) elog(WARN, "Memory allocation failed, can't input lseg '%s'",str); if ((! path_decode(TRUE, 2, str, &isopen, &s, &(lseg->p[0]))) || (*s != '\0')) elog (WARN, "Bad lseg external representation '%s'",str); lseg->m = point_sl(&lseg->p[0], &lseg->p[1]); return(lseg); } char *lseg_out(LSEG *ls) { if (!PointerIsValid((char *)ls)) return(NULL); return( path_encode( FALSE, 2, (Point *) &(ls->p[0]))); } /* 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. */ bool lseg_intersect(LSEG *l1, LSEG *l2) { LINE *ln; Point *interpt; bool 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 = TRUE; else retval = FALSE; if (interpt != NULL) PFREE(interpt); PFREE(ln); return(retval); } bool lseg_parallel(LSEG *l1, LSEG *l2) { return( FPeq(l1->m, l2->m) ); } bool 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 */ } bool lseg_vertical(LSEG *lseg) { return( FPeq(lseg->p[0].x, lseg->p[1].x) ); } bool lseg_horizontal(LSEG *lseg) { return( FPeq(lseg->p[0].y, lseg->p[1].y) ); } bool 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 *result; result = PALLOCTYPE(double); *result = lseg_dt( l1, l2); return(result); } /* distance between l1, l2 */ double lseg_dt(LSEG *l1, LSEG *l2) { double *d, result; if (lseg_intersect(l1, l2)) return(0.0); d = dist_ps(&l1->p[0], l2); 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) { /* no points in path? then result is undefined... */ case 0: result = NULL; break; /* one point in path? then get distance between two points... */ case 1: result = point_distance(pt, &path->p[0]); break; default: /* make sure the path makes sense... */ Assert(path->npts > 1); /* * the distance from a point to a path is the smallest distance * from the point to any of its constituent segments. */ 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, *d2; if (inter_sl(lseg, line)) { result = PALLOCTYPE(double); *result = 0.0; } else { result = dist_pl(&lseg->p[0], line); d2 = dist_pl(&lseg->p[1], line); if (*d2 > *result) { PFREE( result); result = d2; } else { PFREE( d2); }; }; 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? */ bool 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. */ bool 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])) ); } bool on_pb(Point *pt, BOX *box) { return( pt->x <= box->high.x && pt->x >= box->low.x && pt->y <= box->high.y && pt->y >= box->low.y ); } /* 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" */ bool 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 */ } bool on_sl(LSEG *lseg, LINE *line) { return( on_pl(&lseg->p[0], line) && on_pl(&lseg->p[1], line) ); } bool 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. *-------------------------------------------------------------------*/ bool inter_sl(LSEG *lseg, LINE *line) { Point *tmp; tmp = interpt_sl(lseg, line); if (tmp) { PFREE(tmp); return(1); } return(0); } /* XXX segment and box should be able to intersect; tgl - 97/01/09 */ bool inter_sb(LSEG *lseg, BOX *box) { return(0); } /* XXX line and box should be able to intersect; tgl - 97/01/09 */ bool 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 *------------------------------------------------------------------*/ /*--------------------------------------------------------------------- * Make the smallest bounding box for the given polygon. *---------------------------------------------------------------------*/ void make_bound_box(POLYGON *poly) { int i; double x1,y1,x2,y2; if (poly->npts > 0) { x2 = x1 = poly->p[0].x; y2 = y1 = poly->p[0].y; for (i = 1; i < poly->npts; i++) { if (poly->p[i].x < x1) x1 = poly->p[i].x; if (poly->p[i].x > x2) x2 = poly->p[i].x; if (poly->p[i].y < y1) y1 = poly->p[i].y; if (poly->p[i].y > y2) y2 = poly->p[i].y; }; box_fill(&(poly->boundbox), x1, x2, y1, y2); } else { elog (WARN, "Unable to create bounding box for empty polygon", NULL); }; } /*------------------------------------------------------------------ * poly_in - read in the polygon from a string specification * * External format: * "((x0,y0),...,(xn,yn))" * "x0,y0,...,xn,yn" * also supports the older style "(x1,...,xn,y1,...yn)" *------------------------------------------------------------------*/ POLYGON *poly_in(char *str) { POLYGON *poly; int npts; int size; int isopen; #if OLD_FORMAT_IN char *s; int oldstyle; int oddcount; int i; double x1, x2; #endif if (!PointerIsValid((char *)str)) elog (WARN," Bad (null) polygon external representation"); if ((npts = pair_count(str, ',')) <= 0) elog(WARN, "Bad polygon external representation '%s'", str); size = offsetof(POLYGON, p[0]) + (sizeof(poly->p[0]) * npts); if (!PointerIsValid(poly = (POLYGON *) PALLOC(size))) elog(WARN, "Memory allocation failed, can't input polygon '%s'",str); memset((char *) poly, 0, size); /* zero any holes */ poly->size = size; poly->npts = npts; #if OLD_FORMAT_IN s = str; while (isspace( *s)) s++; /* identify old style format as having only one left delimiter in string... */ oldstyle = ((*s == LDELIM) && (strrchr( s, LDELIM) == s)); if (oldstyle) { s++; while (isspace( *s)) s++; for (i=0; ip[i*2].x = x1; poly->p[i*2+1].x = x2; }; oddcount = (npts % 2); if (oddcount) { if (! pair_decode( s, &x1, &x2, &s)) elog (WARN, "Bad polygon external representation '%s'",str); if (*s == DELIM) s++; poly->p[npts-1].x = x1; poly->p[0].y = x2; }; for (i=0; ip[i*2+oddcount].y = x1; poly->p[i*2+1+oddcount].y = x2; }; if (*s == RDELIM) { s++; while (isspace( *s)) s++; if (*s != '\0') elog(WARN, "Bad polygon external representation '%s'", str); } else { elog(WARN, "Bad polygon external representation '%s'", str); }; } else { #endif if ((! path_decode(FALSE, npts, str, &isopen, &s, &(poly->p[0]))) || (*s != '\0')) elog (WARN, "Bad polygon external representation '%s'",str); #if OLD_FORMAT_IN }; #endif; make_bound_box(poly); return( poly); } /* poly_in() */ /*--------------------------------------------------------------- * poly_out - convert internal POLYGON representation to the * character string format "((f8,f8),...,(f8,f8))" * also support old format "(f8,f8,...,f8,f8)" *---------------------------------------------------------------*/ char *poly_out(POLYGON *poly) { #if OLD_FORMAT_OUT int i; char *result, *cp; #endif if (!PointerIsValid((char *)poly)) return NULL; #if OLD_FORMAT_OUT if (!PointerIsValid(result = (char *)PALLOC(poly->npts*(P_MAXLEN+3)+2))) elog(WARN, "Memory allocation failed, can't output polygon", NULL); cp = result; *cp++ = LDELIM; for (i=0; inpts; i++) { if (! pair_encode( poly->p[i].x, poly->p[i].y, cp)) elog (WARN, "Unable to format polygon", NULL); cp += strlen(cp); *cp++ = DELIM; }; *(cp-1) = RDELIM; *cp = '\0'; return(result); #else return( path_encode( TRUE, poly->npts, &(poly->p[0]))); #endif } /*------------------------------------------------------- * 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? *-------------------------------------------------------*/ bool poly_left(POLYGON *polya, POLYGON *polyb) { return (polya->boundbox.high.x < polyb->boundbox.low.x); } /*------------------------------------------------------- * 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? *-------------------------------------------------------*/ bool poly_overleft(POLYGON *polya, POLYGON *polyb) { return (polya->boundbox.low.x <= polyb->boundbox.high.x); } /*------------------------------------------------------- * 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? *-------------------------------------------------------*/ bool poly_right(POLYGON *polya, POLYGON *polyb) { return( polya->boundbox.low.x > polyb->boundbox.high.x); } /*------------------------------------------------------- * 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? *-------------------------------------------------------*/ bool poly_overright(POLYGON *polya, POLYGON *polyb) { return( polya->boundbox.high.x > polyb->boundbox.low.x); } /*------------------------------------------------------- * Is polygon A the same as polygon B? i.e. are all the * points the same? *-------------------------------------------------------*/ bool poly_same(POLYGON *polya, POLYGON *polyb) { int i; if (polya->npts != polyb->npts) return FALSE; for (i = 0; i < polya->npts; i++) { if ((polya->p[i].x != polyb->p[i].x) || (polya->p[i].y != polyb->p[i].y)) return FALSE; }; return TRUE; } /*----------------------------------------------------------------- * Determine if polygon A overlaps polygon B by determining if * their bounding boxes overlap. *-----------------------------------------------------------------*/ bool 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. *-----------------------------------------------------------------*/ bool 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. *-----------------------------------------------------------------*/ bool poly_contained(POLYGON *polya, POLYGON *polyb) { return box_contained(&(polya->boundbox), &(polyb->boundbox)); } /*********************************************************************** ** ** Routines for 2D points. ** ***********************************************************************/ Point * point(float8 *x, float8 *y) { if (! (PointerIsValid(x) && PointerIsValid(y))) return(NULL); return(point_construct(*x, *y)); } /* point() */ Point * point_add(Point *p1, Point *p2) { Point *result; if (! (PointerIsValid(p1) && PointerIsValid(p2))) return(NULL); if (!PointerIsValid(result = PALLOCTYPE(Point))) elog(WARN, "Memory allocation failed, can't add points",NULL); result->x = (p1->x + p2->x); result->y = (p1->y + p2->y); return(result); } /* point_add() */ Point * point_sub(Point *p1, Point *p2) { Point *result; if (! (PointerIsValid(p1) && PointerIsValid(p2))) return(NULL); if (!PointerIsValid(result = PALLOCTYPE(Point))) elog(WARN, "Memory allocation failed, can't add points",NULL); result->x = (p1->x - p2->x); result->y = (p1->y - p2->y); return(result); } /* point_sub() */ Point * point_mul(Point *p1, Point *p2) { Point *result; if (! (PointerIsValid(p1) && PointerIsValid(p2))) return(NULL); if (!PointerIsValid(result = PALLOCTYPE(Point))) elog(WARN, "Memory allocation failed, can't multiply points",NULL); result->x = (p1->x*p2->x) - (p1->y*p2->y); result->y = (p1->x*p2->y) + (p1->y*p2->x); return(result); } /* point_mul() */ Point * point_div(Point *p1, Point *p2) { Point *result; double div; if (! (PointerIsValid(p1) && PointerIsValid(p2))) return(NULL); if (!PointerIsValid(result = PALLOCTYPE(Point))) elog(WARN, "Memory allocation failed, can't multiply path",NULL); div = (p2->x*p2->x) + (p2->y*p2->y); result->x = ((p1->x*p2->x) + (p1->y*p2->y)) / div; result->y = ((p2->x*p1->y) - (p2->y*p1->x)) / div; return(result); } /* point_div() */ /*********************************************************************** ** ** Routines for 2D boxes. ** ***********************************************************************/ BOX * box(Point *p1, Point *p2) { BOX *result; if (! (PointerIsValid(p1) && PointerIsValid(p2))) return(NULL); result = box_construct( p1->x, p2->x, p1->y, p2->y); return(result); } /* box() */ BOX * box_add(BOX *box, Point *p) { BOX *result; if (! (PointerIsValid(box) && PointerIsValid(p))) return(NULL); result = box_construct( (box->high.x + p->x), (box->low.x + p->x), (box->high.y + p->y), (box->low.y + p->y)); return(result); } /* box_add() */ BOX * box_sub(BOX *box, Point *p) { BOX *result; if (! (PointerIsValid(box) && PointerIsValid(p))) return(NULL); result = box_construct( (box->high.x - p->x), (box->low.x - p->x), (box->high.y - p->y), (box->low.y - p->y)); return(result); } /* box_sub() */ BOX * box_mul(BOX *box, Point *p) { BOX *result; Point *high, *low; if (! (PointerIsValid(box) && PointerIsValid(p))) return(NULL); high = point_mul( &box->high, p); low = point_mul( &box->low, p); result = box_construct( high->x, low->x, high->y, low->y); PFREE( high); PFREE( low); return(result); } /* box_mul() */ BOX * box_div(BOX *box, Point *p) { BOX *result; Point *high, *low; if (! (PointerIsValid(box) && PointerIsValid(p))) return(NULL); high = point_div( &box->high, p); low = point_div( &box->low, p); result = box_construct( high->x, low->x, high->y, low->y); PFREE( high); PFREE( low); return(result); } /* box_div() */ /*********************************************************************** ** ** 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. ** ***********************************************************************/ /*********************************************************************** ** ** Routines for 2D paths. ** ***********************************************************************/ POLYGON *path_poly(PATH *path); /* path_add() * Concatenate two paths (only if they are both open). */ PATH * path_add(PATH *p1, PATH *p2) { PATH *result; int size; int i; if (! (PointerIsValid(p1) && PointerIsValid(p2)) || p1->closed || p2->closed) return(NULL); size = offsetof(PATH, p[0]) + (sizeof(p1->p[0]) * (p1->npts+p2->npts)); if (!PointerIsValid(result = PALLOC(size))) elog(WARN, "Memory allocation failed, can't add paths",NULL); result->size = size; result->npts = (p1->npts+p2->npts); result->closed = p1->closed; for (i=0; inpts; i++) { result->p[i].x = p1->p[i].x; result->p[i].y = p1->p[i].y; }; for (i=0; inpts; i++) { result->p[i+p1->npts].x = p2->p[i].x; result->p[i+p1->npts].y = p2->p[i].y; }; return(result); } /* path_add() */ /* path_add_pt() * Translation operator. */ PATH * path_add_pt(PATH *path, Point *point) { PATH *result; int i; if (! (PointerIsValid(path) && PointerIsValid(point))) return(NULL); if (! PointerIsValid(result = path_copy(path))) elog(WARN, "Memory allocation failed, can't add path",NULL); for (i=0; inpts; i++) { result->p[i].x += point->x; result->p[i].y += point->y; }; return(result); } /* path_add_pt() */ PATH * path_sub_pt(PATH *path, Point *point) { PATH *result; int i; if (! (PointerIsValid(path) && PointerIsValid(point))) return(NULL); if (! PointerIsValid(result = path_copy(path))) elog(WARN, "Memory allocation failed, can't subtract path",NULL); for (i=0; inpts; i++) { result->p[i].x -= point->x; result->p[i].y -= point->y; }; return(result); } /* path_sub_pt() */ /* path_mul_pt() * Rotation and scaling operators. */ PATH * path_mul_pt(PATH *path, Point *point) { PATH *result; Point *p; int i; if (! (PointerIsValid(path) && PointerIsValid(point))) return(NULL); if (! PointerIsValid(result = path_copy(path))) elog(WARN, "Memory allocation failed, can't multiply path",NULL); for (i=0; inpts; i++) { p = point_mul( &path->p[i], point); result->p[i].x = p->x; result->p[i].y = p->y; PFREE(p); }; return(result); } /* path_mul_pt() */ PATH * path_div_pt(PATH *path, Point *point) { PATH *result; Point *p; int i; if (! (PointerIsValid(path) && PointerIsValid(point))) return(NULL); if (! PointerIsValid(result = path_copy(path))) elog(WARN, "Memory allocation failed, can't divide path",NULL); for (i=0; inpts; i++) { p = point_div( &path->p[i], point); result->p[i].x = p->x; result->p[i].y = p->y; PFREE(p); }; return(result); } /* path_div_pt() */ POLYGON *path_poly(PATH *path) { POLYGON *poly; int size; int i; if (!PointerIsValid(path)) return(NULL); if (!path->closed) elog(WARN, "Open path cannot be converted to polygon",NULL); size = offsetof(POLYGON, p[0]) + (sizeof(poly->p[0]) * path->npts); if (!PointerIsValid(poly = PALLOC(size))) elog(WARN, "Memory allocation failed, can't convert path to polygon",NULL); poly->size = size; poly->npts = path->npts; for (i=0; inpts; i++) { poly->p[i].x = path->p[i].x; poly->p[i].y = path->p[i].y; }; make_bound_box(poly); return(poly); } /* path_polygon() */ /*********************************************************************** ** ** Routines for 2D polygons. ** ***********************************************************************/ int4 poly_npoints( POLYGON *poly) { if (!PointerIsValid(poly)) return(0); return(poly->npts); } /* poly_npoints() */ BOX * poly_box(POLYGON *poly) { BOX *box; if (!PointerIsValid(poly) || (poly->npts < 1)) return(NULL); box = box_copy( &poly->boundbox); return(box); } /* poly_box() */ POLYGON * box_poly(BOX *box) { POLYGON *poly; int size; if (!PointerIsValid(box)) return(NULL); size = offsetof(POLYGON, p[0]) + (sizeof(poly->p[0]) * 4); if (!PointerIsValid(poly = PALLOC(size))) elog(WARN, "Memory allocation failed, can't convert box to polygon",NULL); poly->size = size; poly->npts = 4; poly->p[0].x = box->low.x; poly->p[0].y = box->low.y; poly->p[1].x = box->low.x; poly->p[1].y = box->high.y; poly->p[2].x = box->high.x; poly->p[2].y = box->high.y; poly->p[3].x = box->high.x; poly->p[3].y = box->low.y; box_fill( &poly->boundbox, box->high.x, box->low.x, box->high.y, box->low.y); return(poly); } /* box_poly() */ PATH * poly_path(POLYGON *poly) { PATH *path; int size; int i; if (!PointerIsValid(poly) || (poly->npts < 0)) return(NULL); size = offsetof(PATH, p[0]) + (sizeof(path->p[0]) * poly->npts); if (!PointerIsValid(path = PALLOC(size))) elog(WARN, "Memory allocation failed, can't convert polygon to path",NULL); path->size = size; path->npts = poly->npts; path->closed = TRUE; for (i=0; inpts; i++) { path->p[i].x = poly->p[i].x; path->p[i].y = poly->p[i].y; }; return(path); } /* poly_path() */ /*------------------------------------------------------------------------- * * circle.c-- * 2D geometric operations * * Copyright (c) 1994, Regents of the University of California * * * IDENTIFICATION * $Header: /cvsroot/pgsql/src/backend/utils/adt/geo_ops.c,v 1.4 1997/04/25 18:40:25 scrappy Exp $ * *------------------------------------------------------------------------- */ #ifndef PI #define PI 3.1415926536 #endif int single_decode(char *str, float8 *x, char **ss); int single_encode(float8 x, char *str); int single_decode(char *str, float8 *x, char **s) { char *cp; if (!PointerIsValid(str)) return(FALSE); while (isspace( *str)) str++; *x = strtod( str, &cp); #ifdef GEODEBUG fprintf( stderr, "single_decode- (%x) try decoding %s to %g\n", (cp-str), str, *x); #endif if (cp <= str) return(FALSE); while (isspace( *cp)) cp++; if (s != NULL) *s = cp; return(TRUE); } int single_encode(float8 x, char *str) { (void) sprintf(str, "%.*g", digits8, x); return(TRUE); } /*********************************************************************** ** ** Routines for circles. ** ***********************************************************************/ /*---------------------------------------------------------- * Formatting and conversion routines. *---------------------------------------------------------*/ /* circle_in - convert a string to internal form. * * External format: (center and radius of circle) * "((f8,f8))" * also supports quick entry style "(f8,f8,f8)" */ CIRCLE *circle_in(char *str) { CIRCLE *circle; char *s, *cp; int depth = 0; if (!PointerIsValid(str)) elog (WARN," Bad (null) circle external representation",NULL); if (!PointerIsValid(circle = PALLOCTYPE(CIRCLE))) elog(WARN, "Memory allocation failed, can't input circle '%s'",str); s = str; while (isspace( *s)) s++; if ((*s == LDELIM_C) || (*s == LDELIM)) { depth++; cp = (s+1); while (isspace( *cp)) cp++; if (*cp == LDELIM) { s = cp; }; }; if (! pair_decode( s, &circle->center.x, &circle->center.y, &s)) elog (WARN, "Bad circle external representation '%s'",str); if (*s == DELIM) s++; while (isspace( *s)) s++; if (! single_decode( s, &circle->radius, &s)) elog (WARN, "Bad circle external representation '%s'",str); while (depth > 0) { if ((*s == RDELIM) || ((*s == RDELIM_C) && (depth == 1))) { depth--; s++; while (isspace( *s)) s++; } else { elog (WARN, "Bad circle external representation '%s'",str); }; }; if (*s != '\0') elog (WARN, "Bad circle external representation '%s'",str); return(circle); } /* circle_in() */ /* circle_out - convert a circle to external form. */ char *circle_out(CIRCLE *circle) { char *result; char *cp; if (!PointerIsValid(circle)) return(NULL); if (!PointerIsValid(result = (char *)PALLOC(3*(P_MAXLEN+1)+3))) elog(WARN, "Memory allocation failed, can't output circle", NULL); cp = result; *cp++ = LDELIM_C; *cp++ = LDELIM; if (! pair_encode( circle->center.x, circle->center.y, cp)) elog (WARN, "Unable to format circle", NULL); cp += strlen(cp); *cp++ = RDELIM; *cp++ = DELIM; if (! single_encode( circle->radius, cp)) elog (WARN, "Unable to format circle", NULL); cp += strlen(cp); *cp++ = RDELIM_C; *cp = '\0'; return(result); } /* circle_out() */ /*---------------------------------------------------------- * Relational operators for CIRCLEs. * <, >, <=, >=, and == are based on circle area. *---------------------------------------------------------*/ /* circles identical? */ bool circle_same(CIRCLE *circle1, CIRCLE *circle2) { return( FPeq(circle1->radius,circle2->radius) && FPeq(circle1->center.x,circle2->center.x) && FPeq(circle1->center.y,circle2->center.y)); } /* circle_overlap - does circle1 overlap circle2? */ bool circle_overlap(CIRCLE *circle1, CIRCLE *circle2) { return( FPle(point_dt(&circle1->center,&circle2->center),(circle1->radius+circle2->radius))); } /* circle_overleft - is the right edge of circle1 to the left of * the right edge of circle2? */ bool circle_overleft(CIRCLE *circle1, CIRCLE *circle2) { return( FPle((circle1->center.x+circle1->radius),(circle2->center.x+circle2->radius))); } /* circle_left - is circle1 strictly left of circle2? */ bool circle_left(CIRCLE *circle1, CIRCLE *circle2) { return( FPle((circle1->center.x+circle1->radius),(circle2->center.x-circle2->radius))); } /* circle_right - is circle1 strictly right of circle2? */ bool circle_right(CIRCLE *circle1, CIRCLE *circle2) { return( FPge((circle1->center.x-circle1->radius),(circle2->center.x+circle2->radius))); } /* circle_overright - is the left edge of circle1 to the right of * the left edge of circle2? */ bool circle_overright(CIRCLE *circle1, CIRCLE *circle2) { return( FPge((circle1->center.x-circle1->radius),(circle2->center.x-circle2->radius))); } /* circle_contained - is circle1 contained by circle2? */ bool circle_contained(CIRCLE *circle1, CIRCLE *circle2) { return( FPle((point_dt(&circle1->center,&circle2->center)+circle1->radius),circle2->radius)); } /* circle_contain - does circle1 contain circle2? */ bool circle_contain(CIRCLE *circle1, CIRCLE *circle2) { return( FPle((point_dt(&circle1->center,&circle2->center)+circle2->radius),circle1->radius)); } /* circle_positionop - * is circle1 entirely {above,below} circle2? */ bool circle_below(CIRCLE *circle1, CIRCLE *circle2) { return( FPle((circle1->center.y+circle1->radius),(circle2->center.y-circle2->radius))); } bool circle_above(CIRCLE *circle1, CIRCLE *circle2) { return( FPge((circle1->center.y-circle1->radius),(circle2->center.y+circle2->radius))); } /* circle_relop - is area(circle1) relop area(circle2), within * our accuracy constraint? */ bool circle_eq(CIRCLE *circle1, CIRCLE *circle2) { return( FPeq(circle_ar(circle1), circle_ar(circle2)) ); } /* circle_eq() */ bool circle_ne(CIRCLE *circle1, CIRCLE *circle2) { return( !circle_eq(circle1, circle2)); } /* circle_ne() */ bool circle_lt(CIRCLE *circle1, CIRCLE *circle2) { return( FPlt(circle_ar(circle1), circle_ar(circle2)) ); } /* circle_lt() */ bool circle_gt(CIRCLE *circle1, CIRCLE *circle2) { return( FPgt(circle_ar(circle1), circle_ar(circle2)) ); } /* circle_gt() */ bool circle_le(CIRCLE *circle1, CIRCLE *circle2) { return( FPle(circle_ar(circle1), circle_ar(circle2)) ); } /* circle_le() */ bool circle_ge(CIRCLE *circle1, CIRCLE *circle2) { return( FPge(circle_ar(circle1), circle_ar(circle2)) ); } /* circle_ge() */ /*---------------------------------------------------------- * "Arithmetic" operators on circles. * circle_foo returns foo as an object (pointer) that can be passed between languages. * circle_xx is an internal routine which returns the * actual value. *---------------------------------------------------------*/ CIRCLE *circle_copy(CIRCLE *circle); CIRCLE * circle_copy(CIRCLE *circle) { CIRCLE *result; if (!PointerIsValid(circle)) return NULL; if (!PointerIsValid(result = PALLOCTYPE(CIRCLE))) elog(WARN, "Memory allocation failed, can't copy circle",NULL); memmove((char *) result, (char *) circle, sizeof(CIRCLE)); return(result); } /* circle_copy() */ /* circle_add_pt() * Translation operator. */ CIRCLE * circle_add_pt(CIRCLE *circle, Point *point) { CIRCLE *result; if (!PointerIsValid(circle) && !PointerIsValid(point)) return(NULL); if (! PointerIsValid(result = circle_copy(circle))) elog(WARN, "Memory allocation failed, can't add circle",NULL); result->center.x += point->x; result->center.y += point->y; return(result); } /* circle_add_pt() */ CIRCLE * circle_sub_pt(CIRCLE *circle, Point *point) { CIRCLE *result; if (!PointerIsValid(circle) && !PointerIsValid(point)) return(NULL); if (! PointerIsValid(result = circle_copy(circle))) elog(WARN, "Memory allocation failed, can't subtract circle",NULL); result->center.x -= point->x; result->center.y -= point->y; return(result); } /* circle_sub_pt() */ /* circle_mul_pt() * Rotation and scaling operators. */ CIRCLE * circle_mul_pt(CIRCLE *circle, Point *point) { CIRCLE *result; Point *p; if (!PointerIsValid(circle) && !PointerIsValid(point)) return(NULL); if (! PointerIsValid(result = circle_copy(circle))) elog(WARN, "Memory allocation failed, can't multiply circle",NULL); p = point_mul( &circle->center, point); result->center.x = p->x; result->center.y = p->y; PFREE(p); result->radius *= HYPOT( point->x, point->y); return(result); } /* circle_mul_pt() */ CIRCLE * circle_div_pt(CIRCLE *circle, Point *point) { CIRCLE *result; Point *p; if (!PointerIsValid(circle) && !PointerIsValid(point)) return(NULL); if (! PointerIsValid(result = circle_copy(circle))) elog(WARN, "Memory allocation failed, can't add circle",NULL); p = point_div( &circle->center, point); result->center.x = p->x; result->center.y = p->y; PFREE(p); result->radius /= HYPOT( point->x, point->y); return(result); } /* circle_div_pt() */ /* circle_area - returns the area of the circle. */ double *circle_area(CIRCLE *circle) { double *result; result = PALLOCTYPE(double); *result = circle_ar(circle); return(result); } /* circle_diameter - returns the diameter of the circle. */ double *circle_diameter(CIRCLE *circle) { double *result; result = PALLOCTYPE(double); *result = (2*circle->radius); return(result); } /* circle_radius - returns the radius of the circle. */ double *circle_radius(CIRCLE *circle) { double *result; result = PALLOCTYPE(double); *result = circle->radius; return(result); } /* circle_distance - returns the distance between * two circles. */ double *circle_distance(CIRCLE *circle1, CIRCLE *circle2) { double *result; result = PALLOCTYPE(double); *result = (point_dt(&circle1->center,&circle2->center) - (circle1->radius + circle2->radius)); if (*result < 0) *result = 0; return(result); } /* circle_distance() */ /* dist_pc - returns the distance between * a point and a circle. */ double *dist_pc(Point *point, CIRCLE *circle) { double *result; result = PALLOCTYPE(double); *result = (point_dt(point,&circle->center) - circle->radius); if (*result < 0) *result = 0; return(result); } /* dist_pc() */ /* circle_center - returns the center point of the circle. */ Point *circle_center(CIRCLE *circle) { Point *result; result = PALLOCTYPE(Point); result->x = circle->center.x; result->y = circle->center.y; return(result); } /* circle_ar - returns the area of the circle. */ double circle_ar(CIRCLE *circle) { return(PI*(circle->radius*circle->radius)); } /* circle_dt - returns the distance between the * center points of two circlees. */ double circle_dt(CIRCLE *circle1, CIRCLE *circle2) { double result; result = point_dt(&circle1->center,&circle2->center); return(result); } /*---------------------------------------------------------- * Conversion operators. *---------------------------------------------------------*/ CIRCLE *circle(Point *center, float8 *radius) { CIRCLE *result; if (! (PointerIsValid(center) && PointerIsValid(radius))) return(NULL); if (!PointerIsValid(result = PALLOCTYPE(CIRCLE))) elog(WARN, "Memory allocation failed, can't convert point to circle",NULL); result->center.x = center->x; result->center.y = center->y; result->radius = *radius; return(result); } POLYGON *circle_poly(int npts, CIRCLE *circle) { POLYGON *poly; int size; int i; double angle; if (!PointerIsValid(circle)) return(NULL); if (FPzero(circle->radius) || (npts <= 2)) elog (WARN, "Unable to convert circle to polygon", NULL); size = offsetof(POLYGON, p[0]) + (sizeof(poly->p[0]) * npts); if (!PointerIsValid(poly = (POLYGON *) PALLOC(size))) elog(WARN, "Memory allocation failed, can't convert circle to polygon",NULL); memset((char *) poly, 0, size); /* zero any holes */ poly->size = size; poly->npts = npts; for (i=0;ip[i].x = circle->center.x - (circle->radius*cos(angle)); poly->p[i].y = circle->center.y + (circle->radius*sin(angle)); }; make_bound_box(poly); return(poly); } /* poly_circle - convert polygon to circle * * XXX This algorithm should use weighted means of line segments * rather than straight average values of points - tgl 97/01/21. */ CIRCLE *poly_circle(POLYGON *poly) { CIRCLE *circle; int i; if (!PointerIsValid(poly)) return(NULL); if (poly->npts <= 2) elog (WARN, "Unable to convert polygon to circle", NULL); if (!PointerIsValid(circle = PALLOCTYPE(CIRCLE))) elog(WARN, "Memory allocation failed, can't convert polygon to circle",NULL); circle->center.x = 0; circle->center.y = 0; circle->radius = 0; for (i=0;inpts;i++) { circle->center.x += poly->p[i].x; circle->center.y += poly->p[i].y; }; circle->center.x /= poly->npts; circle->center.y /= poly->npts; for (i=0;inpts;i++) { circle->radius += point_dt( &poly->p[i], &circle->center); }; circle->radius /= poly->npts; if (FPzero(circle->radius)) elog (WARN, "Unable to convert polygon to circle", NULL); return(circle); }