postgis/liblwgeom/lwalgorithm.c
2014-01-29 17:49:35 +00:00

884 lines
19 KiB
C

/**********************************************************************
* $Id$
*
* PostGIS - Spatial Types for PostgreSQL
* http://postgis.net
* Copyright 2008 Paul Ramsey
*
* This is free software; you can redistribute and/or modify it under
* the terms of the GNU General Public Licence. See the COPYING file.
*
**********************************************************************/
#include "liblwgeom_internal.h"
#include "lwgeom_log.h"
#include <ctype.h> /* for tolower */
/**
* Returns -1 if n < 0.0 and 1 if n > 0.0
*/
int signum(double n)
{
if( n < 0 ) return -1;
if( n > 0 ) return 1;
return 0;
}
int
p4d_same(const POINT4D *p1, const POINT4D *p2)
{
if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) && FP_EQUALS(p1->z,p2->z) && FP_EQUALS(p1->m,p2->m) )
return LW_TRUE;
else
return LW_FALSE;
}
int
p3d_same(const POINT3D *p1, const POINT3D *p2)
{
if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) && FP_EQUALS(p1->z,p2->z) )
return LW_TRUE;
else
return LW_FALSE;
}
int
p2d_same(const POINT2D *p1, const POINT2D *p2)
{
if( FP_EQUALS(p1->x,p2->x) && FP_EQUALS(p1->y,p2->y) )
return LW_TRUE;
else
return LW_FALSE;
}
/**
* lw_segment_side()
*
* Return -1 if point Q is left of segment P
* Return 1 if point Q is right of segment P
* Return 0 if point Q in on segment P
*/
int lw_segment_side(const POINT2D *p1, const POINT2D *p2, const POINT2D *q)
{
double side = ( (q->x - p1->x) * (p2->y - p1->y) - (p2->x - p1->x) * (q->y - p1->y) );
if ( side == 0.0 )
return 0;
else
return signum(side);
}
/**
* Returns the length of a linear segment
*/
double
lw_seg_length(const POINT2D *A1, const POINT2D *A2)
{
return sqrt((A1->x-A2->x)*(A1->x-A2->x)+(A1->y-A2->y)*(A1->y-A2->y));
}
/**
* Returns true if P is on the same side of the plane partition
* defined by A1/A3 as A2 is. Only makes sense if P has already been
* determined to be on the circle defined by A1/A2/A3.
*/
int
lw_pt_in_arc(const POINT2D *P, const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
return lw_segment_side(A1, A3, A2) == lw_segment_side(A1, A3, P);
}
/**
* Returns true if P is between A1/A2. Only makes sense if P has already been
* deterined to be on the line defined by A1/A2.
*/
int
lw_pt_in_seg(const POINT2D *P, const POINT2D *A1, const POINT2D *A2)
{
return ((A1->x <= P->x && P->x < A2->x) || (A1->x >= P->x && P->x > A2->x)) ||
((A1->y <= P->y && P->y < A2->y) || (A1->y >= P->y && P->y > A2->y));
}
/**
* Returns true if arc A is actually a point (all vertices are the same) .
*/
int
lw_arc_is_pt(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
if ( A1->x == A2->x && A2->x == A3->x &&
A1->y == A2->y && A2->y == A3->y )
return LW_TRUE;
else
return LW_FALSE;
}
/**
* Returns the length of a circular arc segment
*/
double
lw_arc_length(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3)
{
POINT2D C;
double radius_A, circumference_A;
int a2_side, clockwise;
double a1, a3;
double angle;
if ( lw_arc_is_pt(A1, A2, A3) )
return 0.0;
radius_A = lw_arc_center(A1, A2, A3, &C);
/* Co-linear! Return linear distance! */
if ( radius_A < 0 )
{
double dx = A1->x - A3->x;
double dy = A1->y - A3->y;
return sqrt(dx*dx + dy*dy);
}
/* Closed circle! Return the circumference! */
circumference_A = M_PI * 2 * radius_A;
if ( p2d_same(A1, A3) )
return circumference_A;
/* Determine the orientation of the arc */
a2_side = lw_segment_side(A1, A3, A2);
/* The side of the A1/A3 line that A2 falls on dictates the sweep
direction from A1 to A3. */
if ( a2_side == -1 )
clockwise = LW_TRUE;
else
clockwise = LW_FALSE;
/* Angles of each point that defines the arc section */
a1 = atan2(A1->y - C.y, A1->x - C.x);
a3 = atan2(A3->y - C.y, A3->x - C.x);
/* What's the sweep from A1 to A3? */
if ( clockwise )
{
if ( a1 > a3 )
angle = a1 - a3;
else
angle = 2*M_PI + a1 - a3;
}
else
{
if ( a3 > a1 )
angle = a3 - a1;
else
angle = 2*M_PI + a3 - a1;
}
/* Length as proportion of circumference */
return circumference_A * (angle / (2*M_PI));
}
int lw_arc_side(const POINT2D *A1, const POINT2D *A2, const POINT2D *A3, const POINT2D *Q)
{
POINT2D C;
double radius_A;
double side_Q, side_A2;
double d;
side_Q = lw_segment_side(A1, A3, Q);
radius_A = lw_arc_center(A1, A2, A3, &C);
side_A2 = lw_segment_side(A1, A3, A2);
/* Linear case */
if ( radius_A < 0 )
return side_Q;
d = distance2d_pt_pt(Q, &C);
/* Q is on the arc boundary */
if ( d == radius_A && side_Q == side_A2 )
{
return 0;
}
/* Q on A1-A3 line, so its on opposite side to A2 */
if ( side_Q == 0 )
{
return -1 * side_A2;
}
/*
* Q is inside the arc boundary, so it's not on the side we
* might think from examining only the end points
*/
if ( d < radius_A && side_Q == side_A2 )
{
side_Q *= -1;
}
return side_Q;
}
/**
* Determines the center of the circle defined by the three given points.
* In the event the circle is complete, the midpoint of the segment defined
* by the first and second points is returned. If the points are colinear,
* as determined by equal slopes, then NULL is returned. If the interior
* point is coincident with either end point, they are taken as colinear.
*/
double
lw_arc_center(const POINT2D *p1, const POINT2D *p2, const POINT2D *p3, POINT2D *result)
{
POINT2D c;
double cx, cy, cr;
double temp, bc, cd, det;
c.x = c.y = 0.0;
LWDEBUGF(2, "lw_arc_center called (%.16f,%.16f), (%.16f,%.16f), (%.16f,%.16f).", p1->x, p1->y, p2->x, p2->y, p3->x, p3->y);
/* Closed circle */
if (fabs(p1->x - p3->x) < EPSILON_SQLMM &&
fabs(p1->y - p3->y) < EPSILON_SQLMM)
{
cx = p1->x + (p2->x - p1->x) / 2.0;
cy = p1->y + (p2->y - p1->y) / 2.0;
c.x = cx;
c.y = cy;
*result = c;
cr = sqrt(pow(cx - p1->x, 2.0) + pow(cy - p1->y, 2.0));
return cr;
}
temp = p2->x*p2->x + p2->y*p2->y;
bc = (p1->x*p1->x + p1->y*p1->y - temp) / 2.0;
cd = (temp - p3->x*p3->x - p3->y*p3->y) / 2.0;
det = (p1->x - p2->x)*(p2->y - p3->y)-(p2->x - p3->x)*(p1->y - p2->y);
/* Check colinearity */
if (fabs(det) < EPSILON_SQLMM)
return -1.0;
det = 1.0 / det;
cx = (bc*(p2->y - p3->y)-cd*(p1->y - p2->y))*det;
cy = ((p1->x - p2->x)*cd-(p2->x - p3->x)*bc)*det;
c.x = cx;
c.y = cy;
*result = c;
cr = sqrt((cx-p1->x)*(cx-p1->x)+(cy-p1->y)*(cy-p1->y));
LWDEBUGF(2, "lw_arc_center center is (%.16f,%.16f)", result->x, result->y);
return cr;
}
int
pt_in_ring_2d(const POINT2D *p, const POINTARRAY *ring)
{
int cn = 0; /* the crossing number counter */
int i;
POINT2D v1, v2;
POINT2D first, last;
getPoint2d_p(ring, 0, &first);
getPoint2d_p(ring, ring->npoints-1, &last);
if ( memcmp(&first, &last, sizeof(POINT2D)) )
{
lwerror("pt_in_ring_2d: V[n] != V[0] (%g %g != %g %g)",
first.x, first.y, last.x, last.y);
return LW_FALSE;
}
LWDEBUGF(2, "pt_in_ring_2d called with point: %g %g", p->x, p->y);
/* printPA(ring); */
/* loop through all edges of the polygon */
getPoint2d_p(ring, 0, &v1);
for (i=0; i<ring->npoints-1; i++)
{
double vt;
getPoint2d_p(ring, i+1, &v2);
/* edge from vertex i to vertex i+1 */
if
(
/* an upward crossing */
((v1.y <= p->y) && (v2.y > p->y))
/* a downward crossing */
|| ((v1.y > p->y) && (v2.y <= p->y))
)
{
vt = (double)(p->y - v1.y) / (v2.y - v1.y);
/* P.x <intersect */
if (p->x < v1.x + vt * (v2.x - v1.x))
{
/* a valid crossing of y=p.y right of p.x */
++cn;
}
}
v1 = v2;
}
LWDEBUGF(3, "pt_in_ring_2d returning %d", cn&1);
return (cn&1); /* 0 if even (out), and 1 if odd (in) */
}
static int
lw_seg_interact(const POINT2D *p1, const POINT2D *p2, const POINT2D *q1, const POINT2D *q2)
{
double minq=FP_MIN(q1->x,q2->x);
double maxq=FP_MAX(q1->x,q2->x);
double minp=FP_MIN(p1->x,p2->x);
double maxp=FP_MAX(p1->x,p2->x);
if (FP_GT(minp,maxq) || FP_LT(maxp,minq))
return LW_FALSE;
minq=FP_MIN(q1->y,q2->y);
maxq=FP_MAX(q1->y,q2->y);
minp=FP_MIN(p1->y,p2->y);
maxp=FP_MAX(p1->y,p2->y);
if (FP_GT(minp,maxq) || FP_LT(maxp,minq))
return LW_FALSE;
return LW_TRUE;
}
/**
** @brief returns the kind of #CG_SEGMENT_INTERSECTION_TYPE behavior of lineseg 1 (constructed from p1 and p2) and lineseg 2 (constructed from q1 and q2)
** @param p1 start point of first straight linesegment
** @param p2 end point of first straight linesegment
** @param q1 start point of second line segment
** @param q2 end point of second line segment
** @return a #CG_SEGMENT_INTERSECTION_TYPE
** Returns one of
** SEG_ERROR = -1,
** SEG_NO_INTERSECTION = 0,
** SEG_COLINEAR = 1,
** SEG_CROSS_LEFT = 2,
** SEG_CROSS_RIGHT = 3,
*/
int lw_segment_intersects(const POINT2D *p1, const POINT2D *p2, const POINT2D *q1, const POINT2D *q2)
{
int pq1, pq2, qp1, qp2;
/* No envelope interaction => we are done. */
if (!lw_seg_interact(p1, p2, q1, p2))
{
return SEG_NO_INTERSECTION;
}
/* Are the start and end points of q on the same side of p? */
pq1=lw_segment_side(p1,p2,q1);
pq2=lw_segment_side(p1,p2,q2);
if ((pq1>0 && pq2>0) || (pq1<0 && pq2<0))
{
return SEG_NO_INTERSECTION;
}
/* Are the start and end points of p on the same side of q? */
qp1=lw_segment_side(q1,q2,p1);
qp2=lw_segment_side(q1,q2,p2);
if ( (qp1 > 0.0 && qp2 > 0.0) || (qp1 < 0.0 && qp2 < 0.0) )
{
return SEG_NO_INTERSECTION;
}
/* Nobody is on one side or another? Must be colinear. */
if ( pq1 == 0.0 && pq2 == 0.0 && qp1 == 0.0 && qp2 == 0.0 )
{
return SEG_COLINEAR;
}
/*
** When one end-point touches, the sidedness is determined by the
** location of the other end-point. Only touches by the first point
** will be considered "real" to avoid double counting.
*/
LWDEBUGF(4, "pq1=%.15g pq2=%.15g", pq1, pq2);
LWDEBUGF(4, "qp1=%.15g qp2=%.15g", qp1, qp2);
/* Second point of p or q touches, it's not a crossing. */
if ( pq2 == 0 || qp2 == 0 )
{
return SEG_NO_INTERSECTION;
}
/* First point of p touches, it's a "crossing". */
if ( pq1 == 0 )
{
if ( pq2 > 0 )
return SEG_CROSS_RIGHT;
else
return SEG_CROSS_LEFT;
}
/* First point of q touches, it's a crossing. */
if ( qp1 == 0 )
{
if ( pq1 < pq2 )
return SEG_CROSS_RIGHT;
else
return SEG_CROSS_LEFT;
}
/* The segments cross, what direction is the crossing? */
if ( pq1 < pq2 )
return SEG_CROSS_RIGHT;
else
return SEG_CROSS_LEFT;
/* This should never happen! */
return SEG_ERROR;
}
/**
** @brief lwline_crossing_direction: returns the kind of #CG_LINE_CROSS_TYPE behavior of 2 linestrings
** @param l1 first line string
** @param l2 second line string
** @return a #CG_LINE_CROSS_TYPE
** LINE_NO_CROSS = 0
** LINE_CROSS_LEFT = -1
** LINE_CROSS_RIGHT = 1
** LINE_MULTICROSS_END_LEFT = -2
** LINE_MULTICROSS_END_RIGHT = 2
** LINE_MULTICROSS_END_SAME_FIRST_LEFT = -3
** LINE_MULTICROSS_END_SAME_FIRST_RIGHT = 3
**
*/
int lwline_crossing_direction(const LWLINE *l1, const LWLINE *l2)
{
int i = 0, j = 0;
POINT2D p1, p2, q1, q2;
POINTARRAY *pa1 = NULL, *pa2 = NULL;
int cross_left = 0;
int cross_right = 0;
int first_cross = 0;
int this_cross = 0;
pa1 = (POINTARRAY*)l1->points;
pa2 = (POINTARRAY*)l2->points;
/* One-point lines can't intersect (and shouldn't exist). */
if ( pa1->npoints < 2 || pa2->npoints < 2 )
return LINE_NO_CROSS;
LWDEBUGF(4, "l1 = %s", lwgeom_to_ewkt((LWGEOM*)l1));
LWDEBUGF(4, "l2 = %s", lwgeom_to_ewkt((LWGEOM*)l2));
/* Initialize first point of q */
getPoint2d_p(pa2, 0, &q1);
for ( i = 1; i < pa2->npoints; i++ )
{
/* Update second point of q to next value */
getPoint2d_p(pa2, i, &q2);
/* Initialize first point of p */
getPoint2d_p(pa1, 0, &p1);
for ( j = 1; j < pa1->npoints; j++ )
{
/* Update second point of p to next value */
getPoint2d_p(pa1, j, &p2);
this_cross = lw_segment_intersects(&p1, &p2, &q1, &q2);
LWDEBUGF(4, "i=%d, j=%d (%.8g %.8g, %.8g %.8g)", this_cross, i, j, p1.x, p1.y, p2.x, p2.y);
if ( this_cross == SEG_CROSS_LEFT )
{
LWDEBUG(4,"this_cross == SEG_CROSS_LEFT");
cross_left++;
if ( ! first_cross )
first_cross = SEG_CROSS_LEFT;
}
if ( this_cross == SEG_CROSS_RIGHT )
{
LWDEBUG(4,"this_cross == SEG_CROSS_RIGHT");
cross_right++;
if ( ! first_cross )
first_cross = SEG_CROSS_LEFT;
}
/*
** Crossing at a co-linearity can be turned handled by extending
** segment to next vertext and seeing if the end points straddle
** the co-linear segment.
*/
if ( this_cross == SEG_COLINEAR )
{
LWDEBUG(4,"this_cross == SEG_COLINEAR");
/* TODO: Add logic here and in segment_intersects()
continue;
*/
}
LWDEBUG(4,"this_cross == SEG_NO_INTERSECTION");
/* Turn second point of p into first point */
p1 = p2;
}
/* Turn second point of q into first point */
q1 = q2;
}
LWDEBUGF(4, "first_cross=%d, cross_left=%d, cross_right=%d", first_cross, cross_left, cross_right);
if ( !cross_left && !cross_right )
return LINE_NO_CROSS;
if ( !cross_left && cross_right == 1 )
return LINE_CROSS_RIGHT;
if ( !cross_right && cross_left == 1 )
return LINE_CROSS_LEFT;
if ( cross_left - cross_right == 1 )
return LINE_MULTICROSS_END_LEFT;
if ( cross_left - cross_right == -1 )
return LINE_MULTICROSS_END_RIGHT;
if ( cross_left - cross_right == 0 && first_cross == SEG_CROSS_LEFT )
return LINE_MULTICROSS_END_SAME_FIRST_LEFT;
if ( cross_left - cross_right == 0 && first_cross == SEG_CROSS_RIGHT )
return LINE_MULTICROSS_END_SAME_FIRST_RIGHT;
return LINE_NO_CROSS;
}
static char *base32 = "0123456789bcdefghjkmnpqrstuvwxyz";
/*
** Calculate the geohash, iterating downwards and gaining precision.
** From geohash-native.c, (c) 2008 David Troy <dave@roundhousetech.com>
** Released under the MIT License.
*/
char *geohash_point(double longitude, double latitude, int precision)
{
int is_even=1, i=0;
double lat[2], lon[2], mid;
char bits[] = {16,8,4,2,1};
int bit=0, ch=0;
char *geohash = NULL;
geohash = lwalloc(precision + 1);
lat[0] = -90.0;
lat[1] = 90.0;
lon[0] = -180.0;
lon[1] = 180.0;
while (i < precision)
{
if (is_even)
{
mid = (lon[0] + lon[1]) / 2;
if (longitude >= mid)
{
ch |= bits[bit];
lon[0] = mid;
}
else
{
lon[1] = mid;
}
}
else
{
mid = (lat[0] + lat[1]) / 2;
if (latitude >= mid)
{
ch |= bits[bit];
lat[0] = mid;
}
else
{
lat[1] = mid;
}
}
is_even = !is_even;
if (bit < 4)
{
bit++;
}
else
{
geohash[i++] = base32[ch];
bit = 0;
ch = 0;
}
}
geohash[i] = 0;
return geohash;
}
/*
** Calculate the geohash, iterating downwards and gaining precision.
** From geohash-native.c, (c) 2008 David Troy <dave@roundhousetech.com>
** Released under the MIT License.
*/
unsigned int geohash_point_as_int(POINT2D *pt)
{
int is_even=1;
double lat[2], lon[2], mid;
int bit=32;
unsigned int ch = 0;
double longitude = pt->x;
double latitude = pt->y;
lat[0] = -90.0;
lat[1] = 90.0;
lon[0] = -180.0;
lon[1] = 180.0;
while (--bit >= 0)
{
if (is_even)
{
mid = (lon[0] + lon[1]) / 2;
if (longitude > mid)
{
ch |= 0x0001 << bit;
lon[0] = mid;
}
else
{
lon[1] = mid;
}
}
else
{
mid = (lat[0] + lat[1]) / 2;
if (latitude > mid)
{
ch |= 0x0001 << bit;
lat[0] = mid;
}
else
{
lat[1] = mid;
}
}
is_even = !is_even;
}
return ch;
}
/*
** Decode a GeoHash into a bounding box. The lat and lon arguments should
** both be passed as double arrays of length 2 at a minimum where the values
** set in them will be the southwest and northeast coordinates of the bounding
** box accordingly. A precision less than 0 indicates that the entire length
** of the GeoHash should be used.
*/
void decode_geohash_bbox(char *geohash, double *lat, double *lon, int precision)
{
int i, j, hashlen;
char c, cd, mask, is_even = 1;
static char bits[] = {16, 8, 4, 2, 1};
lat[0] = -90.0;
lat[1] = 90.0;
lon[0] = -180.0;
lon[1] = 180.0;
hashlen = strlen(geohash);
if (precision < 0 || precision > hashlen)
{
precision = hashlen;
}
for (i = 0; i < precision; i++)
{
c = tolower(geohash[i]);
cd = strchr(base32, c) - base32;
for (j = 0; j < 5; j++)
{
mask = bits[j];
if (is_even)
{
lon[!(cd & mask)] = (lon[0] + lon[1]) / 2;
}
else
{
lat[!(cd & mask)] = (lat[0] + lat[1]) / 2;
}
is_even = !is_even;
}
}
}
int lwgeom_geohash_precision(GBOX bbox, GBOX *bounds)
{
double minx, miny, maxx, maxy;
double latmax, latmin, lonmax, lonmin;
double lonwidth, latwidth;
double latmaxadjust, lonmaxadjust, latminadjust, lonminadjust;
int precision = 0;
/* Get the bounding box, return error if things don't work out. */
minx = bbox.xmin;
miny = bbox.ymin;
maxx = bbox.xmax;
maxy = bbox.ymax;
if ( minx == maxx && miny == maxy )
{
/* It's a point. Doubles have 51 bits of precision.
** 2 * 51 / 5 == 20 */
return 20;
}
lonmin = -180.0;
latmin = -90.0;
lonmax = 180.0;
latmax = 90.0;
/* Shrink a world bounding box until one of the edges interferes with the
** bounds of our rectangle. */
while ( 1 )
{
lonwidth = lonmax - lonmin;
latwidth = latmax - latmin;
latmaxadjust = lonmaxadjust = latminadjust = lonminadjust = 0.0;
if ( minx > lonmin + lonwidth / 2.0 )
{
lonminadjust = lonwidth / 2.0;
}
else if ( maxx < lonmax - lonwidth / 2.0 )
{
lonmaxadjust = -1 * lonwidth / 2.0;
}
if ( miny > latmin + latwidth / 2.0 )
{
latminadjust = latwidth / 2.0;
}
else if (maxy < latmax - latwidth / 2.0 )
{
latmaxadjust = -1 * latwidth / 2.0;
}
/* Only adjust if adjustments are legal (we haven't crossed any edges). */
if ( (lonminadjust || lonmaxadjust) && (latminadjust || latmaxadjust ) )
{
latmin += latminadjust;
lonmin += lonminadjust;
latmax += latmaxadjust;
lonmax += lonmaxadjust;
/* Each adjustment cycle corresponds to 2 bits of storage in the
** geohash. */
precision += 2;
}
else
{
break;
}
}
/* Save the edges of our bounds, in case someone cares later. */
bounds->xmin = lonmin;
bounds->xmax = lonmax;
bounds->ymin = latmin;
bounds->ymax = latmax;
/* Each geohash character (base32) can contain 5 bits of information.
** We are returning the precision in characters, so here we divide. */
return precision / 5;
}
/*
** Return a geohash string for the geometry. <http://geohash.org>
** Where the precision is non-positive, calculate a precision based on the
** bounds of the feature. Big features have loose precision.
** Small features have tight precision.
*/
char *lwgeom_geohash(const LWGEOM *lwgeom, int precision)
{
GBOX gbox;
GBOX gbox_bounds;
double lat, lon;
int result;
gbox_init(&gbox);
gbox_init(&gbox_bounds);
result = lwgeom_calculate_gbox_cartesian(lwgeom, &gbox);
if ( result == LW_FAILURE ) return NULL;
/* Return error if we are being fed something outside our working bounds */
if ( gbox.xmin < -180 || gbox.ymin < -90 || gbox.xmax > 180 || gbox.ymax > 90 )
{
lwerror("Geohash requires inputs in decimal degrees.");
return NULL;
}
/* What is the center of our geometry bounds? We'll use that to
** approximate location. */
lon = gbox.xmin + (gbox.xmax - gbox.xmin) / 2;
lat = gbox.ymin + (gbox.ymax - gbox.ymin) / 2;
if ( precision <= 0 )
{
precision = lwgeom_geohash_precision(gbox, &gbox_bounds);
}
/*
** Return the geohash of the center, with a precision determined by the
** extent of the bounds.
** Possible change: return the point at the center of the precision bounds?
*/
return geohash_point(lon, lat, precision);
}