PostGIS  2.3.8dev-r@@SVN_REVISION@@

## ◆ edge_calculate_gbox()

 int edge_calculate_gbox ( const POINT3D * A1, const POINT3D * A2, GBOX * gbox )

The magic function, given an edge in spherical coordinates, calculate a 3D bounding box that fully contains it, taking into account the curvature of the sphere on which it is inscribed.

Any arc on the sphere defines a plane that bisects the sphere. In this plane, the arc is a portion of a unit circle. Projecting the end points of the axes (1,0,0), (-1,0,0) etc, into the plane and normalizing yields potential extrema points. Those points on the side of the plane-dividing line formed by the end points that is opposite the origin of the plane are extrema and should be added to the bounding box.

Definition at line 1373 of file lwgeodetic.c.

Referenced by ptarray_calculate_gbox_geodetic().

1374 {
1375  POINT2D R1, R2, RX, O;
1376  POINT3D AN, A3;
1377  POINT3D X[6];
1378  int i, o_side;
1379
1380  /* Initialize the box with the edge end points */
1381  gbox_init_point3d(A1, gbox);
1382  gbox_merge_point3d(A2, gbox);
1383
1384  /* Zero length edge, just return! */
1385  if ( p3d_same(A1, A2) )
1386  return LW_SUCCESS;
1387
1388  /* Error out on antipodal edge */
1389  if ( FP_EQUALS(A1->x, -1*A2->x) && FP_EQUALS(A1->y, -1*A2->y) && FP_EQUALS(A1->z, -1*A2->z) )
1390  {
1391  lwerror("Antipodal (180 degrees long) edge detected!");
1392  return LW_FAILURE;
1393  }
1394
1395  /* Create A3, a vector in the plane of A1/A2, orthogonal to A1 */
1396  unit_normal(A1, A2, &AN);
1397  unit_normal(&AN, A1, &A3);
1398
1399  /* Project A1 and A2 into the 2-space formed by the plane A1/A3 */
1400  R1.x = 1.0;
1401  R1.y = 0.0;
1402  R2.x = dot_product(A2, A1);
1403  R2.y = dot_product(A2, &A3);
1404
1405  /* Initialize our 3-space axis points (x+, x-, y+, y-, z+, z-) */
1406  memset(X, 0, sizeof(POINT3D) * 6);
1407  X[0].x = X[2].y = X[4].z = 1.0;
1408  X[1].x = X[3].y = X[5].z = -1.0;
1409
1410  /* Initialize a 2-space origin point. */
1411  O.x = O.y = 0.0;
1412  /* What side of the line joining R1/R2 is O? */
1413  o_side = lw_segment_side(&R1, &R2, &O);
1414
1415  /* Add any extrema! */
1416  for ( i = 0; i < 6; i++ )
1417  {
1418  /* Convert 3-space axis points to 2-space unit vectors */
1419  RX.x = dot_product(&(X[i]), A1);
1420  RX.y = dot_product(&(X[i]), &A3);
1421  normalize2d(&RX);
1422
1423  /* Any axis end on the side of R1/R2 opposite the origin */
1424  /* is an extreme point in the arc, so we add the 3-space */
1425  /* version of the point on R1/R2 to the gbox */
1426  if ( lw_segment_side(&R1, &R2, &RX) != o_side )
1427  {
1428  POINT3D Xn;
1429  Xn.x = RX.x * A1->x + RX.y * A3.x;
1430  Xn.y = RX.x * A1->y + RX.y * A3.y;
1431  Xn.z = RX.x * A1->z + RX.y * A3.z;
1432
1433  gbox_merge_point3d(&Xn, gbox);
1434  }
1435  }
1436
1437  return LW_SUCCESS;
1438 }
double y
Definition: liblwgeom.h:339
#define LW_SUCCESS
Definition: liblwgeom.h:79
double x
Definition: liblwgeom.h:339
int gbox_init_point3d(const POINT3D *p, GBOX *gbox)
Initialize a GBOX using the values of the point.
Definition: g_box.c:251
#define LW_FAILURE
Definition: liblwgeom.h:78
double z
Definition: liblwgeom.h:339
double x
Definition: liblwgeom.h:327
void unit_normal(const POINT3D *P1, const POINT3D *P2, POINT3D *normal)
Calculates the unit normal to two vectors, trying to avoid problems with over-narrow or over-wide cas...
Definition: lwgeodetic.c:506
static double dot_product(const POINT3D *p1, const POINT3D *p2)
Convert cartesion coordinates on unit sphere to lon/lat coordinates static void cart2ll(const POINT3D...
Definition: lwgeodetic.c:411
int gbox_merge_point3d(const POINT3D *p, GBOX *gbox)
Update the GBOX to be large enough to include itself and the new point.
Definition: g_box.c:240
double y
Definition: liblwgeom.h:327
int p3d_same(const POINT3D *p1, const POINT3D *p2)
Definition: lwalgorithm.c:40
#define FP_EQUALS(A, B)
int lw_segment_side(const POINT2D *p1, const POINT2D *p2, const POINT2D *q)
lw_segment_side()
Definition: lwalgorithm.c:64
static void normalize2d(POINT2D *p)
Normalize to a unit vector.
Definition: lwgeodetic.c:489
void lwerror(const char *fmt,...)
Write a notice out to the error handler.
Definition: lwutil.c:102
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