PostGIS  2.4.9dev-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 1404 of file lwgeodetic.c.

Referenced by ptarray_calculate_gbox_geodetic().

1405 {
1406  POINT2D R1, R2, RX, O;
1407  POINT3D AN, A3;
1408  POINT3D X;
1409  int i, o_side;
1410
1411  /* Initialize the box with the edge end points */
1412  gbox_init_point3d(A1, gbox);
1413  gbox_merge_point3d(A2, gbox);
1414
1415  /* Zero length edge, just return! */
1416  if ( p3d_same(A1, A2) )
1417  return LW_SUCCESS;
1418
1419  /* Error out on antipodal edge */
1420  if ( FP_EQUALS(A1->x, -1*A2->x) && FP_EQUALS(A1->y, -1*A2->y) && FP_EQUALS(A1->z, -1*A2->z) )
1421  {
1422  lwerror("Antipodal (180 degrees long) edge detected!");
1423  return LW_FAILURE;
1424  }
1425
1426  /* Create A3, a vector in the plane of A1/A2, orthogonal to A1 */
1427  unit_normal(A1, A2, &AN);
1428  unit_normal(&AN, A1, &A3);
1429
1430  /* Project A1 and A2 into the 2-space formed by the plane A1/A3 */
1431  R1.x = 1.0;
1432  R1.y = 0.0;
1433  R2.x = dot_product(A2, A1);
1434  R2.y = dot_product(A2, &A3);
1435
1436  /* Initialize our 3-space axis points (x+, x-, y+, y-, z+, z-) */
1437  memset(X, 0, sizeof(POINT3D) * 6);
1438  X.x = X.y = X.z = 1.0;
1439  X.x = X.y = X.z = -1.0;
1440
1441  /* Initialize a 2-space origin point. */
1442  O.x = O.y = 0.0;
1443  /* What side of the line joining R1/R2 is O? */
1444  o_side = lw_segment_side(&R1, &R2, &O);
1445
1446  /* Add any extrema! */
1447  for ( i = 0; i < 6; i++ )
1448  {
1449  /* Convert 3-space axis points to 2-space unit vectors */
1450  RX.x = dot_product(&(X[i]), A1);
1451  RX.y = dot_product(&(X[i]), &A3);
1452  normalize2d(&RX);
1453
1454  /* Any axis end on the side of R1/R2 opposite the origin */
1455  /* is an extreme point in the arc, so we add the 3-space */
1456  /* version of the point on R1/R2 to the gbox */
1457  if ( lw_segment_side(&R1, &R2, &RX) != o_side )
1458  {
1459  POINT3D Xn;
1460  Xn.x = RX.x * A1->x + RX.y * A3.x;
1461  Xn.y = RX.x * A1->y + RX.y * A3.y;
1462  Xn.z = RX.x * A1->z + RX.y * A3.z;
1463
1464  gbox_merge_point3d(&Xn, gbox);
1465  }
1466  }
1467
1468  return LW_SUCCESS;
1469 }
double y
Definition: liblwgeom.h:340
#define LW_SUCCESS
Definition: liblwgeom.h:80
double x
Definition: liblwgeom.h:340
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:79
double z
Definition: liblwgeom.h:340
double x
Definition: liblwgeom.h:328
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:537
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:442
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:328
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:520
void lwerror(const char *fmt,...)
Write a notice out to the error handler.
Definition: lwutil.c:190
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