PostGIS  2.1.10dev-r@@SVN_REVISION@@
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 1355 of file lwgeodetic.c.

References dot_product(), FP_EQUALS, gbox_init_point3d(), gbox_merge_point3d(), LW_FAILURE, lw_segment_side(), LW_SUCCESS, lwerror(), normalize2d(), p3d_same(), unit_normal(), POINT2D::x, POINT3D::x, POINT2D::y, POINT3D::y, and POINT3D::z.

Referenced by ptarray_calculate_gbox_geodetic().

1356 {
1357  POINT2D R1, R2, RX, O;
1358  POINT3D AN, A3;
1359  POINT3D X[6];
1360  int i, o_side;
1361 
1362  /* Initialize the box with the edge end points */
1363  gbox_init_point3d(A1, gbox);
1364  gbox_merge_point3d(A2, gbox);
1365 
1366  /* Zero length edge, just return! */
1367  if ( p3d_same(A1, A2) )
1368  return LW_SUCCESS;
1369 
1370  /* Error out on antipodal edge */
1371  if ( FP_EQUALS(A1->x, -1*A2->x) && FP_EQUALS(A1->y, -1*A2->y) && FP_EQUALS(A1->z, -1*A2->z) )
1372  {
1373  lwerror("Antipodal (180 degrees long) edge detected!");
1374  return LW_FAILURE;
1375  }
1376 
1377  /* Create A3, a vector in the plane of A1/A2, orthogonal to A1 */
1378  unit_normal(A1, A2, &AN);
1379  unit_normal(&AN, A1, &A3);
1380 
1381  /* Project A1 and A2 into the 2-space formed by the plane A1/A3 */
1382  R1.x = 1.0;
1383  R1.y = 0.0;
1384  R2.x = dot_product(A2, A1);
1385  R2.y = dot_product(A2, &A3);
1386 
1387  /* Initialize our 3-space axis points (x+, x-, y+, y-, z+, z-) */
1388  memset(X, 0, sizeof(POINT3D) * 6);
1389  X[0].x = X[2].y = X[4].z = 1.0;
1390  X[1].x = X[3].y = X[5].z = -1.0;
1391 
1392  /* Initialize a 2-space origin point. */
1393  O.x = O.y = 0.0;
1394  /* What side of the line joining R1/R2 is O? */
1395  o_side = lw_segment_side(&R1, &R2, &O);
1396 
1397  /* Add any extrema! */
1398  for ( i = 0; i < 6; i++ )
1399  {
1400  /* Convert 3-space axis points to 2-space unit vectors */
1401  RX.x = dot_product(&(X[i]), A1);
1402  RX.y = dot_product(&(X[i]), &A3);
1403  normalize2d(&RX);
1404 
1405  /* Any axis end on the side of R1/R2 opposite the origin */
1406  /* is an extreme point in the arc, so we add the 3-space */
1407  /* version of the point on R1/R2 to the gbox */
1408  if ( lw_segment_side(&R1, &R2, &RX) != o_side )
1409  {
1410  POINT3D Xn;
1411  Xn.x = RX.x * A1->x + RX.y * A3.x;
1412  Xn.y = RX.x * A1->y + RX.y * A3.y;
1413  Xn.z = RX.x * A1->z + RX.y * A3.z;
1414 
1415  gbox_merge_point3d(&Xn, gbox);
1416  }
1417  }
1418 
1419  return LW_SUCCESS;
1420 }
double y
Definition: liblwgeom.h:296
#define LW_SUCCESS
Definition: liblwgeom.h:55
double x
Definition: liblwgeom.h:296
int gbox_init_point3d(const POINT3D *p, GBOX *gbox)
Initialize a GBOX using the values of the point.
Definition: g_box.c:197
#define LW_FAILURE
Definition: liblwgeom.h:54
double z
Definition: liblwgeom.h:296
void lwerror(const char *fmt,...)
Write a notice out to the error handler.
Definition: lwutil.c:67
double x
Definition: liblwgeom.h:284
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:490
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:397
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:186
double y
Definition: liblwgeom.h:284
int p3d_same(const POINT3D *p1, const POINT3D *p2)
Definition: lwalgorithm.c:38
#define FP_EQUALS(A, B)
int lw_segment_side(const POINT2D *p1, const POINT2D *p2, const POINT2D *q)
lw_segment_side()
Definition: lwalgorithm.c:62
static void normalize2d(POINT2D *p)
Normalize to a unit vector.
Definition: lwgeodetic.c:473

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