PostGIS  2.2.8dev-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 1356 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().

1357 {
1358  POINT2D R1, R2, RX, O;
1359  POINT3D AN, A3;
1360  POINT3D X[6];
1361  int i, o_side;
1362 
1363  /* Initialize the box with the edge end points */
1364  gbox_init_point3d(A1, gbox);
1365  gbox_merge_point3d(A2, gbox);
1366 
1367  /* Zero length edge, just return! */
1368  if ( p3d_same(A1, A2) )
1369  return LW_SUCCESS;
1370 
1371  /* Error out on antipodal edge */
1372  if ( FP_EQUALS(A1->x, -1*A2->x) && FP_EQUALS(A1->y, -1*A2->y) && FP_EQUALS(A1->z, -1*A2->z) )
1373  {
1374  lwerror("Antipodal (180 degrees long) edge detected!");
1375  return LW_FAILURE;
1376  }
1377 
1378  /* Create A3, a vector in the plane of A1/A2, orthogonal to A1 */
1379  unit_normal(A1, A2, &AN);
1380  unit_normal(&AN, A1, &A3);
1381 
1382  /* Project A1 and A2 into the 2-space formed by the plane A1/A3 */
1383  R1.x = 1.0;
1384  R1.y = 0.0;
1385  R2.x = dot_product(A2, A1);
1386  R2.y = dot_product(A2, &A3);
1387 
1388  /* Initialize our 3-space axis points (x+, x-, y+, y-, z+, z-) */
1389  memset(X, 0, sizeof(POINT3D) * 6);
1390  X[0].x = X[2].y = X[4].z = 1.0;
1391  X[1].x = X[3].y = X[5].z = -1.0;
1392 
1393  /* Initialize a 2-space origin point. */
1394  O.x = O.y = 0.0;
1395  /* What side of the line joining R1/R2 is O? */
1396  o_side = lw_segment_side(&R1, &R2, &O);
1397 
1398  /* Add any extrema! */
1399  for ( i = 0; i < 6; i++ )
1400  {
1401  /* Convert 3-space axis points to 2-space unit vectors */
1402  RX.x = dot_product(&(X[i]), A1);
1403  RX.y = dot_product(&(X[i]), &A3);
1404  normalize2d(&RX);
1405 
1406  /* Any axis end on the side of R1/R2 opposite the origin */
1407  /* is an extreme point in the arc, so we add the 3-space */
1408  /* version of the point on R1/R2 to the gbox */
1409  if ( lw_segment_side(&R1, &R2, &RX) != o_side )
1410  {
1411  POINT3D Xn;
1412  Xn.x = RX.x * A1->x + RX.y * A3.x;
1413  Xn.y = RX.x * A1->y + RX.y * A3.y;
1414  Xn.z = RX.x * A1->z + RX.y * A3.z;
1415 
1416  gbox_merge_point3d(&Xn, gbox);
1417  }
1418  }
1419 
1420  return LW_SUCCESS;
1421 }
double y
Definition: liblwgeom.h:324
#define LW_SUCCESS
Definition: liblwgeom.h:65
double x
Definition: liblwgeom.h:324
int gbox_init_point3d(const POINT3D *p, GBOX *gbox)
Initialize a GBOX using the values of the point.
Definition: g_box.c:216
#define LW_FAILURE
Definition: liblwgeom.h:64
double z
Definition: liblwgeom.h:324
double x
Definition: liblwgeom.h:312
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:491
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:396
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:205
double y
Definition: liblwgeom.h:312
int p3d_same(const POINT3D *p1, const POINT3D *p2)
Definition: lwalgorithm.c:26
#define FP_EQUALS(A, B)
int lw_segment_side(const POINT2D *p1, const POINT2D *p2, const POINT2D *q)
lw_segment_side()
Definition: lwalgorithm.c:50
static void normalize2d(POINT2D *p)
Normalize to a unit vector.
Definition: lwgeodetic.c:474
void lwerror(const char *fmt,...)
Write a notice out to the error handler.
Definition: lwutil.c:74
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