/**
* If this method returns false, the region does not intersect the given cell.
* Otherwise, either region intersects the cell, or the intersection
* relationship could not be determined.
*/
public function mayIntersect(S2Cell $cell)
{
if ($this->numLoops() == 1) {
return $this->loop(0)->mayIntersect($cell);
}
$cellBound = $cell->getRectBound();
if (!$this->bound->intersects($cellBound)) {
return false;
}
$cellLoop = new S2Loop($cell, $cellBound);
$cellPoly = new S2Polygon($cellLoop);
return $this->intersects($cellPoly);
}
public function getRectBound()
{
if ($this->level > 0) {
// Except for cells at level 0, the latitude and longitude extremes are
// attained at the vertices. Furthermore, the latitude range is
// determined by one pair of diagonally opposite vertices and the
// longitude range is determined by the other pair.
//
// We first determine which corner (i,j) of the cell has the largest
// absolute latitude. To maximize latitude, we want to find the point in
// the cell that has the largest absolute z-coordinate and the smallest
// absolute x- and y-coordinates. To do this we look at each coordinate
// (u and v), and determine whether we want to minimize or maximize that
// coordinate based on the axis direction and the cell's (u,v) quadrant.
$u = $this->uv[0][0] + $this->uv[0][1];
$v = $this->uv[1][0] + $this->uv[1][1];
$i = S2Projections::getUAxis($this->face)->z == 0 ? $u < 0 ? 1 : 0 : ($u > 0 ? 1 : 0);
$j = S2Projections::getVAxis($this->face)->z == 0 ? $v < 0 ? 1 : 0 : ($v > 0 ? 1 : 0);
$lat = R1Interval::fromPointPair($this->getLatitude($i, $j), $this->getLatitude(1 - $i, 1 - $j));
$lat = $lat->expanded(self::MAX_ERROR)->intersection(S2LatLngRect::fullLat());
if ($lat->lo() == -S2::M_PI_2 || $lat->hi() == S2::M_PI_2) {
return new S2LatLngRect($lat, S1Interval::full());
}
$lng = S1Interval::fromPointPair($this->getLongitude($i, 1 - $j), $this->getLongitude(1 - $i, $j));
return new S2LatLngRect($lat, $lng->expanded(self::MAX_ERROR));
}
// The face centers are the +X, +Y, +Z, -X, -Y, -Z axes in that order.
// assert (S2Projections.getNorm(face).get(face % 3) == ((face < 3) ? 1 : -1));
switch ($this->face) {
case 0:
return new S2LatLngRect(new R1Interval(-S2::M_PI_4, S2::M_PI_4), new S1Interval(-S2::M_PI_4, S2::M_PI_4));
case 1:
return new S2LatLngRect(new R1Interval(-S2::M_PI_4, S2::M_PI_4), new S1Interval(S2::M_PI_4, 3 * S2::M_PI_4));
case 2:
return new S2LatLngRect(new R1Interval(POLE_MIN_LAT, S2::M_PI_2), new S1Interval(-S2::M_PI, S2::M_PI));
case 3:
return new S2LatLngRect(new R1Interval(-S2::M_PI_4, S2::M_PI_4), new S1Interval(3 * S2::M_PI_4, -3 * S2::M_PI_4));
case 4:
return new S2LatLngRect(new R1Interval(-S2::M_PI_4, S2::M_PI_4), new S1Interval(-3 * S2::M_PI_4, -S2::M_PI_4));
default:
return new S2LatLngRect(new R1Interval(-S2::M_PI_2, -POLE_MIN_LAT), new S1Interval(-S2::M_PI, S2::M_PI));
}
}
public function getRectBound()
{
if ($this->isEmpty()) {
return S2LatLngRect::emptya();
}
// Convert the axis to a (lat,lng) pair, and compute the cap angle.
$axisLatLng = new S2LatLng($this->axis);
$capAngle = $this->angle()->radians();
$allLongitudes = false;
$lat = array();
$lng = array();
$lng[0] = -S2::M_PI;
$lng[1] = S2::M_PI;
// Check whether cap includes the south pole.
$lat[0] = $axisLatLng->lat()->radians() - $capAngle;
if ($lat[0] <= -S2::M_PI_2) {
$lat[0] = -S2::M_PI_2;
$allLongitudes = true;
}
// Check whether cap includes the north pole.
$lat[1] = $axisLatLng->lat()->radians() + $capAngle;
if ($lat[1] >= S2::M_PI_2) {
$lat[1] = S2::M_PI_2;
$allLongitudes = true;
}
if (!$allLongitudes) {
// Compute the range of longitudes covered by the cap. We use the law
// of sines for spherical triangles. Consider the triangle ABC where
// A is the north pole, B is the center of the cap, and C is the point
// of tangency between the cap boundary and a line of longitude. Then
// C is a right angle, and letting a,b,c denote the sides opposite A,B,C,
// we have sin(a)/sin(A) = sin(c)/sin(C), or sin(A) = sin(a)/sin(c).
// Here "a" is the cap angle, and "c" is the colatitude (90 degrees
// minus the latitude). This formula also works for negative latitudes.
//
// The formula for sin(a) follows from the relationship h = 1 - cos(a).
$sinA = sqrt($this->height * (2 - $this->height));
$sinC = cos($axisLatLng->lat()->radians());
if ($sinA <= $sinC) {
$angleA = asin($sinA / $sinC);
$lng[0] = S2::IEEEremainder($axisLatLng->lng()->radians() - $angleA, 2 * S2::M_PI);
$lng[1] = S2::IEEEremainder($axisLatLng->lng()->radians() + $angleA, 2 * S2::M_PI);
}
}
return new S2LatLngRect(new R1Interval($lat[0], $lat[1]), new S1Interval($lng[0], $lng[1]));
}
