/** Return the leaf cell containing the given S2LatLng. */
public static function fromLatLng(S2LatLng $ll)
{
return self::fromPoint($ll->toPoint());
}
/**
* Return a rectangle that contains all points whose latitude distance from
* this rectangle is at most margin.lat(), and whose longitude distance from
* this rectangle is at most margin.lng(). In particular, latitudes are
* clamped while longitudes are wrapped. Note that any expansion of an empty
* interval remains empty, and both components of the given margin must be
* non-negative.
*
* NOTE: If you are trying to grow a rectangle by a certain *distance* on the
* sphere (e.g. 5km), use the ConvolveWithCap() method instead.
* @return S2LatLngRect
*/
public function expanded(S2LatLng $margin)
{
// assert (margin.lat().radians() >= 0 && margin.lng().radians() >= 0);
if ($this->isEmpty()) {
return $this;
}
return new S2LatLngRect($this->lat->expanded($margin->lat()->radians())->intersection($this->fullLat()), $this->lng->expanded($margin->lng()->radians()));
}
/**
* Return the distance (measured along the surface of the sphere) to the given
* point.
*/
public function getDistance(S2LatLng $o)
{
// This implements the Haversine formula, which is numerically stable for
// small distances but only gets about 8 digits of precision for very large
// distances (e.g. antipodal points). Note that 8 digits is still accurate
// to within about 10cm for a sphere the size of the Earth.
//
// This could be fixed with another sin() and cos() below, but at that point
// you might as well just convert both arguments to S2Points and compute the
// distance that way (which gives about 15 digits of accuracy for all
// distances).
$lat1 = self::lat()->radians();
$lat2 = $o->lat()->radians();
$lng1 = self::lng()->radians();
$lng2 = $o->lng()->radians();
$dlat = sin(0.5 * ($lat2 - $lat1));
$dlng = sin(0.5 * ($lng2 - $lng1));
$x = $dlat * $dlat + $dlng * $dlng * cos($lat1) * cos($lat2);
return S1Angle::sradians(2 * atan2(sqrt($x), sqrt(max(0.0, 1.0 - $x))));
// Return the distance (measured along the surface of the sphere) to the
// given S2LatLng. This is mathematically equivalent to:
//
// S1Angle::FromRadians(ToPoint().Angle(o.ToPoint())
//
// but this implementation is slightly more efficient.
}
public function toDegreesString()
{
$s2LatLng = new S2LatLng($this);
return "(" . $s2LatLng->latDegrees() . ", " . $s2LatLng->lngDegrees() . ")";
}
public function getRectBound()
{
if ($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]));
}