/**
* Return the smallest rectangle containing the intersection of this rectangle
* and the given rectangle. Note that the region of intersection may consist
* of two disjoint rectangles, in which case a single rectangle spanning both
* of them is returned.
*#/
* public S2LatLngRect intersection(S2LatLngRect other) {
* R1Interval intersectLat = lat.intersection(other.lat);
* S1Interval intersectLng = lng.intersection(other.lng);
* if (intersectLat.isEmpty() || intersectLng.isEmpty()) {
* // The lat/lng ranges must either be both empty or both non-empty.
* return empty();
* }
* return new S2LatLngRect(intersectLat, intersectLng);
* }
*
* /**
* Return a rectangle that contains the convolution of this rectangle with a
* cap of the given angle. This expands the rectangle by a fixed distance (as
* opposed to growing the rectangle in latitude-longitude space). The returned
* rectangle includes all points whose minimum distance to the original
* rectangle is at most the given angle.
*#/
* public S2LatLngRect convolveWithCap(S1Angle angle) {
* // The most straightforward approach is to build a cap centered on each
* // vertex and take the union of all the bounding rectangles (including the
* // original rectangle; this is necessary for very large rectangles).
*
* // Optimization: convert the angle to a height exactly once.
* S2Cap cap = S2Cap.fromAxisAngle(new S2Point(1, 0, 0), angle);
*
* S2LatLngRect r = this;
* for (int k = 0; k < 4; ++k) {
* S2Cap vertexCap = S2Cap.fromAxisHeight(getVertex(k).toPoint(), cap
* .height());
* r = r.union(vertexCap.getRectBound());
* }
* return r;
* }
*
* /** Return the surface area of this rectangle on the unit sphere. *#/
* public double area() {
* if (isEmpty()) {
* return 0;
* }
*
* // This is the size difference of the two spherical caps, multiplied by
* // the longitude ratio.
* return lng().getLength() * Math.abs(Math.sin(latHi().radians()) - Math.sin(latLo().radians()));
* }
*
* /** Return true if two rectangles contains the same set of points. *#/
* @Override
* public boolean equals(Object that) {
* if (!(that instanceof S2LatLngRect)) {
* return false;
* }
* S2LatLngRect otherRect = (S2LatLngRect) that;
* return lat().equals(otherRect.lat()) && lng().equals(otherRect.lng());
* }
*
* /**
* Return true if the latitude and longitude intervals of the two rectangles
* are the same up to the given tolerance (see r1interval.h and s1interval.h
* for details).
*#/
* public boolean approxEquals(S2LatLngRect other, double maxError) {
* return (lat.approxEquals(other.lat, maxError) && lng.approxEquals(
* other.lng, maxError));
* }
*
* public boolean approxEquals(S2LatLngRect other) {
* return approxEquals(other, 1e-15);
* }
*
* @Override
* public int hashCode() {
* int value = 17;
* value = 37 * value + lat.hashCode();
* return (37 * value + lng.hashCode());
* }
*
* // //////////////////////////////////////////////////////////////////////
* // S2Region interface (see {@code S2Region} for details):
*
* @Override
* public S2Region clone() {
* return new S2LatLngRect(this.lo(), this.hi());
* }
*/
public function getCapBound()
{
// We consider two possible bounding caps, one whose axis passes
// through the center of the lat-long rectangle and one whose axis
// is the north or south pole. We return the smaller of the two caps.
if ($this->isEmpty()) {
echo __METHOD__ . " empty\n";
return S2Cap::sempty();
}
$poleZ = null;
$poleAngle = null;
if ($this->lat->lo() + $this->lat->hi() < 0) {
// South pole axis yields smaller cap.
$poleZ = -1;
$poleAngle = S2::M_PI_2 + $this->lat->hi();
} else {
$poleZ = 1;
$poleAngle = S2::M_PI_2 - $this->lat->lo();
}
$poleCap = S2Cap::fromAxisAngle(new S2Point(0, 0, $poleZ), S1Angle::sradians($poleAngle));
// For bounding rectangles that span 180 degrees or less in longitude, the
// maximum cap size is achieved at one of the rectangle vertices. For
// rectangles that are larger than 180 degrees, we punt and always return a
// bounding cap centered at one of the two poles.
$lngSpan = $this->lng->hi() - $this->lng->lo();
if (S2::IEEEremainder($lngSpan, 2 * S2::M_PI) >= 0) {
if ($lngSpan < 2 * S2::M_PI) {
$midCap = S2Cap::fromAxisAngle($this->getCenter()->toPoint(), S1Angle::sradians(0));
for ($k = 0; $k < 4; ++$k) {
$midCap = $midCap->addPoint($this->getVertex($k)->toPoint());
}
if ($midCap->height() < $poleCap->height()) {
return $midCap;
}
}
}
return $poleCap;
}
/**
* 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 - $x))));
// Return the distance (measured along the surface of the sphere) to the
// given S2LatLng. This is mathematically equivalent to:
//
// S1Angle::FromRadians(ToPoint().Angle(o.ToPoint())
//
// but this implementation is slightly more efficient.
}
/** Returns the longitude of this point as a new S1Angle. */
public function lng()
{
return S1Angle::sradians($this->lngRadians);
}
/**
* Return the cap opening angle in radians, or a negative number for empty
* caps.
*/
public function angle()
{
// This could also be computed as acos(1 - height_), but the following
// formula is much more accurate when the cap height is small. It
// follows from the relationship h = 1 - cos(theta) = 2 sin^2(theta/2).
if ($this->isEmpty()) {
return S1Angle::sradians(-1);
}
return S1Angle::sradians(2 * asin(sqrt(0.5 * $this->height)));
}