/**
* 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 $poleCap;
}
/**
* Return true if the interior of this interval contains any point of the
* interval 'y' (including its boundary). Works for empty, full, and singleton
* intervals.
*#/
* public boolean interiorIntersects(final S1Interval y) {
* if (isEmpty() || y.isEmpty() || lo() == hi()) {
* return false;
* }
* if (isInverted()) {
* return y.isInverted() || y.lo() < hi() || y.hi() > lo();
* } else {
* if (y.isInverted()) {
* return y.lo() < hi() || y.hi() > lo();
* }
* return (y.lo() < hi() && y.hi() > lo()) || isFull();
* }
* }
*
* /**
* Expand the interval by the minimum amount necessary so that it contains the
* given point "p" (an angle in the range [-Pi, Pi]).
*#/
* public S1Interval addPoint(double p) {
* // assert (Math.abs(p) <= S2.M_PI);
* if (p == -S2.M_PI) {
* p = S2.M_PI;
* }
*
* if (fastContains(p)) {
* return new S1Interval(this);
* }
*
* if (isEmpty()) {
* return S1Interval.fromPoint(p);
* } else {
* // Compute distance from p to each endpoint.
* double dlo = positiveDistance(p, lo());
* double dhi = positiveDistance(hi(), p);
* if (dlo < dhi) {
* return new S1Interval(p, hi());
* } else {
* return new S1Interval(lo(), p);
* }
* // Adding a point can never turn a non-full interval into a full one.
* }
* }
*
* /**
* Return an interval that contains all points within a distance "radius" of
* a point in this interval. Note that the expansion of an empty interval is
* always empty. The radius must be non-negative.
*/
public function expanded($radius)
{
// assert (radius >= 0);
if ($this->isEmpty()) {
return $this;
}
// Check whether this interval will be full after expansion, allowing
// for a 1-bit rounding error when computing each endpoint.
if ($this->getLength() + 2 * $radius >= 2 * S2::M_PI - 1.0E-15) {
return self::full();
}
// NOTE(dbeaumont): Should this remainder be 2 * M_PI or just M_PI ??
// double lo = Math.IEEEremainder(lo() - radius, 2 * S2.M_PI);
$lo = S2::IEEEremainder($this->lo() - $radius, 2 * S2::M_PI);
$hi = S2::IEEEremainder($this->hi() + $radius, 2 * S2::M_PI);
if ($lo == -S2::M_PI) {
$lo = S2::M_PI;
}
return new S1Interval($lo, $hi);
}
public function getRectBound()
{
if ($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]));
}