/**
* @param double|S2Point $radians_or_x
* @param S2Point $y
* Return the angle between two points, which is also equal to the distance
* between these points on the unit sphere. The points do not need to be
* normalized.
*/
public function __construct($radians_or_x = null, $y = null)
{
if ($radians_or_x instanceof S2Point && $y instanceof S2Point) {
$this->radians = $radians_or_x->angle($y);
} else {
$this->radians = $radians_or_x === null ? 0 : $radians_or_x;
}
}
public static function toPoint()
{
return S2Point::normalize(self::toPointRaw());
}
public static function xyzToFace(S2Point $p)
{
$face = $p->largestAbsComponent();
if ($p->get($face) < 0) {
$face += 3;
}
return $face;
}
public function toString()
{
return sprintf("Edge: (%s -> %s)\n or [%s -> %s]", $this->start->toDegreesString(), $this->end->toDegreesString(), $this->start, $this->end);
}
public static function normalize(S2Point $p)
{
$norm = $p->norm();
if ($norm != 0) {
$norm = 1.0 / $norm;
}
return S2Point::mul($p, $norm);
}
/**
* Return the average area for cells at the given level.
*#/
* public static double averageArea(int level) {
* return S2Projections.AVG_AREA.getValue(level);
* }
*
* /**
* Return the average area of cells at this level. This is accurate to within
* a factor of 1.7 (for S2_QUADRATIC_PROJECTION) and is extremely cheap to
* compute.
*#/
* public double averageArea() {
* return averageArea(level);
* }
*
* /**
* Return the approximate area of this cell. This method is accurate to within
* 3% percent for all cell sizes and accurate to within 0.1% for cells at
* level 5 or higher (i.e. 300km square or smaller). It is moderately cheap to
* compute.
*#/
* public double approxArea() {
*
* // All cells at the first two levels have the same area.
* if (level < 2) {
* return averageArea(level);
* }
*
* // First, compute the approximate area of the cell when projected
* // perpendicular to its normal. The cross product of its diagonals gives
* // the normal, and the length of the normal is twice the projected area.
* double flatArea = 0.5 * S2Point.crossProd(
* S2Point.sub(getVertex(2), getVertex(0)), S2Point.sub(getVertex(3), getVertex(1))).norm();
*
* // Now, compensate for the curvature of the cell surface by pretending
* // that the cell is shaped like a spherical cap. The ratio of the
* // area of a spherical cap to the area of its projected disc turns out
* // to be 2 / (1 + sqrt(1 - r*r)) where "r" is the radius of the disc.
* // For example, when r=0 the ratio is 1, and when r=1 the ratio is 2.
* // Here we set Pi*r*r == flat_area to find the equivalent disc.
* return flatArea * 2 / (1 + Math.sqrt(1 - Math.min(S2.M_1_PI * flatArea, 1.0)));
* }
*
* /**
* Return the area of this cell as accurately as possible. This method is more
* expensive but it is accurate to 6 digits of precision even for leaf cells
* (whose area is approximately 1e-18).
*#/
* public double exactArea() {
* S2Point v0 = getVertex(0);
* S2Point v1 = getVertex(1);
* S2Point v2 = getVertex(2);
* S2Point v3 = getVertex(3);
* return S2.area(v0, v1, v2) + S2.area(v0, v2, v3);
* }
*
* // //////////////////////////////////////////////////////////////////////
* // S2Region interface (see {@code S2Region} for details):
*
* @Override
* public S2Region clone() {
* S2Cell clone = new S2Cell();
* clone.face = this.face;
* clone.level = this.level;
* clone.orientation = this.orientation;
* clone.uv = this.uv.clone();
*
* return clone;
* }
*/
public function getCapBound()
{
// Use the cell center in (u,v)-space as the cap axis. This vector is
// very close to GetCenter() and faster to compute. Neither one of these
// vectors yields the bounding cap with minimal surface area, but they
// are both pretty close.
//
// It's possible to show that the two vertices that are furthest from
// the (u,v)-origin never determine the maximum cap size (this is a
// possible future optimization).
$u = 0.5 * ($this->uv[0][0] + $this->uv[0][1]);
$v = 0.5 * ($this->uv[1][0] + $this->uv[1][1]);
$cap = S2Cap::fromAxisHeight(S2Point::normalize(S2Projections::faceUvToXyz($this->face, $u, $v)), 0);
for ($k = 0; $k < 4; ++$k) {
$cap = $cap->addPoint($this->getVertex($k));
}
return $cap;
}
public static function longitude(S2Point $p)
{
// Note that atan2(0, 0) is defined to be zero.
return S1Angle::sradians(atan2($p->get(1), $p->get(0)));
}
/** Return true if the cap is full, i.e. it contains all points. *#/
* public boolean isFull() {
* return height >= 2;
* }
*
* /**
* Return the complement of the interior of the cap. A cap and its complement
* have the same boundary but do not share any interior points. The complement
* operator is not a bijection, since the complement of a singleton cap
* (containing a single point) is the same as the complement of an empty cap.
*#/
* public S2Cap complement() {
* // The complement of a full cap is an empty cap, not a singleton.
* // Also make sure that the complement of an empty cap has height 2.
* double cHeight = isFull() ? -1 : 2 - Math.max(height, 0.0);
* return S2Cap.fromAxisHeight(S2Point.neg(axis), cHeight);
* }
*
* /**
* Return true if and only if this cap contains the given other cap (in a set
* containment sense, e.g. every cap contains the empty cap).
*#/
* public boolean contains(S2Cap other) {
* if (isFull() || other.isEmpty()) {
* return true;
* }
* return angle().radians() >= axis.angle(other.axis)
* + other.angle().radians();
* }
*
* /**
* Return true if and only if the interior of this cap intersects the given
* other cap. (This relationship is not symmetric, since only the interior of
* this cap is used.)
*#/
* public boolean interiorIntersects(S2Cap other) {
* // Interior(X) intersects Y if and only if Complement(Interior(X))
* // does not contain Y.
* return !complement().contains(other);
* }
*
* /**
* Return true if and only if the given point is contained in the interior of
* the region (i.e. the region excluding its boundary). 'p' should be a
* unit-length vector.
*#/
* public boolean interiorContains(S2Point p) {
* // assert (S2.isUnitLength(p));
* return isFull() || S2Point.sub(axis, p).norm2() < 2 * height;
* }
*
* /**
* Increase the cap height if necessary to include the given point. If the cap
* is empty the axis is set to the given point, but otherwise it is left
* unchanged. 'p' should be a unit-length vector.
*/
public function addPoint(S2Point $p)
{
// Compute the squared chord length, then convert it into a height.
// assert (S2.isUnitLength(p));
if ($this->isEmpty()) {
return new S2Cap($p, 0);
} else {
// To make sure that the resulting cap actually includes this point,
// we need to round up the distance calculation. That is, after
// calling cap.AddPoint(p), cap.Contains(p) should be true.
$dist2 = S2Point::sub($this->axis, $p)->norm2();
$newHeight = max($this->height, self::ROUND_UP * 0.5 * $dist2);
return new S2Cap($this->axis, $newHeight);
}
}