/** return a vector orthogonal to this one */
public function ortho()
{
$k = $this->largestAbsComponent();
if ($k == 1) {
$temp = new S2Point(1, 0, 0);
} else {
if ($k == 2) {
$temp = new S2Point(0, 1, 0);
} else {
$temp = new S2Point(0, 0, 1);
}
}
return S2Point::normalize($this->crossProd($this, $temp));
}
public static function toPoint()
{
return S2Point::normalize(self::toPointRaw());
}
/**
* 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;
}
