/**
* A slightly more efficient version of getDistance() where the cross product
* of the two endpoints has been precomputed. The cross product does not need
* to be normalized, but should be computed using S2.robustCrossProd() for the
* most accurate results.
*/
public static S1Angle GetDistance(S2Point x, S2Point a, S2Point b, S2Point aCrossB)
{
Preconditions.CheckArgument(S2.IsUnitLength(x));
Preconditions.CheckArgument(S2.IsUnitLength(a));
Preconditions.CheckArgument(S2.IsUnitLength(b));
// There are three cases. If X is located in the spherical wedge defined by
// A, B, and the axis A x B, then the closest point is on the segment AB.
// Otherwise the closest point is either A or B; the dividing line between
// these two cases is the great circle passing through (A x B) and the
// midpoint of AB.
if (S2.SimpleCcw(aCrossB, a, x) && S2.SimpleCcw(x, b, aCrossB))
{
// The closest point to X lies on the segment AB. We compute the distance
// to the corresponding great circle. The result is accurate for small
// distances but not necessarily for large distances (approaching Pi/2).
var sinDist = Math.Abs(x.DotProd(aCrossB)) / aCrossB.Norm;
return(S1Angle.FromRadians(Math.Asin(Math.Min(1.0, sinDist))));
}
// Otherwise, the closest point is either A or B. The cheapest method is
// just to compute the minimum of the two linear (as opposed to spherical)
// distances and convert the result to an angle. Again, this method is
// accurate for small but not large distances (approaching Pi).
var linearDist2 = Math.Min((x - a).Norm2, (x - b).Norm2);
return(S1Angle.FromRadians(2 * Math.Asin(Math.Min(1.0, 0.5 * Math.Sqrt(linearDist2)))));
}
/**
* Returns the point on edge AB closest to X. x, a and b must be of unit
* length. Throws IllegalArgumentException if this is not the case.
*
*/
public static S2Point GetClosestPoint(S2Point x, S2Point a, S2Point b)
{
Preconditions.CheckArgument(S2.IsUnitLength(x));
Preconditions.CheckArgument(S2.IsUnitLength(a));
Preconditions.CheckArgument(S2.IsUnitLength(b));
var crossProd = S2.RobustCrossProd(a, b);
// Find the closest point to X along the great circle through AB.
var p = x - (crossProd * x.DotProd(crossProd) / crossProd.Norm2);
// If p is on the edge AB, then it's the closest point.
if (S2.SimpleCcw(crossProd, a, p) && S2.SimpleCcw(p, b, crossProd))
{
return(S2Point.Normalize(p));
}
// Otherwise, the closest point is either A or B.
return((x - a).Norm2 <= (x - b).Norm2 ? a : b);
}
