/*
* Given two edges AB and CD such that robustCrossing() is true, return their
* intersection point. Useful properties of getIntersection (GI):
*
* (1) GI(b,a,c,d) == GI(a,b,d,c) == GI(a,b,c,d) (2) GI(c,d,a,b) ==
* GI(a,b,c,d)
*
* The returned intersection point X is guaranteed to be close to the edges AB
* and CD, but if the edges intersect at a very small angle then X may not be
* close to the true mathematical intersection point P. See the description of
* "DEFAULT_INTERSECTION_TOLERANCE" below for details.
*/
public static S2Point GetIntersection(S2Point a0, S2Point a1, S2Point b0, S2Point b1)
{
Preconditions.CheckArgument(RobustCrossing(a0, a1, b0, b1) > 0,
"Input edges a0a1 and b0b1 muct have a true robustCrossing.");
// We use robustCrossProd() to get accurate results even when two endpoints
// are close together, or when the two line segments are nearly parallel.
var aNorm = S2Point.Normalize(S2.RobustCrossProd(a0, a1));
var bNorm = S2Point.Normalize(S2.RobustCrossProd(b0, b1));
var x = S2Point.Normalize(S2.RobustCrossProd(aNorm, bNorm));
// Make sure the intersection point is on the correct side of the sphere.
// Since all vertices are unit length, and edges are less than 180 degrees,
// (a0 + a1) and (b0 + b1) both have positive dot product with the
// intersection point. We use the sum of all vertices to make sure that the
// result is unchanged when the edges are reversed or exchanged.
if (x.DotProd(a0 + a1 + b0 + b1) < 0)
{
x = -x;
}
// The calculation above is sufficient to ensure that "x" is within
// DEFAULT_INTERSECTION_TOLERANCE of the great circles through (a0,a1) and
// (b0,b1).
// However, if these two great circles are very close to parallel, it is
// possible that "x" does not lie between the endpoints of the given line
// segments. In other words, "x" might be on the great circle through
// (a0,a1) but outside the range covered by (a0,a1). In this case we do
// additional clipping to ensure that it does.
if (S2.OrderedCcw(a0, x, a1, aNorm) && S2.OrderedCcw(b0, x, b1, bNorm))
{
return(x);
}
// Find the acceptable endpoint closest to x and return it. An endpoint is
// acceptable if it lies between the endpoints of the other line segment.
var r = new CloserResult(10, x);
if (S2.OrderedCcw(b0, a0, b1, bNorm))
{
r.ReplaceIfCloser(x, a0);
}
if (S2.OrderedCcw(b0, a1, b1, bNorm))
{
r.ReplaceIfCloser(x, a1);
}
if (S2.OrderedCcw(a0, b0, a1, aNorm))
{
r.ReplaceIfCloser(x, b0);
}
if (S2.OrderedCcw(a0, b1, a1, aNorm))
{
r.ReplaceIfCloser(x, b1);
}
return(r.Vmin);
}
/*
* Given two edges AB and CD such that robustCrossing() is true, return their
* intersection point. Useful properties of getIntersection (GI):
*
* (1) GI(b,a,c,d) == GI(a,b,d,c) == GI(a,b,c,d) (2) GI(c,d,a,b) ==
* GI(a,b,c,d)
*
* The returned intersection point X is guaranteed to be close to the edges AB
* and CD, but if the edges intersect at a very small angle then X may not be
* close to the true mathematical intersection point P. See the description of
* "DEFAULT_INTERSECTION_TOLERANCE" below for details.
*/
public static S2Point GetIntersection(S2Point a0, S2Point a1, S2Point b0, S2Point b1)
{
Preconditions.CheckArgument(RobustCrossing(a0, a1, b0, b1) > 0,
"Input edges a0a1 and b0b1 muct have a true robustCrossing.");
// We use robustCrossProd() to get accurate results even when two endpoints
// are close together, or when the two line segments are nearly parallel.
var aNorm = S2Point.Normalize(S2.RobustCrossProd(a0, a1));
var bNorm = S2Point.Normalize(S2.RobustCrossProd(b0, b1));
var x = S2Point.Normalize(S2.RobustCrossProd(aNorm, bNorm));
// Make sure the intersection point is on the correct side of the sphere.
// Since all vertices are unit length, and edges are less than 180 degrees,
// (a0 + a1) and (b0 + b1) both have positive dot product with the
// intersection point. We use the sum of all vertices to make sure that the
// result is unchanged when the edges are reversed or exchanged.
if (x.DotProd(a0 + a1 + b0 + b1) < 0)
{
x = -x;
}
// The calculation above is sufficient to ensure that "x" is within
// DEFAULT_INTERSECTION_TOLERANCE of the great circles through (a0,a1) and
// (b0,b1).
// However, if these two great circles are very close to parallel, it is
// possible that "x" does not lie between the endpoints of the given line
// segments. In other words, "x" might be on the great circle through
// (a0,a1) but outside the range covered by (a0,a1). In this case we do
// additional clipping to ensure that it does.
if (S2.OrderedCcw(a0, x, a1, aNorm) && S2.OrderedCcw(b0, x, b1, bNorm))
{
return x;
}
// Find the acceptable endpoint closest to x and return it. An endpoint is
// acceptable if it lies between the endpoints of the other line segment.
var r = new CloserResult(10, x);
if (S2.OrderedCcw(b0, a0, b1, bNorm))
{
r.ReplaceIfCloser(x, a0);
}
if (S2.OrderedCcw(b0, a1, b1, bNorm))
{
r.ReplaceIfCloser(x, a1);
}
if (S2.OrderedCcw(a0, b0, a1, aNorm))
{
r.ReplaceIfCloser(x, b0);
}
if (S2.OrderedCcw(a0, b1, a1, aNorm))
{
r.ReplaceIfCloser(x, b1);
}
return r.Vmin;
}