private static S1ChordAngle GetMaxDistanceToEdgeBruteForce(S2Cell cell, S2Point a, S2Point b)
{
// If any antipodal endpoint is within the cell, the max distance is Pi.
if (cell.Contains(-a) || cell.Contains(-b))
{
return(S1ChordAngle.Straight);
}
S1ChordAngle max_dist = S1ChordAngle.Negative;
for (int i = 0; i < 4; ++i)
{
S2Point v0 = cell.Vertex(i);
S2Point v1 = cell.Vertex(i + 1);
// If the antipodal edge crosses through the cell, max distance is Pi.
if (S2.CrossingSign(-a, -b, v0, v1) >= 0)
{
return(S1ChordAngle.Straight);
}
S2.UpdateMaxDistance(a, v0, v1, ref max_dist);
S2.UpdateMaxDistance(b, v0, v1, ref max_dist);
S2.UpdateMaxDistance(v0, a, b, ref max_dist);
}
return(max_dist);
}
// Returns the pair of points (a, b) that achieves the minimum distance
// between edges a0a1 and b0b1, where "a" is a point on a0a1 and "b" is a
// point on b0b1. If the two edges intersect, "a" and "b" are both equal to
// the intersection point. Handles a0 == a1 and b0 == b1 correctly.
public static (S2Point, S2Point) GetEdgePairClosestPoints(S2Point a0, S2Point a1, S2Point b0, S2Point b1)
{
if (S2.CrossingSign(a0, a1, b0, b1) > 0)
{
S2Point x = S2.GetIntersection(a0, a1, b0, b1, null);
return(x, x);
}
// We save some work by first determining which vertex/edge pair achieves
// the minimum distance, and then computing the closest point on that edge.
var min_dist = S1ChordAngle.Zero;
AlwaysUpdateMinDistance(a0, b0, b1, ref min_dist, true);
var closest_vertex = 0;
if (UpdateMinDistance(a1, b0, b1, ref min_dist))
{
closest_vertex = 1;
}
if (UpdateMinDistance(b0, a0, a1, ref min_dist))
{
closest_vertex = 2;
}
if (UpdateMinDistance(b1, a0, a1, ref min_dist))
{
closest_vertex = 3;
}
return(closest_vertex switch
{
0 => (a0, Project(a0, b0, b1)),
1 => (a1, Project(a1, b0, b1)),
2 => (Project(b0, a0, a1), b0),
3 => (Project(b1, a0, a1), b1),
_ => throw new ApplicationException("Unreached (to suppress Android compiler warning)"),
});
public void Test_S2_CoincidentZeroLengthEdgesThatDontTouch()
{
// It is important that the edge primitives can handle vertices that exactly
// exactly proportional to each other, i.e. that are not identical but are
// nevertheless exactly coincident when projected onto the unit sphere.
// There are various ways that such points can arise. For example,
// Normalize() itself is not idempotent: there exist distinct points A,B
// such that Normalize(A) == B and Normalize(B) == A. Another issue is
// that sometimes calls to Normalize() are skipped when the result of a
// calculation "should" be unit length mathematically (e.g., when computing
// the cross product of two orthonormal vectors).
//
// This test checks pairs of edges AB and CD where A,B,C,D are exactly
// coincident on the sphere and the norms of A,B,C,D are monotonically
// increasing. Such edge pairs should never intersect. (This is not
// obvious, since it depends on the particular symbolic perturbations used
// by S2Pred.Sign(). It would be better to replace this with a test that
// says that the CCW results must be consistent with each other.)
int kIters = 1000;
for (int iter = 0; iter < kIters; ++iter)
{
// Construct a point P where every component is zero or a power of 2.
var t = new double[3];
for (int i = 0; i < 3; ++i)
{
int binary_exp = S2Testing.Random.Skewed(11);
t[i] = (binary_exp > 1022) ? 0 : Math.Pow(2, -binary_exp);
}
// If all components were zero, try again. Note that normalization may
// convert a non-zero point into a zero one due to underflow (!)
var p = new S2Point(t).Normalize();
if (p == S2Point.Empty)
{
--iter; continue;
}
// Now every non-zero component should have exactly the same mantissa.
// This implies that if we scale the point by an arbitrary factor, every
// non-zero component will still have the same mantissa. Scale the points
// so that they are all distinct and are still very likely to satisfy
// S2.IsUnitLength (which allows for a small amount of error in the norm).
S2Point a = (1 - 3e-16) * p;
S2Point b = (1 - 1e-16) * p;
S2Point c = p;
S2Point d = (1 + 2e-16) * p;
if (!a.IsUnitLength() || !d.IsUnitLength())
{
--iter;
continue;
}
// Verify that the expected edges do not cross.
Assert.True(0 > S2.CrossingSign(a, b, c, d));
S2EdgeCrosser crosser = new(a, b, c);
Assert.True(0 > crosser.CrossingSign(d));
Assert.True(0 > crosser.CrossingSign(c));
}
}
public void Test_S2_CollinearEdgesThatDontTouch()
{
int kIters = 500;
for (int iter = 0; iter < kIters; ++iter)
{
S2Point a = S2Testing.RandomPoint();
S2Point d = S2Testing.RandomPoint();
S2Point b = S2.Interpolate(0.05, a, d);
S2Point c = S2.Interpolate(0.95, a, d);
Assert.True(0 > S2.CrossingSign(a, b, c, d));
Assert.True(0 > S2.CrossingSign(a, b, c, d));
S2EdgeCrosser crosser = new(a, b, c);
Assert.True(0 > crosser.CrossingSign(d));
Assert.True(0 > crosser.CrossingSign(c));
}
}
// As above, but for maximum distances. If one edge crosses the antipodal
// reflection of the other, the distance is Pi.
public static bool UpdateEdgePairMaxDistance(S2Point a0, S2Point a1, S2Point b0, S2Point b1, ref S1ChordAngle max_dist)
{
if (max_dist == S1ChordAngle.Straight)
{
return(false);
}
if (S2.CrossingSign(a0, a1, -b0, -b1) >= 0)
{
max_dist = S1ChordAngle.Straight;
return(true);
}
// Otherwise, the maximum distance is achieved at an endpoint of at least
// one of the two edges. We use "|" rather than "||" below to ensure that
// all four possibilities are always checked.
//
// The calculation below computes each of the six vertex-vertex distances
// twice (this could be optimized).
return(UpdateMaxDistance(a0, b0, b1, ref max_dist) |
UpdateMaxDistance(a1, b0, b1, ref max_dist) |
UpdateMaxDistance(b0, a0, a1, ref max_dist) |
UpdateMaxDistance(b1, a0, a1, ref max_dist));
}
private static S1ChordAngle GetDistanceToEdgeBruteForce(S2Cell cell, S2Point a, S2Point b)
{
if (cell.Contains(a) || cell.Contains(b))
{
return(S1ChordAngle.Zero);
}
S1ChordAngle min_dist = S1ChordAngle.Infinity;
for (int i = 0; i < 4; ++i)
{
S2Point v0 = cell.Vertex(i);
S2Point v1 = cell.Vertex(i + 1);
// If the edge crosses through the cell, max distance is 0.
if (S2.CrossingSign(a, b, v0, v1) >= 0)
{
return(S1ChordAngle.Zero);
}
S2.UpdateMinDistance(a, v0, v1, ref min_dist);
S2.UpdateMinDistance(b, v0, v1, ref min_dist);
S2.UpdateMinDistance(v0, a, b, ref min_dist);
}
return(min_dist);
}
private static void TestCrossing(S2Point a, S2Point b, S2Point c, S2Point d,
int crossing_sign, int signed_crossing_sign)
{
// For degenerate edges, CrossingSign() is documented to return 0 if two
// vertices from different edges are the same and -1 otherwise. The
// TestCrossings() function below uses various argument permutations that
// can sometimes create this case, so we fix it now if necessary.
if (a == c || a == d || b == c || b == d)
{
crossing_sign = 0;
}
// As a sanity check, make sure that the expected value of
// "signed_crossing_sign" is consistent with its documented properties.
if (crossing_sign == 1)
{
Assert.Equal(signed_crossing_sign, S2Pred.Sign(a, b, c));
}
else if (crossing_sign == 0 && signed_crossing_sign != 0)
{
Assert.Equal(signed_crossing_sign, (a == c || b == d) ? 1 : -1);
}
Assert.Equal(crossing_sign, S2.CrossingSign(a, b, c, d));
S2EdgeCrosser crosser = new(a, b, c);
Assert.Equal(crossing_sign, crosser.CrossingSign(d));
Assert.Equal(crossing_sign, crosser.CrossingSign(c));
Assert.Equal(crossing_sign, crosser.CrossingSign(d, c));
Assert.Equal(crossing_sign, crosser.CrossingSign(c, d));
Assert.Equal(signed_crossing_sign != 0, S2.EdgeOrVertexCrossing(a, b, c, d));
crosser.RestartAt(c);
Assert.Equal(signed_crossing_sign != 0, crosser.EdgeOrVertexCrossing(d));
Assert.Equal(signed_crossing_sign != 0, crosser.EdgeOrVertexCrossing(c));
Assert.Equal(signed_crossing_sign != 0, crosser.EdgeOrVertexCrossing(d, c));
Assert.Equal(signed_crossing_sign != 0, crosser.EdgeOrVertexCrossing(c, d));
crosser.RestartAt(c);
Assert.Equal(signed_crossing_sign, crosser.SignedEdgeOrVertexCrossing(d));
Assert.Equal(-signed_crossing_sign, crosser.SignedEdgeOrVertexCrossing(c));
Assert.Equal(-signed_crossing_sign, crosser.SignedEdgeOrVertexCrossing(d, c));
Assert.Equal(signed_crossing_sign, crosser.SignedEdgeOrVertexCrossing(c, d));
// Check that the crosser can be re-used.
crosser.Init(c, d);
crosser.RestartAt(a);
Assert.Equal(crossing_sign, crosser.CrossingSign(b));
Assert.Equal(crossing_sign, crosser.CrossingSign(a));
// Now try all the same tests with CopyingEdgeCrosser.
S2CopyingEdgeCrosser crosser2 = new(a, b, c);
Assert.Equal(crossing_sign, crosser2.CrossingSign(d));
Assert.Equal(crossing_sign, crosser2.CrossingSign(c));
Assert.Equal(crossing_sign, crosser2.CrossingSign(d, c));
Assert.Equal(crossing_sign, crosser2.CrossingSign(c, d));
crosser2.RestartAt(c);
Assert.Equal(signed_crossing_sign != 0, crosser2.EdgeOrVertexCrossing(d));
Assert.Equal(signed_crossing_sign != 0, crosser2.EdgeOrVertexCrossing(c));
Assert.Equal(signed_crossing_sign != 0, crosser2.EdgeOrVertexCrossing(d, c));
Assert.Equal(signed_crossing_sign != 0, crosser2.EdgeOrVertexCrossing(c, d));
crosser2.RestartAt(c);
Assert.Equal(signed_crossing_sign, crosser2.SignedEdgeOrVertexCrossing(d));
Assert.Equal(-signed_crossing_sign, crosser2.SignedEdgeOrVertexCrossing(c));
Assert.Equal(-signed_crossing_sign, crosser2.SignedEdgeOrVertexCrossing(d, c));
Assert.Equal(signed_crossing_sign, crosser2.SignedEdgeOrVertexCrossing(c, d));
// Check that the crosser can be re-used.
crosser2.Init(c, d);
crosser2.RestartAt(a);
Assert.Equal(crossing_sign, crosser2.CrossingSign(b));
Assert.Equal(crossing_sign, crosser2.CrossingSign(a));
}