private static void TestIntervalOps(S1Interval x, S1Interval y, string expected_relation, S1Interval expected_union, S1Interval expected_intersection)
{
// Test all of the interval operations on the given pair of intervals.
// "expected_relation" is a sequence of "T" and "F" characters corresponding
// to the expected results of Contains(), InteriorContains(), Intersects(),
// and InteriorIntersects() respectively.
Assert.Equal(x.Contains(y), expected_relation[0] == 'T');
Assert.Equal(x.InteriorContains(y), expected_relation[1] == 'T');
Assert.Equal(x.Intersects(y), expected_relation[2] == 'T');
Assert.Equal(x.InteriorIntersects(y), expected_relation[3] == 'T');
// bounds() returns a reference to a member variable, so we need to
// make a copy when invoking it on a temporary object.
Assert.Equal(R2Point.FromCoords(x.Union(y).Bounds()).Bounds(), expected_union.Bounds());
Assert.Equal(R2Point.FromCoords(x.Intersection(y).Bounds()).Bounds(),
expected_intersection.Bounds());
Assert.Equal(x.Contains(y), x.Union(y) == x);
Assert.Equal(x.Intersects(y), !x.Intersection(y).IsEmpty());
if (y.Lo == y.Hi)
{
var r = S1Interval.AddPoint(x, y.Lo);
Assert.Equal(r.Bounds(), expected_union.Bounds());
}
}
public void Test_S1IntervalTestBase_Contains()
{
// Contains(double), InteriorContains(double)
Assert.True(!empty.Contains(0) && !empty.Contains(Math.PI) &&
!empty.Contains(-Math.PI));
Assert.True(!empty.InteriorContains(Math.PI) && !empty.InteriorContains(-Math.PI));
Assert.True(full.Contains(0) && full.Contains(Math.PI) && full.Contains(-Math.PI));
Assert.True(full.InteriorContains(Math.PI) && full.InteriorContains(-Math.PI));
Assert.True(quad12.Contains(0) && quad12.Contains(Math.PI) &&
quad12.Contains(-Math.PI));
Assert.True(quad12.InteriorContains(S2.M_PI_2) && !quad12.InteriorContains(0));
Assert.True(!quad12.InteriorContains(Math.PI) &&
!quad12.InteriorContains(-Math.PI));
Assert.True(quad23.Contains(S2.M_PI_2) && quad23.Contains(-S2.M_PI_2));
Assert.True(quad23.Contains(Math.PI) && quad23.Contains(-Math.PI));
Assert.True(!quad23.Contains(0));
Assert.True(!quad23.InteriorContains(S2.M_PI_2) &&
!quad23.InteriorContains(-S2.M_PI_2));
Assert.True(quad23.InteriorContains(Math.PI) && quad23.InteriorContains(-Math.PI));
Assert.True(!quad23.InteriorContains(0));
Assert.True(pi.Contains(Math.PI) && pi.Contains(-Math.PI) && !pi.Contains(0));
Assert.True(!pi.InteriorContains(Math.PI) && !pi.InteriorContains(-Math.PI));
Assert.True(mipi.Contains(Math.PI) && mipi.Contains(-Math.PI) && !mipi.Contains(0));
Assert.True(!mipi.InteriorContains(Math.PI) && !mipi.InteriorContains(-Math.PI));
Assert.True(zero.Contains(0) && !zero.InteriorContains(0));
}
// Returns the minimum distance from X to the latitude line segment defined by
// the given latitude and longitude interval.
private static S1Angle GetDistance(S2LatLng x, S1Angle lat, S1Interval interval)
{
Assert.True(x.IsValid());
Assert.True(interval.IsValid());
// Is X inside the longitude interval?
if (interval.Contains(x.LngRadians))
{
return(S1Angle.FromRadians((x.Lat() - lat).Abs()));
}
// Return the distance to the closer endpoint.
return(new[] { x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Lo))),
x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Hi))) }.Min());
}
/**
* Returns the minimum distance from X to the latitude line segment defined by
* the given latitude and longitude interval.
*/
private static S1Angle getDistance(S2LatLng x, S1Angle lat, S1Interval interval)
{
assertTrue(x.IsValid);
assertTrue(interval.IsValid);
// Is X inside the longitude interval?
if (interval.Contains(x.Lng.Radians))
{
return(S1Angle.FromRadians(Math.Abs(x.Lat.Radians - lat.Radians)));
}
// Return the distance to the closer endpoint.
return(S1Angle.Min(x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Lo))),
x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Hi)))));
}
/**
* Returns the minimum distance from X to the latitude line segment defined by
* the given latitude and longitude interval.
*/
private static S1Angle getDistance(S2LatLng x, S1Angle lat, S1Interval interval)
{
assertTrue(x.IsValid);
assertTrue(interval.IsValid);
// Is X inside the longitude interval?
if (interval.Contains(x.Lng.Radians))
return S1Angle.FromRadians(Math.Abs(x.Lat.Radians - lat.Radians));
// Return the distance to the closer endpoint.
return S1Angle.Min(x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Lo))),
x.GetDistance(new S2LatLng(lat, S1Angle.FromRadians(interval.Hi))));
}
private void TestFaceClipping(S2Point a_raw, S2Point b_raw)
{
S2Point a = a_raw.Normalize();
S2Point b = b_raw.Normalize();
// First we test GetFaceSegments.
FaceSegmentVector segments = new();
GetFaceSegments(a, b, segments);
int n = segments.Count;
Assert.True(n >= 1);
var msg = new StringBuilder($"\nA={a_raw}\nB={b_raw}\nN={S2.RobustCrossProd(a, b)}\nSegments:\n");
int i1 = 0;
foreach (var s in segments)
{
msg.AppendLine($"{i1++}: face={s.face}, a={s.a}, b={s.b}");
}
_logger.WriteLine(msg.ToString());
R2Rect biunit = new(new R1Interval(-1, 1), new R1Interval(-1, 1));
var kErrorRadians = kFaceClipErrorRadians;
// The first and last vertices should approximately equal A and B.
Assert.True(a.Angle(S2.FaceUVtoXYZ(segments[0].face, segments[0].a)) <=
kErrorRadians);
Assert.True(b.Angle(S2.FaceUVtoXYZ(segments[n - 1].face, segments[n - 1].b)) <=
kErrorRadians);
S2Point norm = S2.RobustCrossProd(a, b).Normalize();
S2Point a_tangent = norm.CrossProd(a);
S2Point b_tangent = b.CrossProd(norm);
for (int i = 0; i < n; ++i)
{
// Vertices may not protrude outside the biunit square.
Assert.True(biunit.Contains(segments[i].a));
Assert.True(biunit.Contains(segments[i].b));
if (i == 0)
{
continue;
}
// The two representations of each interior vertex (on adjacent faces)
// must correspond to exactly the same S2Point.
Assert.NotEqual(segments[i - 1].face, segments[i].face);
Assert.Equal(S2.FaceUVtoXYZ(segments[i - 1].face, segments[i - 1].b),
S2.FaceUVtoXYZ(segments[i].face, segments[i].a));
// Interior vertices should be in the plane containing A and B, and should
// be contained in the wedge of angles between A and B (i.e., the dot
// products with a_tangent and b_tangent should be non-negative).
S2Point p = S2.FaceUVtoXYZ(segments[i].face, segments[i].a).Normalize();
Assert.True(Math.Abs(p.DotProd(norm)) <= kErrorRadians);
Assert.True(p.DotProd(a_tangent) >= -kErrorRadians);
Assert.True(p.DotProd(b_tangent) >= -kErrorRadians);
}
// Now we test ClipToPaddedFace (sometimes with a padding of zero). We do
// this by defining an (x,y) coordinate system for the plane containing AB,
// and converting points along the great circle AB to angles in the range
// [-Pi, Pi]. We then accumulate the angle intervals spanned by each
// clipped edge; the union over all 6 faces should approximately equal the
// interval covered by the original edge.
double padding = S2Testing.Random.OneIn(10) ? 0.0 : 1e-10 * Math.Pow(1e-5, S2Testing.Random.RandDouble());
S2Point x_axis = a, y_axis = a_tangent;
S1Interval expected_angles = new(0, a.Angle(b));
S1Interval max_angles = expected_angles.Expanded(kErrorRadians);
S1Interval actual_angles = new();
for (int face = 0; face < 6; ++face)
{
if (ClipToPaddedFace(a, b, face, padding, out var a_uv, out var b_uv))
{
S2Point a_clip = S2.FaceUVtoXYZ(face, a_uv).Normalize();
S2Point b_clip = S2.FaceUVtoXYZ(face, b_uv).Normalize();
Assert.True(Math.Abs(a_clip.DotProd(norm)) <= kErrorRadians);
Assert.True(Math.Abs(b_clip.DotProd(norm)) <= kErrorRadians);
if (a_clip.Angle(a) > kErrorRadians)
{
Assert2.DoubleEqual(1 + padding, Math.Max(Math.Abs(a_uv[0]), Math.Abs(a_uv[1])));
}
if (b_clip.Angle(b) > kErrorRadians)
{
Assert2.DoubleEqual(1 + padding, Math.Max(Math.Abs(b_uv[0]), Math.Abs(b_uv[1])));
}
double a_angle = Math.Atan2(a_clip.DotProd(y_axis), a_clip.DotProd(x_axis));
double b_angle = Math.Atan2(b_clip.DotProd(y_axis), b_clip.DotProd(x_axis));
// Rounding errors may cause b_angle to be slightly less than a_angle.
// We handle this by constructing the interval with FromPointPair(),
// which is okay since the interval length is much less than Math.PI.
S1Interval face_angles = S1Interval.FromPointPair(a_angle, b_angle);
Assert.True(max_angles.Contains(face_angles));
actual_angles = actual_angles.Union(face_angles);
}
}
Assert.True(actual_angles.Expanded(kErrorRadians).Contains(expected_angles));
}