// Compute the convex hull of the input geometry provided.
//
// If there is no geometry, this method returns an empty loop containing no
// points (see S2Loop.IsEmpty).
//
// If the geometry spans more than half of the sphere, this method returns a
// full loop containing the entire sphere (see S2Loop.IsFull).
//
// If the geometry contains 1 or 2 points, or a single edge, this method
// returns a very small loop consisting of three vertices (which are a
// superset of the input vertices).
//
// Note that this method does not clear the geometry; you can continue
// adding to it and call this method again if desired.
public S2Loop GetConvexHull()
{
// Test whether the bounding cap is convex. We need this to proceed with
// the algorithm below in order to construct a point "origin" that is
// definitely outside the convex hull.
S2Cap cap = GetCapBound();
if (cap.Height() >= 1 - 10 * S2Pred.DBL_ERR)
{
return(S2Loop.kFull);
}
// This code implements Andrew's monotone chain algorithm, which is a simple
// variant of the Graham scan. Rather than sorting by x-coordinate, instead
// we sort the points in CCW order around an origin O such that all points
// are guaranteed to be on one side of some geodesic through O. This
// ensures that as we scan through the points, each new point can only
// belong at the end of the chain (i.e., the chain is monotone in terms of
// the angle around O from the starting point).
S2Point origin = cap.Center.Ortho();
points_.Sort(new OrderedCcwAround(origin));
// Remove duplicates. We need to do this before checking whether there are
// fewer than 3 points.
var tmp = points_.Distinct().ToList();
points_.Clear();
points_.AddRange(tmp);
// Special cases for fewer than 3 points.
if (points_.Count < 3)
{
if (!points_.Any())
{
return(S2Loop.kEmpty);
}
else if (points_.Count == 1)
{
return(GetSinglePointLoop(points_[0]));
}
else
{
return(GetSingleEdgeLoop(points_[0], points_[1]));
}
}
// Verify that all points lie within a 180 degree span around the origin.
System.Diagnostics.Debug.Assert(S2Pred.Sign(origin, points_.First(), points_.Last()) >= 0);
// Generate the lower and upper halves of the convex hull. Each half
// consists of the maximal subset of vertices such that the edge chain makes
// only left (CCW) turns.
var lower = new List <S2Point>();
var upper = new List <S2Point>();
GetMonotoneChain(lower);
points_.Reverse();
GetMonotoneChain(upper);
// Remove the duplicate vertices and combine the chains.
System.Diagnostics.Debug.Assert(lower.First() == upper.Last());
System.Diagnostics.Debug.Assert(lower.Last() == upper.First());
lower.RemoveAt(lower.Count - 1);
upper.RemoveAt(lower.Count - 1);
lower.AddRange(upper);
return(new S2Loop(lower));
}
public void Test_S2Cap_Basic()
{
// Test basic properties of empty and full caps.
S2Cap empty = S2Cap.Empty;
S2Cap full = S2Cap.Full;
Assert.True(empty.IsValid());
Assert.True(empty.IsEmpty());
Assert.True(empty.Complement().IsFull());
Assert.True(full.IsValid());
Assert.True(full.IsFull());
Assert.True(full.Complement().IsEmpty());
Assert.Equal(2, full.Height());
Assert2.DoubleEqual(180.0, full.Radius.Degrees());
// Test ==/!=.
Assert.Equal(full, full);
Assert.Equal(empty, empty);
Assert.NotEqual(full, empty);
// Test the S1Angle constructor using out-of-range arguments.
Assert.True(new S2Cap(new S2Point(1, 0, 0), S1Angle.FromRadians(-20)).IsEmpty());
Assert.True(new S2Cap(new S2Point(1, 0, 0), S1Angle.FromRadians(5)).IsFull());
Assert.True(new S2Cap(new S2Point(1, 0, 0), S1Angle.Infinity).IsFull());
// Check that the default S2Cap is identical to Empty().
var default_empty = S2Cap.Empty;
Assert.True(default_empty.IsValid());
Assert.True(default_empty.IsEmpty());
Assert.Equal(empty.Center, default_empty.Center);
Assert.Equal(empty.Height(), default_empty.Height());
// Containment and intersection of empty and full caps.
Assert.True(empty.Contains(empty));
Assert.True(full.Contains(empty));
Assert.True(full.Contains(full));
Assert.False(empty.InteriorIntersects(empty));
Assert.True(full.InteriorIntersects(full));
Assert.False(full.InteriorIntersects(empty));
// Singleton cap containing the x-axis.
S2Cap xaxis = S2Cap.FromPoint(new S2Point(1, 0, 0));
Assert.True(xaxis.Contains(new S2Point(1, 0, 0)));
Assert.False(xaxis.Contains(new S2Point(1, 1e-20, 0)));
Assert.Equal(0, xaxis.Radius.Radians());
// Singleton cap containing the y-axis.
S2Cap yaxis = S2Cap.FromPoint(new S2Point(0, 1, 0));
Assert.False(yaxis.Contains(xaxis.Center));
Assert.Equal(0, xaxis.Height());
// Check that the complement of a singleton cap is the full cap.
S2Cap xcomp = xaxis.Complement();
Assert.True(xcomp.IsValid());
Assert.True(xcomp.IsFull());
Assert.True(xcomp.Contains(xaxis.Center));
// Check that the complement of the complement is *not* the original.
Assert.True(xcomp.Complement().IsValid());
Assert.True(xcomp.Complement().IsEmpty());
Assert.False(xcomp.Complement().Contains(xaxis.Center));
// Check that very small caps can be represented accurately.
// Here "kTinyRad" is small enough that unit vectors perturbed by this
// amount along a tangent do not need to be renormalized.
S2Cap tiny = new(new S2Point(1, 2, 3).Normalize(), S1Angle.FromRadians(kTinyRad));
var tangent = tiny.Center.CrossProd(new S2Point(3, 2, 1)).Normalize();
Assert.True(tiny.Contains(tiny.Center + 0.99 * kTinyRad * tangent));
Assert.False(tiny.Contains(tiny.Center + 1.01 * kTinyRad * tangent));
// Basic tests on a hemispherical cap.
S2Cap hemi = S2Cap.FromCenterHeight(new S2Point(1, 0, 1).Normalize(), 1);
Assert.Equal(-hemi.Center, hemi.Complement().Center);
Assert.Equal(1, hemi.Complement().Height());
Assert.True(hemi.Contains(new S2Point(1, 0, 0)));
Assert.False(hemi.Complement().Contains(new S2Point(1, 0, 0)));
Assert.True(hemi.Contains(new S2Point(1, 0, -(1 - kEps)).Normalize()));
Assert.False(hemi.InteriorContains(new S2Point(1, 0, -(1 + kEps)).Normalize()));
// A concave cap. Note that the error bounds for point containment tests
// increase with the cap angle, so we need to use a larger error bound
// here. (It would be painful to do this everywhere, but this at least
// gives an example of how to compute the maximum error.)
S2Point center = GetLatLngPoint(80, 10);
S1ChordAngle radius = new(S1Angle.FromDegrees(150));
double max_error =
radius.GetS2PointConstructorMaxError() +
radius.S1AngleConstructorMaxError +
3 * S2.DoubleEpsilon; // GetLatLngPoint() error
S2Cap concave = new(center, radius);
S2Cap concave_min = new(center, radius.PlusError(-max_error));
S2Cap concave_max = new(center, radius.PlusError(max_error));
Assert.True(concave_max.Contains(GetLatLngPoint(-70, 10)));
Assert.False(concave_min.Contains(GetLatLngPoint(-70, 10)));
Assert.True(concave_max.Contains(GetLatLngPoint(-50, -170)));
Assert.False(concave_min.Contains(GetLatLngPoint(-50, -170)));
// Cap containment tests.
Assert.False(empty.Contains(xaxis));
Assert.False(empty.InteriorIntersects(xaxis));
Assert.True(full.Contains(xaxis));
Assert.True(full.InteriorIntersects(xaxis));
Assert.False(xaxis.Contains(full));
Assert.False(xaxis.InteriorIntersects(full));
Assert.True(xaxis.Contains(xaxis));
Assert.False(xaxis.InteriorIntersects(xaxis));
Assert.True(xaxis.Contains(empty));
Assert.False(xaxis.InteriorIntersects(empty));
Assert.True(hemi.Contains(tiny));
Assert.True(hemi.Contains(new S2Cap(new S2Point(1, 0, 0), S1Angle.FromRadians(S2.M_PI_4 - kEps))));
Assert.False(hemi.Contains(new S2Cap(new S2Point(1, 0, 0), S1Angle.FromRadians(S2.M_PI_4 + kEps))));
Assert.True(concave.Contains(hemi));
Assert.True(concave.InteriorIntersects(hemi.Complement()));
Assert.False(concave.Contains(S2Cap.FromCenterHeight(-concave.Center, 0.1)));
}