public void Test_GetCentroid_Polygon()
{
// GetCentroid returns the centroid multiplied by the area of the polygon.
Assert.True(S2.ApproxEquals(
new S2Point(S2.M_PI_4, S2.M_PI_4, S2.M_PI_4),
S2.GetCentroid(MakeLaxPolygonOrDie("0:0, 0:90, 90:0"))));
}
// Returns the centroid of all shapes whose dimension is maximal within the
// index, multiplied by the measure of those shapes. For example, if the
// index contains points and polylines, then the result is defined as the
// centroid of the polylines multiplied by the total length of those
// polylines. The points would be ignored when computing the centroid.
//
// The measure of a given shape is defined as follows:
//
// - For dimension 0 shapes, the measure is shape.num_edges().
// - For dimension 1 shapes, the measure is GetLength(shape).
// - For dimension 2 shapes, the measure is GetArea(shape).
//
// Note that the centroid is not unit length, so you may need to call
// Normalize() before passing it to other S2 functions. Note that this
// function returns (0, 0, 0) if the index contains no geometry.
//
// The centroid is scaled by the total measure of the shapes for two reasons:
// (1) it is cheaper to compute this way, and (2) this makes it easier to
// compute the centroid of a collection of shapes (since the individual
// centroids can simply be summed).
public static S2Point GetCentroid(S2ShapeIndex index)
{
int dim = GetDimension(index);
var centroid = S2Point.Empty;
for (int i = 0; i < index.NumShapeIds(); ++i)
{
var shape = index.Shape(i);
if (shape != null && shape.Dimension() == dim)
{
centroid += S2.GetCentroid(shape);
}
}
return(centroid);
}
public void Test_LoopTestBase_GetAreaAndCentroid()
{
Assert.Equal(S2.M_4_PI, S2.GetArea(full_));
Assert.Equal(S2Point.Empty, S2.GetCentroid(full_));
Assert2.DoubleEqual(S2.GetArea(north_hemi_), S2.M_2_PI);
Assert2.Near(S2.M_2_PI, S2.GetArea(east_hemi_), 1e-12);
// Construct spherical caps of random height, and approximate their boundary
// with closely spaces vertices. Then check that the area and centroid are
// correct.
for (int iter = 0; iter < 50; ++iter)
{
// Choose a coordinate frame for the spherical cap.
S2Testing.GetRandomFrame(out var x, out var y, out var z);
// Given two points at latitude phi and whose longitudes differ by dtheta,
// the geodesic between the two points has a maximum latitude of
// atan(tan(phi) / cos(dtheta/2)). This can be derived by positioning
// the two points at (-dtheta/2, phi) and (dtheta/2, phi).
//
// We want to position the vertices close enough together so that their
// maximum distance from the boundary of the spherical cap is kMaxDist.
// Thus we want Math.Abs(atan(tan(phi) / cos(dtheta/2)) - phi) <= kMaxDist.
const double kMaxDist = 1e-6;
double height = 2 * S2Testing.Random.RandDouble();
double phi = Math.Asin(1 - height);
double max_dtheta = 2 * Math.Acos(Math.Tan(Math.Abs(phi)) / Math.Tan(Math.Abs(phi) + kMaxDist));
max_dtheta = Math.Min(Math.PI, max_dtheta); // At least 3 vertices.
S2PointLoopSpan loop = new();
for (double theta = 0; theta < S2.M_2_PI;
theta += S2Testing.Random.RandDouble() * max_dtheta)
{
loop.Add(Math.Cos(theta) * Math.Cos(phi) * x +
Math.Sin(theta) * Math.Cos(phi) * y +
Math.Sin(phi) * z);
}
double area = S2.GetArea(loop);
S2Point centroid = S2.GetCentroid(loop);
double expected_area = S2.M_2_PI * height;
Assert.True(Math.Abs(area - expected_area) <= S2.M_2_PI * kMaxDist);
S2Point expected_centroid = expected_area * (1 - 0.5 * height) * z;
Assert.True((centroid - expected_centroid).Norm() <= 2 * kMaxDist);
}
}
public void Test_GetCentroid_Points()
{
// GetCentroid() returns the centroid multiplied by the number of points.
Assert.Equal(new S2Point(1, 1, 0),
S2.GetCentroid(MakeIndexOrDie("0:0 | 0:90 # #").Shape(0)));
}
