// Returns the centroid of the shape multiplied by the measure of the shape,
// which 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 result is not unit length, so you may need to call
// Normalize() before passing it to other S2 functions.
//
// The result is scaled by the measure defined above 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. (This requires simply summing the
// centroids of all shapes in the collection whose dimension is maximal.)
public static S2Point GetCentroid(S2Shape shape)
{
var centroid = S2Point.Empty;
S2Point[] vertices;
int dimension = shape.Dimension();
int num_chains = shape.NumChains();
for (int chain_id = 0; chain_id < num_chains; ++chain_id)
{
switch (dimension)
{
case 0:
centroid += shape.GetEdge(chain_id).V0;
break;
case 1:
GetChainVertices(shape, chain_id, out vertices);
centroid += S2PolylineMeasures.GetCentroid(vertices);
break;
default:
GetChainVertices(shape, chain_id, out vertices);
centroid += S2.GetCentroid(vertices.ToList());
break;
}
}
return(centroid);
}
public void Test_GetLengthAndCentroid_GreatCircles()
{
// Construct random great circles and divide them randomly into segments.
// Then make sure that the length and centroid are correct. Note that
// because of the way the centroid is computed, it does not matter how
// we split the great circle into segments.
for (int iter = 0; iter < 100; ++iter)
{
// Choose a coordinate frame for the great circle.
S2Testing.GetRandomFrame(out var x, out var y, out _);
var lineList = new List <S2Point>();
double theta = 0;
while (theta < S2.M_2_PI)
{
lineList.Add(Math.Cos(theta) * x + Math.Sin(theta) * y);
theta += S2Testing.Random.RandDouble();
}
// Close the circle.
lineList.Add(lineList[0]);
var line = lineList.ToArray();
S1Angle length = S2PolylineMeasures.GetLength(line);
Assert.True(Math.Abs(length.Radians - S2.M_2_PI) <= 2e-14);
S2Point centroid = S2PolylineMeasures.GetCentroid(line);
Assert.True(centroid.Norm() <= 2e-14);
}
}
// For shapes of dimension 1, returns the sum of all polyline lengths on the
// unit sphere. Otherwise returns zero. (See GetPerimeter for shapes of
// dimension 2.)
//
// All edges are modeled as spherical geodesics. The result can be converted
// to a distance on the Earth's surface (with a worst-case error of 0.562%
// near the equator) using the functions in s2earth.h.
public static S1Angle GetLength(S2Shape shape)
{
if (shape.Dimension() != 1)
{
return(S1Angle.Zero);
}
var length = S1Angle.Zero;
int num_chains = shape.NumChains();
for (int chain_id = 0; chain_id < num_chains; ++chain_id)
{
GetChainVertices(shape, chain_id, out var vertices);
length += S2PolylineMeasures.GetLength(vertices);
}
return(length);
}
