public void Test_S2_Frames()
{
var z = new S2Point(0.2, 0.5, -3.3).Normalize();
var m = S2.GetFrame(z);
Assert.True(S2.ApproxEquals(m.Col(2), z));
Assert.True(m.Col(0).IsUnitLength());
Assert.True(m.Col(1).IsUnitLength());
Assert2.DoubleEqual(m.Det(), 1);
Assert.True(S2.ApproxEquals(S2.ToFrame(m, m.Col(0)), new(1, 0, 0)));
Assert.True(S2.ApproxEquals(S2.ToFrame(m, m.Col(1)), new(0, 1, 0)));
Assert.True(S2.ApproxEquals(S2.ToFrame(m, m.Col(2)), new(0, 0, 1)));
Assert.True(S2.ApproxEquals(S2.FromFrame(m, new(1, 0, 0)), m.Col(0)));
Assert.True(S2.ApproxEquals(S2.FromFrame(m, new(0, 1, 0)), m.Col(1)));
Assert.True(S2.ApproxEquals(S2.FromFrame(m, new(0, 0, 1)), m.Col(2)));
}
public void AddPoints(S2Cap index_cap, int num_points, TestIndex index)
{
int sqrt_num_points = (int)Math.Ceiling(Math.Sqrt(num_points));
S2PointVector3 frame = S2Testing.GetRandomFrameAt(index_cap.Center);
double radius = index_cap.RadiusAngle().Radians;
double spacing = 2 * radius / sqrt_num_points;
for (int i = 0; i < sqrt_num_points; ++i)
{
for (int j = 0; j < sqrt_num_points; ++j)
{
S2Point point = new(Math.Tan((i + 0.5) * spacing - radius),
Math.Tan((j + 0.5) * spacing - radius), 1.0);
index.Add(S2.FromFrame(frame, point.Normalize()),
i * sqrt_num_points + j);
}
}
}