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// Copyright 2005 Google Inc. All Rights Reserved.
#include "s2cap.h"
#include "base/commandlineflags.h"
#include "base/logging.h"
#include "testing/base/public/gunit.h"
#include "s2.h"
#include "s2cell.h"
#include "s2latlng.h"
#include "s2latlngrect.h"
static S2Point GetLatLngPoint(double lat_degrees, double lng_degrees) {
return S2LatLng::FromDegrees(lat_degrees, lng_degrees).ToPoint();
}
// About 9 times the double-precision roundoff relative error.
static const double kEps = 1e-15;
TEST(S2Cap, Basic) {
// Test basic properties of empty and full caps.
S2Cap empty = S2Cap::Empty();
S2Cap full = S2Cap::Full();
EXPECT_TRUE(empty.is_valid());
EXPECT_TRUE(empty.is_empty());
EXPECT_TRUE(empty.Complement().is_full());
EXPECT_TRUE(full.is_valid());
EXPECT_TRUE(full.is_full());
EXPECT_TRUE(full.Complement().is_empty());
EXPECT_EQ(2, full.height());
EXPECT_DOUBLE_EQ(180.0, full.angle().degrees());
// Check that the default S2Cap is identical to Empty().
S2Cap default_empty;
EXPECT_TRUE(default_empty.is_valid());
EXPECT_TRUE(default_empty.is_empty());
EXPECT_EQ(empty.axis(), default_empty.axis());
EXPECT_EQ(empty.height(), default_empty.height());
// Containment and intersection of empty and full caps.
EXPECT_TRUE(empty.Contains(empty));
EXPECT_TRUE(full.Contains(empty));
EXPECT_TRUE(full.Contains(full));
EXPECT_FALSE(empty.InteriorIntersects(empty));
EXPECT_TRUE(full.InteriorIntersects(full));
EXPECT_FALSE(full.InteriorIntersects(empty));
// Singleton cap containing the x-axis.
S2Cap xaxis = S2Cap::FromAxisHeight(S2Point(1, 0, 0), 0);
EXPECT_TRUE(xaxis.Contains(S2Point(1, 0, 0)));
EXPECT_TRUE(xaxis.VirtualContainsPoint(S2Point(1, 0, 0)));
EXPECT_FALSE(xaxis.Contains(S2Point(1, 1e-20, 0)));
EXPECT_FALSE(xaxis.VirtualContainsPoint(S2Point(1, 1e-20, 0)));
EXPECT_EQ(0, xaxis.angle().radians());
// Singleton cap containing the y-axis.
S2Cap yaxis = S2Cap::FromAxisAngle(S2Point(0, 1, 0), S1Angle::Radians(0));
EXPECT_FALSE(yaxis.Contains(xaxis.axis()));
EXPECT_EQ(0, xaxis.height());
// Check that the complement of a singleton cap is the full cap.
S2Cap xcomp = xaxis.Complement();
EXPECT_TRUE(xcomp.is_valid());
EXPECT_TRUE(xcomp.is_full());
EXPECT_TRUE(xcomp.Contains(xaxis.axis()));
// Check that the complement of the complement is *not* the original.
EXPECT_TRUE(xcomp.Complement().is_valid());
EXPECT_TRUE(xcomp.Complement().is_empty());
EXPECT_FALSE(xcomp.Complement().Contains(xaxis.axis()));
// 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.
static const double kTinyRad = 1e-10;
S2Cap tiny = S2Cap::FromAxisAngle(S2Point(1, 2, 3).Normalize(),
S1Angle::Radians(kTinyRad));
S2Point tangent = tiny.axis().CrossProd(S2Point(3, 2, 1)).Normalize();
EXPECT_TRUE(tiny.Contains(tiny.axis() + 0.99 * kTinyRad * tangent));
EXPECT_FALSE(tiny.Contains(tiny.axis() + 1.01 * kTinyRad * tangent));
// Basic tests on a hemispherical cap.
S2Cap hemi = S2Cap::FromAxisHeight(S2Point(1, 0, 1).Normalize(), 1);
EXPECT_EQ(-hemi.axis(), S2Point(hemi.Complement().axis()));
EXPECT_EQ(1, hemi.Complement().height());
EXPECT_TRUE(hemi.Contains(S2Point(1, 0, 0)));
EXPECT_FALSE(hemi.Complement().Contains(S2Point(1, 0, 0)));
EXPECT_TRUE(hemi.Contains(S2Point(1, 0, -(1-kEps)).Normalize()));
EXPECT_FALSE(hemi.InteriorContains(S2Point(1, 0, -(1+kEps)).Normalize()));
// A concave cap.
S2Cap concave = S2Cap::FromAxisAngle(GetLatLngPoint(80, 10),
S1Angle::Degrees(150));
EXPECT_TRUE(concave.Contains(GetLatLngPoint(-70 * (1 - kEps), 10)));
EXPECT_FALSE(concave.Contains(GetLatLngPoint(-70 * (1 + kEps), 10)));
EXPECT_TRUE(concave.Contains(GetLatLngPoint(-50 * (1 - kEps), -170)));
EXPECT_FALSE(concave.Contains(GetLatLngPoint(-50 * (1 + kEps), -170)));
// Cap containment tests.
EXPECT_FALSE(empty.Contains(xaxis));
EXPECT_FALSE(empty.InteriorIntersects(xaxis));
EXPECT_TRUE(full.Contains(xaxis));
EXPECT_TRUE(full.InteriorIntersects(xaxis));
EXPECT_FALSE(xaxis.Contains(full));
EXPECT_FALSE(xaxis.InteriorIntersects(full));
EXPECT_TRUE(xaxis.Contains(xaxis));
EXPECT_FALSE(xaxis.InteriorIntersects(xaxis));
EXPECT_TRUE(xaxis.Contains(empty));
EXPECT_FALSE(xaxis.InteriorIntersects(empty));
EXPECT_TRUE(hemi.Contains(tiny));
EXPECT_TRUE(hemi.Contains(
S2Cap::FromAxisAngle(S2Point(1, 0, 0),
S1Angle::Radians(M_PI_4 - kEps))));
EXPECT_FALSE(hemi.Contains(
S2Cap::FromAxisAngle(S2Point(1, 0, 0),
S1Angle::Radians(M_PI_4 + kEps))));
EXPECT_TRUE(concave.Contains(hemi));
EXPECT_TRUE(concave.InteriorIntersects(hemi.Complement()));
EXPECT_FALSE(concave.Contains(S2Cap::FromAxisHeight(-concave.axis(), 0.1)));
}
TEST(S2Cap, GetRectBound) {
// Empty and full caps.
EXPECT_TRUE(S2Cap::Empty().GetRectBound().is_empty());
EXPECT_TRUE(S2Cap::Full().GetRectBound().is_full());
static const double kDegreeEps = 1e-13;
// Maximum allowable error for latitudes and longitudes measured in
// degrees. (EXPECT_DOUBLE_EQ isn't sufficient.)
// Cap that includes the south pole.
S2LatLngRect rect = S2Cap::FromAxisAngle(GetLatLngPoint(-45, 57),
S1Angle::Degrees(50)).GetRectBound();
EXPECT_NEAR(rect.lat_lo().degrees(), -90, kDegreeEps);
EXPECT_NEAR(rect.lat_hi().degrees(), 5, kDegreeEps);
EXPECT_TRUE(rect.lng().is_full());
// Cap that is tangent to the north pole.
rect = S2Cap::FromAxisAngle(S2Point(1, 0, 1).Normalize(),
S1Angle::Radians(M_PI_4 + 1e-16)).GetRectBound();
EXPECT_NEAR(rect.lat().lo(), 0, kEps);
EXPECT_NEAR(rect.lat().hi(), M_PI_2, kEps);
EXPECT_TRUE(rect.lng().is_full());
rect = S2Cap::FromAxisAngle(S2Point(1, 0, 1).Normalize(),
S1Angle::Degrees(45 + 5e-15)).GetRectBound();
EXPECT_NEAR(rect.lat_lo().degrees(), 0, kDegreeEps);
EXPECT_NEAR(rect.lat_hi().degrees(), 90, kDegreeEps);
EXPECT_TRUE(rect.lng().is_full());
// The eastern hemisphere.
rect = S2Cap::FromAxisAngle(S2Point(0, 1, 0),
S1Angle::Radians(M_PI_2 + 2e-16)).GetRectBound();
EXPECT_NEAR(rect.lat_lo().degrees(), -90, kDegreeEps);
EXPECT_NEAR(rect.lat_hi().degrees(), 90, kDegreeEps);
EXPECT_TRUE(rect.lng().is_full());
// A cap centered on the equator.
rect = S2Cap::FromAxisAngle(GetLatLngPoint(0, 50),
S1Angle::Degrees(20)).GetRectBound();
EXPECT_NEAR(rect.lat_lo().degrees(), -20, kDegreeEps);
EXPECT_NEAR(rect.lat_hi().degrees(), 20, kDegreeEps);
EXPECT_NEAR(rect.lng_lo().degrees(), 30, kDegreeEps);
EXPECT_NEAR(rect.lng_hi().degrees(), 70, kDegreeEps);
// A cap centered on the north pole.
rect = S2Cap::FromAxisAngle(GetLatLngPoint(90, 123),
S1Angle::Degrees(10)).GetRectBound();
EXPECT_NEAR(rect.lat_lo().degrees(), 80, kDegreeEps);
EXPECT_NEAR(rect.lat_hi().degrees(), 90, kDegreeEps);
EXPECT_TRUE(rect.lng().is_full());
}
TEST(S2Cap, S2CellMethods) {
// For each cube face, we construct some cells on
// that face and some caps whose positions are relative to that face,
// and then check for the expected intersection/containment results.
// The distance from the center of a face to one of its vertices.
static const double kFaceRadius = atan(sqrt(2));
for (int face = 0; face < 6; ++face) {
// The cell consisting of the entire face.
S2Cell root_cell = S2Cell::FromFacePosLevel(face, 0, 0);
// A leaf cell at the midpoint of the v=1 edge.
S2Cell edge_cell(S2::FaceUVtoXYZ(face, 0, 1 - kEps));
// A leaf cell at the u=1, v=1 corner.
S2Cell corner_cell(S2::FaceUVtoXYZ(face, 1 - kEps, 1 - kEps));
// Quick check for full and empty caps.
EXPECT_TRUE(S2Cap::Full().Contains(root_cell));
EXPECT_FALSE(S2Cap::Empty().MayIntersect(root_cell));
// Check intersections with the bounding caps of the leaf cells that are
// adjacent to 'corner_cell' along the Hilbert curve. Because this corner
// is at (u=1,v=1), the curve stays locally within the same cube face.
S2CellId first = corner_cell.id().advance(-3);
S2CellId last = corner_cell.id().advance(4);
for (S2CellId id = first; id < last; id = id.next()) {
S2Cell cell(id);
EXPECT_EQ(id == corner_cell.id(),
cell.GetCapBound().Contains(corner_cell));
EXPECT_EQ(id.parent().contains(corner_cell.id()),
cell.GetCapBound().MayIntersect(corner_cell));
}
int anti_face = (face + 3) % 6; // Opposite face.
for (int cap_face = 0; cap_face < 6; ++cap_face) {
// A cap that barely contains all of 'cap_face'.
S2Point center = S2::GetNorm(cap_face);
S2Cap covering = S2Cap::FromAxisAngle(
center, S1Angle::Radians(kFaceRadius + kEps));
EXPECT_EQ(cap_face == face, covering.Contains(root_cell));
EXPECT_EQ(cap_face != anti_face, covering.MayIntersect(root_cell));
EXPECT_EQ(center.DotProd(edge_cell.GetCenter()) > 0.1,
covering.Contains(edge_cell));
EXPECT_EQ(covering.MayIntersect(edge_cell), covering.Contains(edge_cell));
EXPECT_EQ(cap_face == face, covering.Contains(corner_cell));
EXPECT_EQ(center.DotProd(corner_cell.GetCenter()) > 0,
covering.MayIntersect(corner_cell));
// A cap that barely intersects the edges of 'cap_face'.
S2Cap bulging = S2Cap::FromAxisAngle(
center, S1Angle::Radians(M_PI_4 + kEps));
EXPECT_FALSE(bulging.Contains(root_cell));
EXPECT_EQ(cap_face != anti_face, bulging.MayIntersect(root_cell));
EXPECT_EQ(cap_face == face, bulging.Contains(edge_cell));
EXPECT_EQ(center.DotProd(edge_cell.GetCenter()) > 0.1,
bulging.MayIntersect(edge_cell));
EXPECT_FALSE(bulging.Contains(corner_cell));
EXPECT_FALSE(bulging.MayIntersect(corner_cell));
// A singleton cap.
S2Cap singleton = S2Cap::FromAxisAngle(center, S1Angle::Radians(0));
EXPECT_EQ(cap_face == face, singleton.MayIntersect(root_cell));
EXPECT_FALSE(singleton.MayIntersect(edge_cell));
EXPECT_FALSE(singleton.MayIntersect(corner_cell));
}
}
}
TEST(S2Cap, Expanded) {
EXPECT_TRUE(S2Cap::Empty().Expanded(S1Angle::Radians(2)).is_empty());
EXPECT_TRUE(S2Cap::Full().Expanded(S1Angle::Radians(2)).is_full());
S2Cap cap50 = S2Cap::FromAxisAngle(S2Point(1, 0, 0), S1Angle::Degrees(50));
S2Cap cap51 = S2Cap::FromAxisAngle(S2Point(1, 0, 0), S1Angle::Degrees(51));
EXPECT_TRUE(cap50.Expanded(S1Angle::Radians(0)).ApproxEquals(cap50));
EXPECT_TRUE(cap50.Expanded(S1Angle::Degrees(1)).ApproxEquals(cap51));
EXPECT_FALSE(cap50.Expanded(S1Angle::Degrees(129.99)).is_full());
EXPECT_TRUE(cap50.Expanded(S1Angle::Degrees(130.01)).is_full());
}
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