func TestCapContains(t *testing.T) {
tests := []struct {
c1, c2 Cap
want bool
}{
{empty, empty, true},
{full, empty, true},
{full, full, true},
{empty, xAxis, false},
{full, xAxis, true},
{xAxis, full, false},
{xAxis, xAxis, true},
{xAxis, empty, true},
{hemi, tiny, true},
{hemi, CapFromCenterAngle(xAxisPt, s1.Angle(math.Pi/4-epsilon)), true},
{hemi, CapFromCenterAngle(xAxisPt, s1.Angle(math.Pi/4+epsilon)), false},
{concave, hemi, true},
{concave, CapFromCenterHeight(Point{concave.center.Mul(-1.0)}, 0.1), false},
}
for _, test := range tests {
if got := test.c1.Contains(test.c2); got != test.want {
t.Errorf("%v.Contains(%v) = %t; want %t", test.c1, test.c2, got, test.want)
}
}
}
func TestCapExpanded(t *testing.T) {
cap50 := CapFromCenterAngle(xAxisPt, 50.0*s1.Degree)
cap51 := CapFromCenterAngle(xAxisPt, 51.0*s1.Degree)
if !empty.Expanded(s1.Angle(fullHeight)).IsEmpty() {
t.Error("Expanding empty cap should return an empty cap")
}
if !full.Expanded(s1.Angle(fullHeight)).IsFull() {
t.Error("Expanding a full cap should return an full cap")
}
if !cap50.Expanded(0).ApproxEqual(cap50) {
t.Error("Expanding a cap by 0° should be equal to the original")
}
if !cap50.Expanded(1 * s1.Degree).ApproxEqual(cap51) {
t.Error("Expanding 50° by 1° should equal the 51° cap")
}
if cap50.Expanded(129.99 * s1.Degree).IsFull() {
t.Error("Expanding 50° by 129.99° should not give a full cap")
}
if !cap50.Expanded(130.01 * s1.Degree).IsFull() {
t.Error("Expanding 50° by 130.01° should give a full cap")
}
}
// This is named GetDistance() in the C++ API.
func (x Point) DistanceToEdgeWithNormal(a, b, a_cross_b Point) s1.Angle {
// There are three cases. If X is located in the spherical wedge
// defined by A, B, and the axis A x B, then the closest point is on
// the segment AB. Otherwise the closest point is either A or B; the
// dividing line between these two cases is the great circle passing
// through (A x B) and the midpoint of AB.
if CCW(a_cross_b, a, x) && CCW(x, b, a_cross_b) {
// The closest point to X lies on the segment AB. We compute
// the distance to the corresponding great circle. The result
// is accurate for small distances but not necessarily for
// large distances (approaching Pi/2).
//
// TODO: sanity check a != b
sin_dist := math.Abs(x.Dot(a_cross_b.Vector)) / a_cross_b.Norm()
return s1.Angle(math.Asin(math.Min(1.0, sin_dist)))
}
// Otherwise, the closest point is either A or B. The cheapest method is
// just to compute the minimum of the two linear (as opposed to spherical)
// distances and convert the result to an angle. Again, this method is
// accurate for small but not large distances (approaching Pi).
xa := x.Sub(a.Vector).Norm2()
xb := x.Sub(b.Vector).Norm2()
linear_dist2 := math.Min(xa, xb)
return s1.Angle(2 * math.Asin(math.Min(1.0, 0.5*math.Sqrt(linear_dist2))))
}
// Radius returns the cap's radius.
func (c Cap) Radius() s1.Angle {
if c.IsEmpty() {
return s1.Angle(emptyHeight)
}
// This could also be computed as acos(1 - height_), but the following
// formula is much more accurate when the cap height is small. It
// follows from the relationship h = 1 - cos(r) = 2 sin^2(r/2).
return s1.Angle(2 * math.Asin(math.Sqrt(0.5*c.height)))
}
func rectFromDegrees(latLo, lngLo, latHi, lngHi float64) Rect {
// Convenience method to construct a rectangle. This method is
// intentionally *not* in the S2LatLngRect interface because the
// argument order is ambiguous, but is fine for the test.
return Rect{
Lat: r1.Interval{
Lo: (s1.Angle(latLo) * s1.Degree).Radians(),
Hi: (s1.Angle(latHi) * s1.Degree).Radians(),
},
Lng: s1.IntervalFromEndpoints(
(s1.Angle(lngLo) * s1.Degree).Radians(),
(s1.Angle(lngHi) * s1.Degree).Radians(),
),
}
}
func randomEdgeCrossingCap(maxLengthMeters float64, s2cap Cap) Edge {
center := samplePoint(s2cap)
edgeCap := CapFromCenterAngle(center, s1.Angle(maxLengthMeters/kEarthRadiusMeters/2))
p0 := samplePoint(edgeCap)
p1 := samplePoint(edgeCap)
return Edge{p0, p1}
}
func Perturb(x Point, maxPerturb float64) Point {
// Perturb "x" randomly within the radius of maxPerturb.
if maxPerturb == 0 {
return x
}
s2cap := CapFromCenterAngle(Point{x.Normalize()}, s1.Angle(maxPerturb))
return samplePoint(s2cap)
}
// Distance returns the angle between two LatLngs.
func (ll LatLng) Distance(ll2 LatLng) s1.Angle {
// Haversine formula, as used in C++ S2LatLng::GetDistance.
lat1, lat2 := ll.Lat.Radians(), ll2.Lat.Radians()
lng1, lng2 := ll.Lng.Radians(), ll2.Lng.Radians()
dlat := math.Sin(0.5 * (lat2 - lat1))
dlng := math.Sin(0.5 * (lng2 - lng1))
x := dlat*dlat + dlng*dlng*math.Cos(lat1)*math.Cos(lat2)
return s1.Angle(2*math.Atan2(math.Sqrt(x), math.Sqrt(math.Max(0, 1-x)))) * s1.Radian
}
func EdgeInterpolate(t float64, a, b Point) Point {
if t == 0 {
return a
}
if t == 1 {
return b
}
ab := a.Angle(b.Vector)
return EdgeInterpolateAtDistance(s1.Angle(t)*ab, a, b, ab)
}
func TestRadiusToHeight(t *testing.T) {
tests := []struct {
got s1.Angle
want float64
}{
// Above/below boundary checks.
{s1.Angle(-0.5), emptyHeight},
{s1.Angle(0), 0},
{s1.Angle(math.Pi), fullHeight},
{s1.Angle(2 * math.Pi), fullHeight},
// Degree tests.
{-7.0 * s1.Degree, emptyHeight},
{-0.0 * s1.Degree, 0},
{0.0 * s1.Degree, 0},
{12.0 * s1.Degree, 0.02185239926619},
{30.0 * s1.Degree, 0.13397459621556},
{45.0 * s1.Degree, 0.29289321881345},
{90.0 * s1.Degree, 1.0},
{179.99 * s1.Degree, 1.99999998476912},
{180.0 * s1.Degree, fullHeight},
{270.0 * s1.Degree, fullHeight},
// Radians tests.
{-1.0 * s1.Radian, emptyHeight},
{-0.0 * s1.Radian, 0},
{0.0 * s1.Radian, 0},
{1.0 * s1.Radian, 0.45969769413186},
{math.Pi / 2.0 * s1.Radian, 1.0},
{2.0 * s1.Radian, 1.41614683654714},
{3.0 * s1.Radian, 1.98999249660044},
{math.Pi * s1.Radian, fullHeight},
{4.0 * s1.Radian, fullHeight},
}
for _, test := range tests {
// float64Eq comes from s2latlng_test.go
if got := radiusToHeight(test.got); !float64Eq(got, test.want) {
t.Errorf("radiusToHeight(%v) = %v; want %v", test.got, got, test.want)
}
}
}
func (r Rect) CapBound() Cap {
// We consider two possible bounding caps, one whose axis passes
// through the center of the lat-lng rectangle and one whose axis
// is the north or south pole. We return the smaller of the two caps.
if r.IsEmpty() {
return EmptyCap()
}
var poleZ, poleAngle float64
// var poleAngle s1.Angle
if r.Lat.Lo+r.Lat.Hi < 0 {
// South pole axis yields smaller cap.
poleZ = -1
poleAngle = math.Pi/2 + r.Lat.Hi
} else {
poleZ = 1
poleAngle = math.Pi/2 - r.Lat.Lo
}
poleCap := CapFromCenterAngle(PointFromCoords(0, 0, poleZ), s1.Angle(poleAngle))
// For bounding rectangles that span 180 degrees or less in longitude,
// the maximum cap size is achieved at one of the rectangle vertices.
// For rectangles that are larger than 180 degrees, we punt and always
// return a bounding cap centered at one of the two poles.
lngSpan := r.Lng.Hi - r.Lng.Lo
if math.Remainder(lngSpan, 2*math.Pi) >= 0 {
if lngSpan < 2*math.Pi {
midCap := CapFromCenterAngle(PointFromLatLng(r.Center()), s1.Angle(0))
for k := 0; k < 4; k++ {
midCap.AddPoint(PointFromLatLng(r.Vertex(k)))
}
if midCap.height < poleCap.height {
return midCap
}
}
}
return poleCap
}
// Size returns the size of the Rect.
func (r Rect) Size() LatLng {
return LatLng{s1.Angle(r.Lat.Length()) * s1.Radian, s1.Angle(r.Lng.Length()) * s1.Radian}
}
// Center returns the center of the rectangle.
func (r Rect) Center() LatLng {
return LatLng{s1.Angle(r.Lat.Center()) * s1.Radian, s1.Angle(r.Lng.Center()) * s1.Radian}
}
// Hi returns the other corner of the rectangle.
func (r Rect) Hi() LatLng {
return LatLng{s1.Angle(r.Lat.Hi) * s1.Radian, s1.Angle(r.Lng.Hi) * s1.Radian}
}
// Lo returns one corner of the rectangle.
func (r Rect) Lo() LatLng {
return LatLng{s1.Angle(r.Lat.Lo) * s1.Radian, s1.Angle(r.Lng.Lo) * s1.Radian}
}
func GenerateRandomEarthEdges(edgeLengthMetersMax, capSpanMeters float64, numEdges int, edges *[]Edge) {
s2cap := CapFromCenterAngle(randomPoint(), s1.Angle(capSpanMeters/kEarthRadiusMeters))
for i := 0; i < numEdges; i++ {
*edges = append(*edges, randomEdgeCrossingCap(edgeLengthMetersMax, s2cap))
}
}
// LatLngFromDegrees returns a LatLng for the coordinates given in degrees.
func LatLngFromDegrees(lat, lng float64) LatLng {
return LatLng{s1.Angle(lat) * s1.Degree, s1.Angle(lng) * s1.Degree}
}
func LatLngFromRadians(lat_radians, lng_radians float64) LatLng {
return LatLng{s1.Angle(lat_radians), s1.Angle(lng_radians)}
}
func latitude(p Point) s1.Angle {
return s1.Angle(math.Atan2(p.Z, math.Sqrt(p.X*p.X+p.Y*p.Y))) * s1.Radian
}
func longitude(p Point) s1.Angle {
return s1.Angle(math.Atan2(p.Y, p.X)) * s1.Radian
}
func runTestCase(t *testing.T, test TestCase) bool {
for iter := 0; iter < 250; iter++ {
options := PolygonBuilderOptions{
edge_splice_fraction: .866,
validate: false,
vertex_merge_radius: s1.Angle(0),
}
options.undirected_edges = evalTristate(test.undirectedEdges)
options.xor_edges = evalTristate(test.xorEdges)
minMerge := (s1.Angle(test.minMerge) * s1.Degree).Radians()
maxMerge := (s1.Angle(test.maxMerge) * s1.Degree).Radians()
minSin := math.Sin((s1.Angle(test.minVertexAngle) * s1.Degree).Radians())
// Half of the time we allow edges to be split into smaller
// pieces (up to 5 levels, i.e. up to 32 pieces).
maxSplits := max(0, rand.Intn(10)-4)
if !test.canSplit {
maxSplits = 0
}
// We choose randomly among two different values for the edge
// fraction, just to exercise that code.
edgeFraction := options.edge_splice_fraction
var vertexMerge, maxPerturb float64
if minSin < edgeFraction && oneIn(2) {
edgeFraction = minSin
}
if maxSplits == 0 && oneIn(2) {
// Turn off edge splicing completely.
edgeFraction = 0
vertexMerge = minMerge + smallFraction()*(maxMerge-minMerge)
maxPerturb = 0.5 * math.Min(vertexMerge-minMerge, maxMerge-vertexMerge)
} else {
// Splice edges. These bounds also assume that edges
// may be split.
//
// If edges are actually split, need to bump up the
// minimum merge radius to ensure that split edges
// in opposite directions are unified. Otherwise
// there will be tiny degenerate loops created.
if maxSplits > 0 {
minMerge += 1e-15
}
minMerge /= edgeFraction
maxMerge *= minSin
if maxMerge < minMerge {
t.Errorf("%v < %v", maxMerge, minMerge)
}
vertexMerge = minMerge + smallFraction()*(maxMerge-minMerge)
maxPerturb = 0.5 * math.Min(edgeFraction*(vertexMerge-minMerge), maxMerge-vertexMerge)
}
// We can perturb by any amount up to the maximum, but choosing
// a lower maximum decreases the error bounds when checking the
// output.
maxPerturb *= smallFraction()
// This is the minimum length of a split edge to prevent
// unexpected merging and/or splicing.
minEdge := minMerge + (vertexMerge+2*maxPerturb)/minSin
options.vertex_merge_radius = s1.Angle(vertexMerge)
options.edge_splice_fraction = edgeFraction
options.validate = true
builder := NewPolygonBuilder(options)
// On each iteration we randomly rotate the test case around
// the sphere. This causes the PolygonBuilder to choose
// different first edges when trying to build loops.
x, y, z := randomFrame()
m := r3.MatrixFromCols(x.Vector, y.Vector, z.Vector)
for _, chain := range test.chainsIn {
addChain(chain, m, maxSplits, maxPerturb, minEdge, &builder)
}
var loops []*Loop
var unusedEdges []Edge
if test.xorEdges < 0 {
builder.AssembleLoops(&loops, &unusedEdges)
} else {
var polygon Polygon
builder.AssemblePolygon(&polygon, &unusedEdges)
polygon.Release(&loops)
}
expected := []*Loop{}
for _, str := range test.loopsOut {
if str != "" {
vertices := getVertices(str, m)
expected = append(expected, NewLoopFromPath(vertices))
}
}
// We assume that the vertex locations in the expected output
// polygon are separated from the corresponding vertex
// locations in the input edges by at most half of the
// minimum merge radius. Essentially this means that the
// expected output vertices should be near the centroid of the
// various input vertices.
//
// If any edges were split, we need to allow a bit more error
// due to inaccuracies in the interpolated positions.
// Similarly, if any vertices were perturbed, we need to bump
// up the error to allow for numerical errors in the actual
// perturbation.
maxError := 0.5*minMerge + maxPerturb
if maxSplits > 0 || maxPerturb > 0 {
maxError += 1e-15
}
ok0 := findMissingLoops(loops, expected, m, maxSplits, maxError, "Actual")
ok1 := findMissingLoops(expected, loops, m, maxSplits, maxError, "Expected")
ok2 := unexpectedUnusedEdgeCount(len(unusedEdges), test.numUnusedEdges, maxSplits)
if ok0 || ok1 || ok2 {
// We found a problem.
dumpUnusedEdges(unusedEdges, m, test.numUnusedEdges)
fmt.Printf(`During iteration %d:
undirected: %v
xor: %v
maxSplits: %d
maxPerturb: %.6g
vertexMergeRadius: %.6g
edgeSpliceFraction: %.6g
minEdge: %.6g
maxError: %.6g
`, iter, options.undirected_edges, options.xor_edges, maxSplits,
s1.Angle(maxPerturb).Degrees(),
options.vertex_merge_radius.Degrees(),
options.edge_splice_fraction,
s1.Angle(minEdge).Degrees(),
s1.Angle(maxError).Degrees())
return false
}
}
return true
}
var (
empty = EmptyCap()
full = FullCap()
defaultCap = EmptyCap()
xAxisPt = PointFromCoords(1, 0, 0)
yAxisPt = PointFromCoords(0, 1, 0)
xAxis = CapFromPoint(xAxisPt)
yAxis = CapFromPoint(yAxisPt)
xComp = xAxis.Complement()
hemi = CapFromCenterHeight(Point{PointFromCoords(1, 0, 1).Normalize()}, 1)
concave = CapFromCenterAngle(PointFromLatLng(LatLngFromDegrees(80, 10)),
s1.Angle(150.0)*s1.Degree)
tiny = CapFromCenterAngle(Point{PointFromCoords(1, 2, 3).Normalize()},
s1.Angle(tinyRad))
)
func TestCapBasicEmptyFullValid(t *testing.T) {
tests := []struct {
got Cap
empty, full, valid bool
}{
{Cap{}, false, false, false},
{empty, true, false, true},
{empty.Complement(), false, true, true},
{full, false, true, true},
{full.Complement(), true, false, true},
lastParent = parent
}
count := 0
for j := 0; j < child.NumVertices(); j++ {
if _, ok := vertices[*child.vertex(j)]; ok {
count++
}
}
if count > 1 {
return false
}
}
return true
}
var intersectionTolerance = s1.Angle(1.5e-15)
func (p *Polygon) InitToIntersection(a, b *Polygon) {
p.InitToIntersectionSloppy(a, b, intersectionTolerance)
}
func (p *Polygon) InitToIntersectionSloppy(a, b *Polygon, vertexMergeRadius s1.Angle) {
if !a.bound.Intersects(b.bound) {
return
}
// We want the boundary of A clipped to the interior of B,
// plus the boundary of B clipped to the interior of A,
// plus one copy of any directed edges that are in both boundaries.
options := DIRECTED_XOR()
options.vertex_merge_radius = vertexMergeRadius
// Angle returns the angle between v and ov.
func (v Vector) Angle(ov Vector) s1.Angle {
return s1.Angle(math.Atan2(v.Cross(ov).Norm(), v.Dot(ov))) * s1.Radian
}