Grand test fixup (#138)

* start fixing up tests

* fix up tests + automate with drone

* fiddle with linting

* messing about with drone.yml

* some more fiddling

* hmmm

* add cache

* add vendor directory

* verbose

* ci updates

* update some little things

* update sig

1 files changed, 519 insertions, 0 deletions

diff --git a/vendor/github.com/golang/geo/s2/cap.go b/vendor/github.com/golang/geo/s2/cap.go
new file mode 100644
index 000000000..c4fb2e1e0
--- /dev/null
+++ b/vendor/github.com/golang/geo/s2/cap.go
@@ -0,0 +1,519 @@
+// Copyright 2014 Google Inc. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package s2
+
+import (
+	"fmt"
+	"io"
+	"math"
+
+	"github.com/golang/geo/r1"
+	"github.com/golang/geo/s1"
+)
+
+var (
+	// centerPoint is the default center for Caps
+	centerPoint = PointFromCoords(1.0, 0, 0)
+)
+
+// Cap represents a disc-shaped region defined by a center and radius.
+// Technically this shape is called a "spherical cap" (rather than disc)
+// because it is not planar; the cap represents a portion of the sphere that
+// has been cut off by a plane. The boundary of the cap is the circle defined
+// by the intersection of the sphere and the plane. For containment purposes,
+// the cap is a closed set, i.e. it contains its boundary.
+//
+// For the most part, you can use a spherical cap wherever you would use a
+// disc in planar geometry. The radius of the cap is measured along the
+// surface of the sphere (rather than the straight-line distance through the
+// interior). Thus a cap of radius π/2 is a hemisphere, and a cap of radius
+// π covers the entire sphere.
+//
+// The center is a point on the surface of the unit sphere. (Hence the need for
+// it to be of unit length.)
+//
+// A cap can also be defined by its center point and height. The height is the
+// distance from the center point to the cutoff plane. There is also support for
+// "empty" and "full" caps, which contain no points and all points respectively.
+//
+// Here are some useful relationships between the cap height (h), the cap
+// radius (r), the maximum chord length from the cap's center (d), and the
+// radius of cap's base (a).
+//
+//     h = 1 - cos(r)
+//       = 2 * sin^2(r/2)
+//   d^2 = 2 * h
+//       = a^2 + h^2
+//
+// The zero value of Cap is an invalid cap. Use EmptyCap to get a valid empty cap.
+type Cap struct {
+	center Point
+	radius s1.ChordAngle
+}
+
+// CapFromPoint constructs a cap containing a single point.
+func CapFromPoint(p Point) Cap {
+	return CapFromCenterChordAngle(p, 0)
+}
+
+// CapFromCenterAngle constructs a cap with the given center and angle.
+func CapFromCenterAngle(center Point, angle s1.Angle) Cap {
+	return CapFromCenterChordAngle(center, s1.ChordAngleFromAngle(angle))
+}
+
+// CapFromCenterChordAngle constructs a cap where the angle is expressed as an
+// s1.ChordAngle. This constructor is more efficient than using an s1.Angle.
+func CapFromCenterChordAngle(center Point, radius s1.ChordAngle) Cap {
+	return Cap{
+		center: center,
+		radius: radius,
+	}
+}
+
+// CapFromCenterHeight constructs a cap with the given center and height. A
+// negative height yields an empty cap; a height of 2 or more yields a full cap.
+// The center should be unit length.
+func CapFromCenterHeight(center Point, height float64) Cap {
+	return CapFromCenterChordAngle(center, s1.ChordAngleFromSquaredLength(2*height))
+}
+
+// CapFromCenterArea constructs a cap with the given center and surface area.
+// Note that the area can also be interpreted as the solid angle subtended by the
+// cap (because the sphere has unit radius). A negative area yields an empty cap;
+// an area of 4*π or more yields a full cap.
+func CapFromCenterArea(center Point, area float64) Cap {
+	return CapFromCenterChordAngle(center, s1.ChordAngleFromSquaredLength(area/math.Pi))
+}
+
+// EmptyCap returns a cap that contains no points.
+func EmptyCap() Cap {
+	return CapFromCenterChordAngle(centerPoint, s1.NegativeChordAngle)
+}
+
+// FullCap returns a cap that contains all points.
+func FullCap() Cap {
+	return CapFromCenterChordAngle(centerPoint, s1.StraightChordAngle)
+}
+
+// IsValid reports whether the Cap is considered valid.
+func (c Cap) IsValid() bool {
+	return c.center.Vector.IsUnit() && c.radius <= s1.StraightChordAngle
+}
+
+// IsEmpty reports whether the cap is empty, i.e. it contains no points.
+func (c Cap) IsEmpty() bool {
+	return c.radius < 0
+}
+
+// IsFull reports whether the cap is full, i.e. it contains all points.
+func (c Cap) IsFull() bool {
+	return c.radius == s1.StraightChordAngle
+}
+
+// Center returns the cap's center point.
+func (c Cap) Center() Point {
+	return c.center
+}
+
+// Height returns the height of the cap. This is the distance from the center
+// point to the cutoff plane.
+func (c Cap) Height() float64 {
+	return float64(0.5 * c.radius)
+}
+
+// Radius returns the cap radius as an s1.Angle. (Note that the cap angle
+// is stored internally as a ChordAngle, so this method requires a trigonometric
+// operation and may yield a slightly different result than the value passed
+// to CapFromCenterAngle).
+func (c Cap) Radius() s1.Angle {
+	return c.radius.Angle()
+}
+
+// Area returns the surface area of the Cap on the unit sphere.
+func (c Cap) Area() float64 {
+	return 2.0 * math.Pi * math.Max(0, c.Height())
+}
+
+// Contains reports whether this cap contains the other.
+func (c Cap) Contains(other Cap) bool {
+	// In a set containment sense, every cap contains the empty cap.
+	if c.IsFull() || other.IsEmpty() {
+		return true
+	}
+	return c.radius >= ChordAngleBetweenPoints(c.center, other.center).Add(other.radius)
+}
+
+// Intersects reports whether this cap intersects the other cap.
+// i.e. whether they have any points in common.
+func (c Cap) Intersects(other Cap) bool {
+	if c.IsEmpty() || other.IsEmpty() {
+		return false
+	}
+
+	return c.radius.Add(other.radius) >= ChordAngleBetweenPoints(c.center, other.center)
+}
+
+// InteriorIntersects reports whether this caps interior intersects the other cap.
+func (c Cap) InteriorIntersects(other Cap) bool {
+	// Make sure this cap has an interior and the other cap is non-empty.
+	if c.radius <= 0 || other.IsEmpty() {
+		return false
+	}
+
+	return c.radius.Add(other.radius) > ChordAngleBetweenPoints(c.center, other.center)
+}
+
+// ContainsPoint reports whether this cap contains the point.
+func (c Cap) ContainsPoint(p Point) bool {
+	return ChordAngleBetweenPoints(c.center, p) <= c.radius
+}
+
+// InteriorContainsPoint reports whether the point is within the interior of this cap.
+func (c Cap) InteriorContainsPoint(p Point) bool {
+	return c.IsFull() || ChordAngleBetweenPoints(c.center, p) < c.radius
+}
+
+// Complement returns the complement of the interior of the cap. A cap and its
+// complement have the same boundary but do not share any interior points.
+// The complement operator is not a bijection because the complement of a
+// singleton cap (containing a single point) is the same as the complement
+// of an empty cap.
+func (c Cap) Complement() Cap {
+	if c.IsFull() {
+		return EmptyCap()
+	}
+	if c.IsEmpty() {
+		return FullCap()
+	}
+
+	return CapFromCenterChordAngle(Point{c.center.Mul(-1)}, s1.StraightChordAngle.Sub(c.radius))
+}
+
+// CapBound returns a bounding spherical cap. This is not guaranteed to be exact.
+func (c Cap) CapBound() Cap {
+	return c
+}
+
+// RectBound returns a bounding latitude-longitude rectangle.
+// The bounds are not guaranteed to be tight.
+func (c Cap) RectBound() Rect {
+	if c.IsEmpty() {
+		return EmptyRect()
+	}
+
+	capAngle := c.Radius().Radians()
+	allLongitudes := false
+	lat := r1.Interval{
+		Lo: latitude(c.center).Radians() - capAngle,
+		Hi: latitude(c.center).Radians() + capAngle,
+	}
+	lng := s1.FullInterval()
+
+	// Check whether cap includes the south pole.
+	if lat.Lo <= -math.Pi/2 {
+		lat.Lo = -math.Pi / 2
+		allLongitudes = true
+	}
+
+	// Check whether cap includes the north pole.
+	if lat.Hi >= math.Pi/2 {
+		lat.Hi = math.Pi / 2
+		allLongitudes = true
+	}
+
+	if !allLongitudes {
+		// Compute the range of longitudes covered by the cap. We use the law
+		// of sines for spherical triangles. Consider the triangle ABC where
+		// A is the north pole, B is the center of the cap, and C is the point
+		// of tangency between the cap boundary and a line of longitude. Then
+		// C is a right angle, and letting a,b,c denote the sides opposite A,B,C,
+		// we have sin(a)/sin(A) = sin(c)/sin(C), or sin(A) = sin(a)/sin(c).
+		// Here "a" is the cap angle, and "c" is the colatitude (90 degrees
+		// minus the latitude). This formula also works for negative latitudes.
+		//
+		// The formula for sin(a) follows from the relationship h = 1 - cos(a).
+		sinA := c.radius.Sin()
+		sinC := math.Cos(latitude(c.center).Radians())
+		if sinA <= sinC {
+			angleA := math.Asin(sinA / sinC)
+			lng.Lo = math.Remainder(longitude(c.center).Radians()-angleA, math.Pi*2)
+			lng.Hi = math.Remainder(longitude(c.center).Radians()+angleA, math.Pi*2)
+		}
+	}
+	return Rect{lat, lng}
+}
+
+// Equal reports whether this cap is equal to the other cap.
+func (c Cap) Equal(other Cap) bool {
+	return (c.radius == other.radius && c.center == other.center) ||
+		(c.IsEmpty() && other.IsEmpty()) ||
+		(c.IsFull() && other.IsFull())
+}
+
+// ApproxEqual reports whether this cap is equal to the other cap within the given tolerance.
+func (c Cap) ApproxEqual(other Cap) bool {
+	const epsilon = 1e-14
+	r2 := float64(c.radius)
+	otherR2 := float64(other.radius)
+	return c.center.ApproxEqual(other.center) &&
+		math.Abs(r2-otherR2) <= epsilon ||
+		c.IsEmpty() && otherR2 <= epsilon ||
+		other.IsEmpty() && r2 <= epsilon ||
+		c.IsFull() && otherR2 >= 2-epsilon ||
+		other.IsFull() && r2 >= 2-epsilon
+}
+
+// AddPoint increases the cap if necessary to include the given point. If this cap is empty,
+// then the center is set to the point with a zero height. p must be unit-length.
+func (c Cap) AddPoint(p Point) Cap {
+	if c.IsEmpty() {
+		c.center = p
+		c.radius = 0
+		return c
+	}
+
+	// After calling cap.AddPoint(p), cap.Contains(p) must be true. However
+	// we don't need to do anything special to achieve this because Contains()
+	// does exactly the same distance calculation that we do here.
+	if newRad := ChordAngleBetweenPoints(c.center, p); newRad > c.radius {
+		c.radius = newRad
+	}
+	return c
+}
+
+// AddCap increases the cap height if necessary to include the other cap. If this cap is empty,
+// it is set to the other cap.
+func (c Cap) AddCap(other Cap) Cap {
+	if c.IsEmpty() {
+		return other
+	}
+	if other.IsEmpty() {
+		return c
+	}
+
+	// We round up the distance to ensure that the cap is actually contained.
+	// TODO(roberts): Do some error analysis in order to guarantee this.
+	dist := ChordAngleBetweenPoints(c.center, other.center).Add(other.radius)
+	if newRad := dist.Expanded(dblEpsilon * float64(dist)); newRad > c.radius {
+		c.radius = newRad
+	}
+	return c
+}
+
+// Expanded returns a new cap expanded by the given angle. If the cap is empty,
+// it returns an empty cap.
+func (c Cap) Expanded(distance s1.Angle) Cap {
+	if c.IsEmpty() {
+		return EmptyCap()
+	}
+	return CapFromCenterChordAngle(c.center, c.radius.Add(s1.ChordAngleFromAngle(distance)))
+}
+
+func (c Cap) String() string {
+	return fmt.Sprintf("[Center=%v, Radius=%f]", c.center.Vector, c.Radius().Degrees())
+}
+
+// radiusToHeight converts an s1.Angle into the height of the cap.
+func radiusToHeight(r s1.Angle) float64 {
+	if r.Radians() < 0 {
+		return float64(s1.NegativeChordAngle)
+	}
+	if r.Radians() >= math.Pi {
+		return float64(s1.RightChordAngle)
+	}
+	return float64(0.5 * s1.ChordAngleFromAngle(r))
+
+}
+
+// ContainsCell reports whether the cap contains the given cell.
+func (c Cap) ContainsCell(cell Cell) bool {
+	// If the cap does not contain all cell vertices, return false.
+	var vertices [4]Point
+	for k := 0; k < 4; k++ {
+		vertices[k] = cell.Vertex(k)
+		if !c.ContainsPoint(vertices[k]) {
+			return false
+		}
+	}
+	// Otherwise, return true if the complement of the cap does not intersect the cell.
+	return !c.Complement().intersects(cell, vertices)
+}
+
+// IntersectsCell reports whether the cap intersects the cell.
+func (c Cap) IntersectsCell(cell Cell) bool {
+	// If the cap contains any cell vertex, return true.
+	var vertices [4]Point
+	for k := 0; k < 4; k++ {
+		vertices[k] = cell.Vertex(k)
+		if c.ContainsPoint(vertices[k]) {
+			return true
+		}
+	}
+	return c.intersects(cell, vertices)
+}
+
+// intersects reports whether the cap intersects any point of the cell excluding
+// its vertices (which are assumed to already have been checked).
+func (c Cap) intersects(cell Cell, vertices [4]Point) bool {
+	// If the cap is a hemisphere or larger, the cell and the complement of the cap
+	// are both convex. Therefore since no vertex of the cell is contained, no other
+	// interior point of the cell is contained either.
+	if c.radius >= s1.RightChordAngle {
+		return false
+	}
+
+	// We need to check for empty caps due to the center check just below.
+	if c.IsEmpty() {
+		return false
+	}
+
+	// Optimization: return true if the cell contains the cap center. This allows half
+	// of the edge checks below to be skipped.
+	if cell.ContainsPoint(c.center) {
+		return true
+	}
+
+	// At this point we know that the cell does not contain the cap center, and the cap
+	// does not contain any cell vertex. The only way that they can intersect is if the
+	// cap intersects the interior of some edge.
+	sin2Angle := c.radius.Sin2()
+	for k := 0; k < 4; k++ {
+		edge := cell.Edge(k).Vector
+		dot := c.center.Vector.Dot(edge)
+		if dot > 0 {
+			// The center is in the interior half-space defined by the edge. We do not need
+			// to consider these edges, since if the cap intersects this edge then it also
+			// intersects the edge on the opposite side of the cell, because the center is
+			// not contained with the cell.
+			continue
+		}
+
+		// The Norm2() factor is necessary because "edge" is not normalized.
+		if dot*dot > sin2Angle*edge.Norm2() {
+			return false
+		}
+
+		// Otherwise, the great circle containing this edge intersects the interior of the cap. We just
+		// need to check whether the point of closest approach occurs between the two edge endpoints.
+		dir := edge.Cross(c.center.Vector)
+		if dir.Dot(vertices[k].Vector) < 0 && dir.Dot(vertices[(k+1)&3].Vector) > 0 {
+			return true
+		}
+	}
+	return false
+}
+
+// CellUnionBound computes a covering of the Cap. In general the covering
+// consists of at most 4 cells except for very large caps, which may need
+// up to 6 cells. The output is not sorted.
+func (c Cap) CellUnionBound() []CellID {
+	// TODO(roberts): The covering could be made quite a bit tighter by mapping
+	// the cap to a rectangle in (i,j)-space and finding a covering for that.
+
+	// Find the maximum level such that the cap contains at most one cell vertex
+	// and such that CellID.AppendVertexNeighbors() can be called.
+	level := MinWidthMetric.MaxLevel(c.Radius().Radians()) - 1
+
+	// If level < 0, more than three face cells are required.
+	if level < 0 {
+		cellIDs := make([]CellID, 6)
+		for face := 0; face < 6; face++ {
+			cellIDs[face] = CellIDFromFace(face)
+		}
+		return cellIDs
+	}
+	// The covering consists of the 4 cells at the given level that share the
+	// cell vertex that is closest to the cap center.
+	return cellIDFromPoint(c.center).VertexNeighbors(level)
+}
+
+// Centroid returns the true centroid of the cap multiplied by its surface area
+// The result lies on the ray from the origin through the cap's center, but it
+// is not unit length. Note that if you just want the "surface centroid", i.e.
+// the normalized result, then it is simpler to call Center.
+//
+// The reason for multiplying the result by the cap area is to make it
+// easier to compute the centroid of more complicated shapes. The centroid
+// of a union of disjoint regions can be computed simply by adding their
+// Centroid() results. Caveat: for caps that contain a single point
+// (i.e., zero radius), this method always returns the origin (0, 0, 0).
+// This is because shapes with no area don't affect the centroid of a
+// union whose total area is positive.
+func (c Cap) Centroid() Point {
+	// From symmetry, the centroid of the cap must be somewhere on the line
+	// from the origin to the center of the cap on the surface of the sphere.
+	// When a sphere is divided into slices of constant thickness by a set of
+	// parallel planes, all slices have the same surface area. This implies
+	// that the radial component of the centroid is simply the midpoint of the
+	// range of radial distances spanned by the cap. That is easily computed
+	// from the cap height.
+	if c.IsEmpty() {
+		return Point{}
+	}
+	r := 1 - 0.5*c.Height()
+	return Point{c.center.Mul(r * c.Area())}
+}
+
+// Union returns the smallest cap which encloses this cap and other.
+func (c Cap) Union(other Cap) Cap {
+	// If the other cap is larger, swap c and other for the rest of the computations.
+	if c.radius < other.radius {
+		c, other = other, c
+	}
+
+	if c.IsFull() || other.IsEmpty() {
+		return c
+	}
+
+	// TODO: This calculation would be more efficient using s1.ChordAngles.
+	cRadius := c.Radius()
+	otherRadius := other.Radius()
+	distance := c.center.Distance(other.center)
+	if cRadius >= distance+otherRadius {
+		return c
+	}
+
+	resRadius := 0.5 * (distance + cRadius + otherRadius)
+	resCenter := InterpolateAtDistance(0.5*(distance-cRadius+otherRadius), c.center, other.center)
+	return CapFromCenterAngle(resCenter, resRadius)
+}
+
+// Encode encodes the Cap.
+func (c Cap) Encode(w io.Writer) error {
+	e := &encoder{w: w}
+	c.encode(e)
+	return e.err
+}
+
+func (c Cap) encode(e *encoder) {
+	e.writeFloat64(c.center.X)
+	e.writeFloat64(c.center.Y)
+	e.writeFloat64(c.center.Z)
+	e.writeFloat64(float64(c.radius))
+}
+
+// Decode decodes the Cap.
+func (c *Cap) Decode(r io.Reader) error {
+	d := &decoder{r: asByteReader(r)}
+	c.decode(d)
+	return d.err
+}
+
+func (c *Cap) decode(d *decoder) {
+	c.center.X = d.readFloat64()
+	c.center.Y = d.readFloat64()
+	c.center.Z = d.readFloat64()
+	c.radius = s1.ChordAngle(d.readFloat64())
+}