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

vendor/github.com/golang/geo/s2/projections.go

@@ -0,0 +1,241 @@
+// Copyright 2018 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 (
+	"math"
+
+	"github.com/golang/geo/r2"
+	"github.com/golang/geo/s1"
+)
+
+// Projection defines an interface for different ways of mapping between s2 and r2 Points.
+// It can also define the coordinate wrapping behavior along each axis.
+type Projection interface {
+	// Project converts a point on the sphere to a projected 2D point.
+	Project(p Point) r2.Point
+
+	// Unproject converts a projected 2D point to a point on the sphere.
+	//
+	// If wrapping is defined for a given axis (see below), then this method
+	// should accept any real number for the corresponding coordinate.
+	Unproject(p r2.Point) Point
+
+	// FromLatLng is a convenience function equivalent to Project(LatLngToPoint(ll)),
+	// but the implementation is more efficient.
+	FromLatLng(ll LatLng) r2.Point
+
+	// ToLatLng is a convenience function equivalent to LatLngFromPoint(Unproject(p)),
+	// but the implementation is more efficient.
+	ToLatLng(p r2.Point) LatLng
+
+	// Interpolate returns the point obtained by interpolating the given
+	// fraction of the distance along the line from A to B.
+	// Fractions < 0 or > 1 result in extrapolation instead.
+	Interpolate(f float64, a, b r2.Point) r2.Point
+
+	// WrapDistance reports the coordinate wrapping distance along each axis.
+	// If this value is non-zero for a given axis, the coordinates are assumed
+	// to "wrap" with the given period. For example, if WrapDistance.Y == 360
+	// then (x, y) and (x, y + 360) should map to the same Point.
+	//
+	// This information is used to ensure that edges takes the shortest path
+	// between two given points. For example, if coordinates represent
+	// (latitude, longitude) pairs in degrees and WrapDistance().Y == 360,
+	// then the edge (5:179, 5:-179) would be interpreted as spanning 2 degrees
+	// of longitude rather than 358 degrees.
+	//
+	// If a given axis does not wrap, its WrapDistance should be set to zero.
+	WrapDistance() r2.Point
+
+	// WrapDestination that wraps the coordinates of B if necessary in order to
+	// obtain the shortest edge AB. For example, suppose that A = [170, 20],
+	// B = [-170, 20], and the projection wraps so that [x, y] == [x + 360, y].
+	// Then this function would return [190, 20] for point B (reducing the edge
+	// length in the "x" direction from 340 to 20).
+	WrapDestination(a, b r2.Point) r2.Point
+
+	// We do not support implementations of this interface outside this package.
+	privateInterface()
+}
+
+// PlateCarreeProjection defines the "plate carree" (square plate) projection,
+// which converts points on the sphere to (longitude, latitude) pairs.
+// Coordinates can be scaled so that they represent radians, degrees, etc, but
+// the projection is always centered around (latitude=0, longitude=0).
+//
+// Note that (x, y) coordinates are backwards compared to the usual (latitude,
+// longitude) ordering, in order to match the usual convention for graphs in
+// which "x" is horizontal and "y" is vertical.
+type PlateCarreeProjection struct {
+	xWrap       float64
+	toRadians   float64 // Multiplier to convert coordinates to radians.
+	fromRadians float64 // Multiplier to convert coordinates from radians.
+}
+
+// NewPlateCarreeProjection constructs a plate carree projection where the
+// x-coordinates (lng) span [-xScale, xScale] and the y coordinates (lat)
+// span [-xScale/2, xScale/2]. For example if xScale==180 then the x
+// range is [-180, 180] and the y range is [-90, 90].
+//
+// By default coordinates are expressed in radians, i.e. the x range is
+// [-Pi, Pi] and the y range is [-Pi/2, Pi/2].
+func NewPlateCarreeProjection(xScale float64) Projection {
+	return &PlateCarreeProjection{
+		xWrap:       2 * xScale,
+		toRadians:   math.Pi / xScale,
+		fromRadians: xScale / math.Pi,
+	}
+}
+
+// Project converts a point on the sphere to a projected 2D point.
+func (p *PlateCarreeProjection) Project(pt Point) r2.Point {
+	return p.FromLatLng(LatLngFromPoint(pt))
+}
+
+// Unproject converts a projected 2D point to a point on the sphere.
+func (p *PlateCarreeProjection) Unproject(pt r2.Point) Point {
+	return PointFromLatLng(p.ToLatLng(pt))
+}
+
+// FromLatLng returns the LatLng projected into an R2 Point.
+func (p *PlateCarreeProjection) FromLatLng(ll LatLng) r2.Point {
+	return r2.Point{
+		X: p.fromRadians * ll.Lng.Radians(),
+		Y: p.fromRadians * ll.Lat.Radians(),
+	}
+}
+
+// ToLatLng returns the LatLng projected from the given R2 Point.
+func (p *PlateCarreeProjection) ToLatLng(pt r2.Point) LatLng {
+	return LatLng{
+		Lat: s1.Angle(p.toRadians * pt.Y),
+		Lng: s1.Angle(p.toRadians * math.Remainder(pt.X, p.xWrap)),
+	}
+}
+
+// Interpolate returns the point obtained by interpolating the given
+// fraction of the distance along the line from A to B.
+func (p *PlateCarreeProjection) Interpolate(f float64, a, b r2.Point) r2.Point {
+	return a.Mul(1 - f).Add(b.Mul(f))
+}
+
+// WrapDistance reports the coordinate wrapping distance along each axis.
+func (p *PlateCarreeProjection) WrapDistance() r2.Point {
+	return r2.Point{p.xWrap, 0}
+}
+
+// WrapDestination wraps the points if needed to get the shortest edge.
+func (p *PlateCarreeProjection) WrapDestination(a, b r2.Point) r2.Point {
+	return wrapDestination(a, b, p.WrapDistance)
+}
+
+func (p *PlateCarreeProjection) privateInterface() {}
+
+// MercatorProjection defines the spherical Mercator projection. Google Maps
+// uses this projection together with WGS84 coordinates, in which case it is
+// known as the "Web Mercator" projection (see Wikipedia). This class makes
+// no assumptions regarding the coordinate system of its input points, but
+// simply applies the spherical Mercator projection to them.
+//
+// The Mercator projection is finite in width (x) but infinite in height (y).
+// "x" corresponds to longitude, and spans a finite range such as [-180, 180]
+// (with coordinate wrapping), while "y" is a function of latitude and spans
+// an infinite range. (As "y" coordinates get larger, points get closer to
+// the north pole but never quite reach it.) The north and south poles have
+// infinite "y" values. (Note that this will cause problems if you tessellate
+// a Mercator edge where one endpoint is a pole. If you need to do this, clip
+// the edge first so that the "y" coordinate is no more than about 5 * maxX.)
+type MercatorProjection struct {
+	xWrap       float64
+	toRadians   float64 // Multiplier to convert coordinates to radians.
+	fromRadians float64 // Multiplier to convert coordinates from radians.
+}
+
+// NewMercatorProjection constructs a Mercator projection with the given maximum
+// longitude axis value corresponding to a range of [-maxLng, maxLng].
+// The horizontal and vertical axes are scaled equally.
+func NewMercatorProjection(maxLng float64) Projection {
+	return &MercatorProjection{
+		xWrap:       2 * maxLng,
+		toRadians:   math.Pi / maxLng,
+		fromRadians: maxLng / math.Pi,
+	}
+}
+
+// Project converts a point on the sphere to a projected 2D point.
+func (p *MercatorProjection) Project(pt Point) r2.Point {
+	return p.FromLatLng(LatLngFromPoint(pt))
+}
+
+// Unproject converts a projected 2D point to a point on the sphere.
+func (p *MercatorProjection) Unproject(pt r2.Point) Point {
+	return PointFromLatLng(p.ToLatLng(pt))
+}
+
+// FromLatLng returns the LatLng projected into an R2 Point.
+func (p *MercatorProjection) FromLatLng(ll LatLng) r2.Point {
+	// This formula is more accurate near zero than the log(tan()) version.
+	// Note that latitudes of +/- 90 degrees yield "y" values of +/- infinity.
+	sinPhi := math.Sin(float64(ll.Lat))
+	y := 0.5 * math.Log((1+sinPhi)/(1-sinPhi))
+	return r2.Point{p.fromRadians * float64(ll.Lng), p.fromRadians * y}
+}
+
+// ToLatLng returns the LatLng projected from the given R2 Point.
+func (p *MercatorProjection) ToLatLng(pt r2.Point) LatLng {
+	// This formula is more accurate near zero than the atan(exp()) version.
+	x := p.toRadians * math.Remainder(pt.X, p.xWrap)
+	k := math.Exp(2 * p.toRadians * pt.Y)
+	var y float64
+	if math.IsInf(k, 0) {
+		y = math.Pi / 2
+	} else {
+		y = math.Asin((k - 1) / (k + 1))
+	}
+	return LatLng{s1.Angle(y), s1.Angle(x)}
+}
+
+// Interpolate returns the point obtained by interpolating the given
+// fraction of the distance along the line from A to B.
+func (p *MercatorProjection) Interpolate(f float64, a, b r2.Point) r2.Point {
+	return a.Mul(1 - f).Add(b.Mul(f))
+}
+
+// WrapDistance reports the coordinate wrapping distance along each axis.
+func (p *MercatorProjection) WrapDistance() r2.Point {
+	return r2.Point{p.xWrap, 0}
+}
+
+// WrapDestination wraps the points if needed to get the shortest edge.
+func (p *MercatorProjection) WrapDestination(a, b r2.Point) r2.Point {
+	return wrapDestination(a, b, p.WrapDistance)
+}
+
+func (p *MercatorProjection) privateInterface() {}
+
+func wrapDestination(a, b r2.Point, wrapDistance func() r2.Point) r2.Point {
+	wrap := wrapDistance()
+	x := b.X
+	y := b.Y
+	// The code below ensures that "b" is unmodified unless wrapping is required.
+	if wrap.X > 0 && math.Abs(x-a.X) > 0.5*wrap.X {
+		x = a.X + math.Remainder(x-a.X, wrap.X)
+	}
+	if wrap.Y > 0 && math.Abs(y-a.Y) > 0.5*wrap.Y {
+		y = a.Y + math.Remainder(y-a.Y, wrap.Y)
+	}
+	return r2.Point{x, y}
+}