102 lines
3.4 KiB
Go
102 lines
3.4 KiB
Go
// Copyright 2014 Google Inc. All rights reserved.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package s2
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import (
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"fmt"
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"math"
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"github.com/golang/geo/r3"
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"github.com/golang/geo/s1"
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)
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const (
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northPoleLat = s1.Angle(math.Pi/2) * s1.Radian
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southPoleLat = -northPoleLat
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)
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// LatLng represents a point on the unit sphere as a pair of angles.
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type LatLng struct {
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Lat, Lng s1.Angle
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}
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// LatLngFromDegrees returns a LatLng for the coordinates given in degrees.
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func LatLngFromDegrees(lat, lng float64) LatLng {
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return LatLng{s1.Angle(lat) * s1.Degree, s1.Angle(lng) * s1.Degree}
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}
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// IsValid returns true iff the LatLng is normalized, with Lat ∈ [-π/2,π/2] and Lng ∈ [-π,π].
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func (ll LatLng) IsValid() bool {
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return math.Abs(ll.Lat.Radians()) <= math.Pi/2 && math.Abs(ll.Lng.Radians()) <= math.Pi
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}
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// Normalized returns the normalized version of the LatLng,
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// with Lat clamped to [-π/2,π/2] and Lng wrapped in [-π,π].
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func (ll LatLng) Normalized() LatLng {
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lat := ll.Lat
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if lat > northPoleLat {
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lat = northPoleLat
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} else if lat < southPoleLat {
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lat = southPoleLat
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}
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lng := s1.Angle(math.Remainder(ll.Lng.Radians(), 2*math.Pi)) * s1.Radian
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return LatLng{lat, lng}
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}
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func (ll LatLng) String() string { return fmt.Sprintf("[%v, %v]", ll.Lat, ll.Lng) }
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// Distance returns the angle between two LatLngs.
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func (ll LatLng) Distance(ll2 LatLng) s1.Angle {
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// Haversine formula, as used in C++ S2LatLng::GetDistance.
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lat1, lat2 := ll.Lat.Radians(), ll2.Lat.Radians()
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lng1, lng2 := ll.Lng.Radians(), ll2.Lng.Radians()
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dlat := math.Sin(0.5 * (lat2 - lat1))
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dlng := math.Sin(0.5 * (lng2 - lng1))
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x := dlat*dlat + dlng*dlng*math.Cos(lat1)*math.Cos(lat2)
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return s1.Angle(2*math.Atan2(math.Sqrt(x), math.Sqrt(math.Max(0, 1-x)))) * s1.Radian
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}
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// NOTE(mikeperrow): The C++ implementation publicly exposes latitude/longitude
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// functions. Let's see if that's really necessary before exposing the same functionality.
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func latitude(p Point) s1.Angle {
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return s1.Angle(math.Atan2(p.Z, math.Sqrt(p.X*p.X+p.Y*p.Y))) * s1.Radian
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}
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func longitude(p Point) s1.Angle {
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return s1.Angle(math.Atan2(p.Y, p.X)) * s1.Radian
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}
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// PointFromLatLng returns an Point for the given LatLng.
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// The maximum error in the result is 1.5 * dblEpsilon. (This does not
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// include the error of converting degrees, E5, E6, or E7 into radians.)
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func PointFromLatLng(ll LatLng) Point {
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phi := ll.Lat.Radians()
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theta := ll.Lng.Radians()
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cosphi := math.Cos(phi)
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return Point{r3.Vector{math.Cos(theta) * cosphi, math.Sin(theta) * cosphi, math.Sin(phi)}}
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}
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// LatLngFromPoint returns an LatLng for a given Point.
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func LatLngFromPoint(p Point) LatLng {
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return LatLng{latitude(p), longitude(p)}
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}
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// ApproxEqual reports whether the latitude and longitude of the two LatLngs
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// are the same up to a small tolerance.
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func (ll LatLng) ApproxEqual(other LatLng) bool {
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return ll.Lat.ApproxEqual(other.Lat) && ll.Lng.ApproxEqual(other.Lng)
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}
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