latlng.go

Documentation: github.com/golang/geo/s2

     1  // Copyright 2014 Google Inc. All rights reserved.
     2  //
     3  // Licensed under the Apache License, Version 2.0 (the "License");
     4  // you may not use this file except in compliance with the License.
     5  // You may obtain a copy of the License at
     6  //
     7  //     http://www.apache.org/licenses/LICENSE-2.0
     8  //
     9  // Unless required by applicable law or agreed to in writing, software
    10  // distributed under the License is distributed on an "AS IS" BASIS,
    11  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    12  // See the License for the specific language governing permissions and
    13  // limitations under the License.
    14  
    15  package s2
    16  
    17  import (
    18  	"fmt"
    19  	"math"
    20  
    21  	"github.com/golang/geo/r3"
    22  	"github.com/golang/geo/s1"
    23  )
    24  
    25  const (
    26  	northPoleLat = s1.Angle(math.Pi/2) * s1.Radian
    27  	southPoleLat = -northPoleLat
    28  )
    29  
    30  // LatLng represents a point on the unit sphere as a pair of angles.
    31  type LatLng struct {
    32  	Lat, Lng s1.Angle
    33  }
    34  
    35  // LatLngFromDegrees returns a LatLng for the coordinates given in degrees.
    36  func LatLngFromDegrees(lat, lng float64) LatLng {
    37  	return LatLng{s1.Angle(lat) * s1.Degree, s1.Angle(lng) * s1.Degree}
    38  }
    39  
    40  // IsValid returns true iff the LatLng is normalized, with Lat ∈ [-π/2,π/2] and Lng ∈ [-π,π].
    41  func (ll LatLng) IsValid() bool {
    42  	return math.Abs(ll.Lat.Radians()) <= math.Pi/2 && math.Abs(ll.Lng.Radians()) <= math.Pi
    43  }
    44  
    45  // Normalized returns the normalized version of the LatLng,
    46  // with Lat clamped to [-π/2,π/2] and Lng wrapped in [-π,π].
    47  func (ll LatLng) Normalized() LatLng {
    48  	lat := ll.Lat
    49  	if lat > northPoleLat {
    50  		lat = northPoleLat
    51  	} else if lat < southPoleLat {
    52  		lat = southPoleLat
    53  	}
    54  	lng := s1.Angle(math.Remainder(ll.Lng.Radians(), 2*math.Pi)) * s1.Radian
    55  	return LatLng{lat, lng}
    56  }
    57  
    58  func (ll LatLng) String() string { return fmt.Sprintf("[%v, %v]", ll.Lat, ll.Lng) }
    59  
    60  // Distance returns the angle between two LatLngs.
    61  func (ll LatLng) Distance(ll2 LatLng) s1.Angle {
    62  	// Haversine formula, as used in C++ S2LatLng::GetDistance.
    63  	lat1, lat2 := ll.Lat.Radians(), ll2.Lat.Radians()
    64  	lng1, lng2 := ll.Lng.Radians(), ll2.Lng.Radians()
    65  	dlat := math.Sin(0.5 * (lat2 - lat1))
    66  	dlng := math.Sin(0.5 * (lng2 - lng1))
    67  	x := dlat*dlat + dlng*dlng*math.Cos(lat1)*math.Cos(lat2)
    68  	return s1.Angle(2*math.Atan2(math.Sqrt(x), math.Sqrt(math.Max(0, 1-x)))) * s1.Radian
    69  }
    70  
    71  // NOTE(mikeperrow): The C++ implementation publicly exposes latitude/longitude
    72  // functions. Let's see if that's really necessary before exposing the same functionality.
    73  
    74  func latitude(p Point) s1.Angle {
    75  	return s1.Angle(math.Atan2(p.Z, math.Sqrt(p.X*p.X+p.Y*p.Y))) * s1.Radian
    76  }
    77  
    78  func longitude(p Point) s1.Angle {
    79  	return s1.Angle(math.Atan2(p.Y, p.X)) * s1.Radian
    80  }
    81  
    82  // PointFromLatLng returns an Point for the given LatLng.
    83  // The maximum error in the result is 1.5 * dblEpsilon. (This does not
    84  // include the error of converting degrees, E5, E6, or E7 into radians.)
    85  func PointFromLatLng(ll LatLng) Point {
    86  	phi := ll.Lat.Radians()
    87  	theta := ll.Lng.Radians()
    88  	cosphi := math.Cos(phi)
    89  	return Point{r3.Vector{math.Cos(theta) * cosphi, math.Sin(theta) * cosphi, math.Sin(phi)}}
    90  }
    91  
    92  // LatLngFromPoint returns an LatLng for a given Point.
    93  func LatLngFromPoint(p Point) LatLng {
    94  	return LatLng{latitude(p), longitude(p)}
    95  }
    96  
    97  // ApproxEqual reports whether the latitude and longitude of the two LatLngs
    98  // are the same up to a small tolerance.
    99  func (ll LatLng) ApproxEqual(other LatLng) bool {
   100  	return ll.Lat.ApproxEqual(other.Lat) && ll.Lng.ApproxEqual(other.Lng)
   101  }
   102
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