destination: Vincenty Direct Calculation of a Destination
In SDMTools: Species Distribution Modelling Tools: Tools for processing data associated with species distribution modelling exercises
Description
Usage
Arguments
Details
Value
Author(s)
Source
References
Examples
Description
destination estimates the destination latitude and
longitude given a starting latitude and longitude, a
bearing and distance.
For general information on
Vincenty's formula, see e.g.,
http://en.wikipedia.org/wiki/Vincenty's_formulae. It
states:
Vincenty's formulae are two related
iterative methods used in geodesy to calculate the distance
between two points on the surface of an spheroid, developed
by Thaddeus Vincenty in 1975. They are based on the
assumption that the figure of the Earth is an oblate
spheroid, and hence are more accurate than methods such as
great-circle distance which assume a spherical Earth.
Note: this method assumes a locations are lat &
lon given in WGS 84.
Usage
1
destination(lat, lon, bearing, distance)
Arguments
lat
a single value or vector of values
representing latitude in decimal degrees from -90 to 90
degrees.
lon
a single value or vector of values
representing longitude in decimal degrees from -180 to
180 degrees.
bearing
a single value or vector of values
representing the bearings (directions) of interest
ranging from 0 to 360 degrees.
distance
a single value or vector of values
representing the distances in metres to the destination.
Details
Typical useages are:
a single start
location, bearing and distance to give a single output
location
–output would be a single destination location
a single start location with one or more bearings or
distances to give multiple output locations
–output
would be a destination locations for each combination of
bearings and distances
multiple start locations with
a single bearing or distance
–output would be a
destination locations representing the bearing and distance
from each of the start locations
multiple start
locations with multiple bearings or distances
–output
would be a destination locations representing the
combinations of bearings and distances from each of the
start locations
– NOTE that the bearing and distance
vectors must be of the same length of the input lat and
long.
See examples for all possible usages.
Value
Returns a data.frame with:
lon1
the original
longitude
lat1
the original latitude
bearing
the bearing used
distance
the
distance used
lon2
the destination longitude
lat2
the destination latitude
Author(s)
Jeremy VanDerWal jjvanderwal@gmail.com
Source
The source code here was modified from
http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html.
Destinations were validated against Geoscience
Australia calculations
(http://www.ga.gov.au/geodesy/datums/vincenty_direct.jsp).
References
Vincenty, T. 1975. Direct and Inverse Solutions of
Geodesics on the Ellipsoid with application of Nested
Equations. Survey Review, vol XXII no 176.
http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
###single lat lons
lats = -85; lons = 165
#single bearing & single distance
destination(lats,lons,bearing=180,distance=500000)
#multiple bearings
destination(lats,lons,bearing=seq(0,360,length.out=9),distance=500000)
#multiple bearings
destination(lats,lons,bearing=45,distance=seq(0,5000000,length.out=11))
#multiple bearings, multiple distances
destination(lats,lons,bearing=seq(0,360,length.out=9),
distance=seq(0,5000000,length.out=11))
###multiple lat lons
lats = seq(-90,90,length.out=9); lons = seq(-180,180,length.out=9)
#multiple lat lons but single bearings / distances
destination(lats,lons,bearing=45,distance=500000)
#different bearings for each lat lon
destination(lats,lons,bearing=seq(0,360,length.out=9),distance=500000)
#different distances for each lat lon
destination(lats,lons,bearing=45,distance=seq(0,5000000,length.out=9))
#different bearings & distances for each lat lon
destination(lats,lons,bearing=seq(0,360,length.out=9),
distance=seq(0,5000000,length.out=9))
Example output
lon1 lat1 bearing distance lon2 lat2
1 165 -85 180 5e+05 165 -89.48412
lon1 lat1 bearing distance lon2 lat2
1 165 -85 0 5e+05 165.0000 -80.51547
2 165 -85 45 5e+05 186.2767 -81.23674
3 165 -85 90 5e+05 206.9805 -83.28751
4 165 -85 135 5e+05 225.0793 -86.34296
5 165 -85 180 5e+05 165.0000 -89.48412
6 165 -85 225 5e+05 104.9207 -86.34296
7 165 -85 270 5e+05 123.0195 -83.28751
8 165 -85 315 5e+05 143.7233 -81.23674
9 165 -85 360 5e+05 165.0000 -80.51547
lon1 lat1 bearing distance lon2 lat2
1 165 -85 45 0 165.0000 -85.00000
2 165 -85 45 500000 186.2767 -81.23674
3 165 -85 45 1000000 194.3648 -77.00867
4 165 -85 45 1500000 198.4876 -72.65156
5 165 -85 45 2000000 200.9868 -68.24188
6 165 -85 45 2500000 202.6751 -63.80524
7 165 -85 45 3000000 203.9030 -59.35241
8 165 -85 45 3500000 204.8455 -54.88866
9 165 -85 45 4000000 205.5997 -50.41686
10 165 -85 45 4500000 206.2236 -45.93872
11 165 -85 45 5000000 206.7542 -41.45533
lon1 lat1 bearing distance lon2 lat2
1 165 -85 0 0 165.00000 -85.00000
2 165 -85 45 0 165.00000 -85.00000
3 165 -85 90 0 165.00000 -85.00000
4 165 -85 135 0 165.00000 -85.00000
5 165 -85 180 0 165.00000 -85.00000
6 165 -85 225 0 165.00000 -85.00000
7 165 -85 270 0 165.00000 -85.00000
8 165 -85 315 0 165.00000 -85.00000
9 165 -85 360 0 165.00000 -85.00000
10 165 -85 0 500000 165.00000 -80.51547
11 165 -85 45 500000 186.27674 -81.23674
12 165 -85 90 500000 206.98052 -83.28751
13 165 -85 135 500000 225.07926 -86.34296
14 165 -85 180 500000 165.00000 -89.48412
15 165 -85 225 500000 104.92074 -86.34296
16 165 -85 270 500000 123.01948 -83.28751
17 165 -85 315 500000 143.72326 -81.23674
18 165 -85 360 500000 165.00000 -80.51547
19 165 -85 0 1000000 165.00000 -76.03018
20 165 -85 45 1000000 194.36480 -77.00867
21 165 -85 90 1000000 226.08902 -79.74152
22 165 -85 135 1000000 267.14337 -83.52598
23 165 -85 180 1000000 345.00000 -86.03181
24 165 -85 225 1000000 62.85663 -83.52598
25 165 -85 270 1000000 103.91098 -79.74152
26 165 -85 315 1000000 135.63520 -77.00867
27 165 -85 360 1000000 165.00000 -76.03018
28 165 -85 0 1500000 165.00000 -71.54378
29 165 -85 45 1500000 198.48759 -72.65156
30 165 -85 90 1500000 234.97881 -75.66280
31 165 -85 135 1500000 280.68253 -79.48211
32 165 -85 180 1500000 345.00000 -81.54741
33 165 -85 225 1500000 49.31747 -79.48211
34 165 -85 270 1500000 95.02119 -75.66280
35 165 -85 315 1500000 131.51241 -72.65156
36 165 -85 360 1500000 165.00000 -71.54378
37 165 -85 0 2000000 165.00000 -67.05596
38 165 -85 45 2000000 200.98685 -68.24188
39 165 -85 90 2000000 239.92864 -71.39773
40 165 -85 135 2000000 286.60774 -75.18329
41 165 -85 180 2000000 345.00000 -77.06232
42 165 -85 225 2000000 43.39226 -75.18329
43 165 -85 270 2000000 90.07136 -71.39773
44 165 -85 315 2000000 129.01315 -68.24188
45 165 -85 360 2000000 165.00000 -67.05596
46 165 -85 0 2500000 165.00000 -62.56645
47 165 -85 45 2500000 202.67511 -63.80524
48 165 -85 90 2500000 243.07011 -67.04909
49 165 -85 135 2500000 289.89284 -70.79914
50 165 -85 180 2500000 345.00000 -72.57621
51 165 -85 225 2500000 40.10716 -70.79914
52 165 -85 270 2500000 86.92989 -67.04909
53 165 -85 315 2500000 127.32489 -63.80524
54 165 -85 360 2500000 165.00000 -62.56645
55 165 -85 0 3000000 165.00000 -58.07500
56 165 -85 45 3000000 203.90296 -59.35241
57 165 -85 90 3000000 245.25162 -62.65581
58 165 -85 135 3000000 291.98889 -66.37620
59 165 -85 180 3000000 345.00000 -68.08874
60 165 -85 225 3000000 38.01111 -66.37620
61 165 -85 270 3000000 84.74838 -62.65581
62 165 -85 315 3000000 126.09704 -59.35241
63 165 -85 360 3000000 165.00000 -58.07500
64 165 -85 0 3500000 165.00000 -53.58143
65 165 -85 45 3500000 204.84548 -54.88866
66 165 -85 90 3500000 246.86769 -58.23553
67 165 -85 135 3500000 293.45408 -61.93185
68 165 -85 180 3500000 345.00000 -63.59964
69 165 -85 225 3500000 36.54592 -61.93185
70 165 -85 270 3500000 83.13231 -58.23553
71 165 -85 315 3500000 125.15452 -54.88866
72 165 -85 360 3500000 165.00000 -53.58143
73 165 -85 0 4000000 165.00000 -49.08560
74 165 -85 45 4000000 205.59967 -50.41686
75 165 -85 90 4000000 248.12472 -53.79729
76 165 -85 135 4000000 294.54626 -57.47396
77 165 -85 180 4000000 345.00000 -59.10866
78 165 -85 225 4000000 35.45374 -57.47396
79 165 -85 270 4000000 81.87528 -53.79729
80 165 -85 315 4000000 124.40033 -50.41686
81 165 -85 360 4000000 165.00000 -49.08560
82 165 -85 0 4500000 165.00000 -44.58742
83 165 -85 45 4500000 206.22359 -45.93872
84 165 -85 90 4500000 249.14066 -49.34619
85 165 -85 135 4500000 295.40047 -53.00656
86 165 -85 180 4500000 345.00000 -54.61559
87 165 -85 225 4500000 34.59953 -53.00656
88 165 -85 270 4500000 80.85934 -49.34619
89 165 -85 315 4500000 123.77641 -45.93872
90 165 -85 360 4500000 165.00000 -44.58742
91 165 -85 0 5000000 165.00000 -40.08688
92 165 -85 45 5000000 206.75418 -41.45533
93 165 -85 90 5000000 249.98779 -44.88534
94 165 -85 135 5000000 296.09422 -48.53192
95 165 -85 180 5000000 345.00000 -50.12029
96 165 -85 225 5000000 33.90578 -48.53192
97 165 -85 270 5000000 80.01221 -44.88534
98 165 -85 315 5000000 123.24582 -41.45533
99 165 -85 360 5000000 165.00000 -40.08688
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 45 5e+05 -135.000000 -85.515907
2 -135 -67.5 45 5e+05 -127.717000 -64.140175
3 -90 -45.0 45 5e+05 -85.749336 -41.734728
4 -45 -22.5 45 5e+05 -41.639949 -19.274173
5 0 0.0 45 5e+05 3.176623 3.193071
6 45 22.5 45 5e+05 48.518228 25.651625
7 90 45.0 45 5e+05 94.748702 48.087166
8 135 67.5 45 5e+05 144.499670 70.428481
9 180 90.0 45 5e+05 315.000000 85.515907
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 0 5e+05 -1.800000e+02 -85.515907
2 -135 -67.5 45 5e+05 -1.277170e+02 -64.140175
3 -90 -45.0 90 5e+05 -8.366621e+01 -44.824007
4 -45 -22.5 135 5e+05 -4.148177e+01 -25.651625
5 0 0.0 180 5e+05 5.502676e-16 -4.514189
6 45 22.5 225 5e+05 4.163995e+01 19.274173
7 90 45.0 270 5e+05 8.366621e+01 44.824007
8 135 67.5 315 5e+05 1.255003e+02 70.428481
9 180 90.0 360 5e+05 0.000000e+00 85.515907
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 45 0 -180.00000 -90.00000
2 -135 -67.5 45 625000 -126.17124 -63.25135
3 -90 -45.0 45 1250000 -80.13712 -36.57743
4 -45 -22.5 45 1875000 -32.99689 -10.13013
5 0 0.0 45 2500000 16.28258 15.75991
6 45 22.5 45 3125000 70.80455 40.24084
7 90 45.0 45 3750000 141.53713 59.98943
8 135 67.5 45 4375000 239.64657 62.45299
9 180 90.0 45 5000000 315.00000 45.10506
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 0 0 -1.800000e+02 -90.000000
2 -135 -67.5 45 625000 -1.261712e+02 -63.251354
3 -90 -45.0 90 1250000 -7.433028e+01 -43.911517
4 -45 -22.5 135 1875000 -3.074451e+01 -33.797267
5 0 0.0 180 2500000 2.896532e-15 -22.563681
6 45 22.5 225 3125000 2.557305e+01 1.623163
7 90 45.0 270 3750000 4.672582e+01 36.021757
8 135 67.5 315 4375000 3.035343e+01 62.452993
9 180 90.0 360 5000000 0.000000e+00 45.105056
SDMTools documentation built on Jan. 11, 2020, 9:23 a.m.
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Description Usage Arguments Details Value Author(s) Source References Examples
Description
destination estimates the destination latitude and
longitude given a starting latitude and longitude, a
bearing and distance.
For general information on
Vincenty's formula, see e.g.,
http://en.wikipedia.org/wiki/Vincenty's_formulae. It
states:
Vincenty's formulae are two related
iterative methods used in geodesy to calculate the distance
between two points on the surface of an spheroid, developed
by Thaddeus Vincenty in 1975. They are based on the
assumption that the figure of the Earth is an oblate
spheroid, and hence are more accurate than methods such as
great-circle distance which assume a spherical Earth.
Note: this method assumes a locations are lat &
lon given in WGS 84.
Usage
1 | destination(lat, lon, bearing, distance)
|
Arguments
lat |
a single value or vector of values representing latitude in decimal degrees from -90 to 90 degrees. |
lon |
a single value or vector of values representing longitude in decimal degrees from -180 to 180 degrees. |
bearing |
a single value or vector of values representing the bearings (directions) of interest ranging from 0 to 360 degrees. |
distance |
a single value or vector of values representing the distances in metres to the destination. |
Details
Typical useages are:
a single start location, bearing and distance to give a single output location
–output would be a single destination locationa single start location with one or more bearings or distances to give multiple output locations
–output would be a destination locations for each combination of bearings and distancesmultiple start locations with a single bearing or distance
–output would be a destination locations representing the bearing and distance from each of the start locationsmultiple start locations with multiple bearings or distances
–output would be a destination locations representing the combinations of bearings and distances from each of the start locations
– NOTE that the bearing and distance vectors must be of the same length of the input lat and long.
See examples for all possible usages.
Value
Returns a data.frame with:
lon1 |
the original longitude |
lat1 |
the original latitude |
bearing |
the bearing used |
distance |
the distance used |
lon2 |
the destination longitude |
lat2 |
the destination latitude |
Author(s)
Jeremy VanDerWal jjvanderwal@gmail.com
Source
The source code here was modified from
http://www.movable-type.co.uk/scripts/latlong-vincenty-direct.html.
Destinations were validated against Geoscience
Australia calculations
(http://www.ga.gov.au/geodesy/datums/vincenty_direct.jsp).
References
Vincenty, T. 1975. Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of Nested Equations. Survey Review, vol XXII no 176. http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ###single lat lons
lats = -85; lons = 165
#single bearing & single distance
destination(lats,lons,bearing=180,distance=500000)
#multiple bearings
destination(lats,lons,bearing=seq(0,360,length.out=9),distance=500000)
#multiple bearings
destination(lats,lons,bearing=45,distance=seq(0,5000000,length.out=11))
#multiple bearings, multiple distances
destination(lats,lons,bearing=seq(0,360,length.out=9),
distance=seq(0,5000000,length.out=11))
###multiple lat lons
lats = seq(-90,90,length.out=9); lons = seq(-180,180,length.out=9)
#multiple lat lons but single bearings / distances
destination(lats,lons,bearing=45,distance=500000)
#different bearings for each lat lon
destination(lats,lons,bearing=seq(0,360,length.out=9),distance=500000)
#different distances for each lat lon
destination(lats,lons,bearing=45,distance=seq(0,5000000,length.out=9))
#different bearings & distances for each lat lon
destination(lats,lons,bearing=seq(0,360,length.out=9),
distance=seq(0,5000000,length.out=9))
|
Example output
lon1 lat1 bearing distance lon2 lat2
1 165 -85 180 5e+05 165 -89.48412
lon1 lat1 bearing distance lon2 lat2
1 165 -85 0 5e+05 165.0000 -80.51547
2 165 -85 45 5e+05 186.2767 -81.23674
3 165 -85 90 5e+05 206.9805 -83.28751
4 165 -85 135 5e+05 225.0793 -86.34296
5 165 -85 180 5e+05 165.0000 -89.48412
6 165 -85 225 5e+05 104.9207 -86.34296
7 165 -85 270 5e+05 123.0195 -83.28751
8 165 -85 315 5e+05 143.7233 -81.23674
9 165 -85 360 5e+05 165.0000 -80.51547
lon1 lat1 bearing distance lon2 lat2
1 165 -85 45 0 165.0000 -85.00000
2 165 -85 45 500000 186.2767 -81.23674
3 165 -85 45 1000000 194.3648 -77.00867
4 165 -85 45 1500000 198.4876 -72.65156
5 165 -85 45 2000000 200.9868 -68.24188
6 165 -85 45 2500000 202.6751 -63.80524
7 165 -85 45 3000000 203.9030 -59.35241
8 165 -85 45 3500000 204.8455 -54.88866
9 165 -85 45 4000000 205.5997 -50.41686
10 165 -85 45 4500000 206.2236 -45.93872
11 165 -85 45 5000000 206.7542 -41.45533
lon1 lat1 bearing distance lon2 lat2
1 165 -85 0 0 165.00000 -85.00000
2 165 -85 45 0 165.00000 -85.00000
3 165 -85 90 0 165.00000 -85.00000
4 165 -85 135 0 165.00000 -85.00000
5 165 -85 180 0 165.00000 -85.00000
6 165 -85 225 0 165.00000 -85.00000
7 165 -85 270 0 165.00000 -85.00000
8 165 -85 315 0 165.00000 -85.00000
9 165 -85 360 0 165.00000 -85.00000
10 165 -85 0 500000 165.00000 -80.51547
11 165 -85 45 500000 186.27674 -81.23674
12 165 -85 90 500000 206.98052 -83.28751
13 165 -85 135 500000 225.07926 -86.34296
14 165 -85 180 500000 165.00000 -89.48412
15 165 -85 225 500000 104.92074 -86.34296
16 165 -85 270 500000 123.01948 -83.28751
17 165 -85 315 500000 143.72326 -81.23674
18 165 -85 360 500000 165.00000 -80.51547
19 165 -85 0 1000000 165.00000 -76.03018
20 165 -85 45 1000000 194.36480 -77.00867
21 165 -85 90 1000000 226.08902 -79.74152
22 165 -85 135 1000000 267.14337 -83.52598
23 165 -85 180 1000000 345.00000 -86.03181
24 165 -85 225 1000000 62.85663 -83.52598
25 165 -85 270 1000000 103.91098 -79.74152
26 165 -85 315 1000000 135.63520 -77.00867
27 165 -85 360 1000000 165.00000 -76.03018
28 165 -85 0 1500000 165.00000 -71.54378
29 165 -85 45 1500000 198.48759 -72.65156
30 165 -85 90 1500000 234.97881 -75.66280
31 165 -85 135 1500000 280.68253 -79.48211
32 165 -85 180 1500000 345.00000 -81.54741
33 165 -85 225 1500000 49.31747 -79.48211
34 165 -85 270 1500000 95.02119 -75.66280
35 165 -85 315 1500000 131.51241 -72.65156
36 165 -85 360 1500000 165.00000 -71.54378
37 165 -85 0 2000000 165.00000 -67.05596
38 165 -85 45 2000000 200.98685 -68.24188
39 165 -85 90 2000000 239.92864 -71.39773
40 165 -85 135 2000000 286.60774 -75.18329
41 165 -85 180 2000000 345.00000 -77.06232
42 165 -85 225 2000000 43.39226 -75.18329
43 165 -85 270 2000000 90.07136 -71.39773
44 165 -85 315 2000000 129.01315 -68.24188
45 165 -85 360 2000000 165.00000 -67.05596
46 165 -85 0 2500000 165.00000 -62.56645
47 165 -85 45 2500000 202.67511 -63.80524
48 165 -85 90 2500000 243.07011 -67.04909
49 165 -85 135 2500000 289.89284 -70.79914
50 165 -85 180 2500000 345.00000 -72.57621
51 165 -85 225 2500000 40.10716 -70.79914
52 165 -85 270 2500000 86.92989 -67.04909
53 165 -85 315 2500000 127.32489 -63.80524
54 165 -85 360 2500000 165.00000 -62.56645
55 165 -85 0 3000000 165.00000 -58.07500
56 165 -85 45 3000000 203.90296 -59.35241
57 165 -85 90 3000000 245.25162 -62.65581
58 165 -85 135 3000000 291.98889 -66.37620
59 165 -85 180 3000000 345.00000 -68.08874
60 165 -85 225 3000000 38.01111 -66.37620
61 165 -85 270 3000000 84.74838 -62.65581
62 165 -85 315 3000000 126.09704 -59.35241
63 165 -85 360 3000000 165.00000 -58.07500
64 165 -85 0 3500000 165.00000 -53.58143
65 165 -85 45 3500000 204.84548 -54.88866
66 165 -85 90 3500000 246.86769 -58.23553
67 165 -85 135 3500000 293.45408 -61.93185
68 165 -85 180 3500000 345.00000 -63.59964
69 165 -85 225 3500000 36.54592 -61.93185
70 165 -85 270 3500000 83.13231 -58.23553
71 165 -85 315 3500000 125.15452 -54.88866
72 165 -85 360 3500000 165.00000 -53.58143
73 165 -85 0 4000000 165.00000 -49.08560
74 165 -85 45 4000000 205.59967 -50.41686
75 165 -85 90 4000000 248.12472 -53.79729
76 165 -85 135 4000000 294.54626 -57.47396
77 165 -85 180 4000000 345.00000 -59.10866
78 165 -85 225 4000000 35.45374 -57.47396
79 165 -85 270 4000000 81.87528 -53.79729
80 165 -85 315 4000000 124.40033 -50.41686
81 165 -85 360 4000000 165.00000 -49.08560
82 165 -85 0 4500000 165.00000 -44.58742
83 165 -85 45 4500000 206.22359 -45.93872
84 165 -85 90 4500000 249.14066 -49.34619
85 165 -85 135 4500000 295.40047 -53.00656
86 165 -85 180 4500000 345.00000 -54.61559
87 165 -85 225 4500000 34.59953 -53.00656
88 165 -85 270 4500000 80.85934 -49.34619
89 165 -85 315 4500000 123.77641 -45.93872
90 165 -85 360 4500000 165.00000 -44.58742
91 165 -85 0 5000000 165.00000 -40.08688
92 165 -85 45 5000000 206.75418 -41.45533
93 165 -85 90 5000000 249.98779 -44.88534
94 165 -85 135 5000000 296.09422 -48.53192
95 165 -85 180 5000000 345.00000 -50.12029
96 165 -85 225 5000000 33.90578 -48.53192
97 165 -85 270 5000000 80.01221 -44.88534
98 165 -85 315 5000000 123.24582 -41.45533
99 165 -85 360 5000000 165.00000 -40.08688
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 45 5e+05 -135.000000 -85.515907
2 -135 -67.5 45 5e+05 -127.717000 -64.140175
3 -90 -45.0 45 5e+05 -85.749336 -41.734728
4 -45 -22.5 45 5e+05 -41.639949 -19.274173
5 0 0.0 45 5e+05 3.176623 3.193071
6 45 22.5 45 5e+05 48.518228 25.651625
7 90 45.0 45 5e+05 94.748702 48.087166
8 135 67.5 45 5e+05 144.499670 70.428481
9 180 90.0 45 5e+05 315.000000 85.515907
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 0 5e+05 -1.800000e+02 -85.515907
2 -135 -67.5 45 5e+05 -1.277170e+02 -64.140175
3 -90 -45.0 90 5e+05 -8.366621e+01 -44.824007
4 -45 -22.5 135 5e+05 -4.148177e+01 -25.651625
5 0 0.0 180 5e+05 5.502676e-16 -4.514189
6 45 22.5 225 5e+05 4.163995e+01 19.274173
7 90 45.0 270 5e+05 8.366621e+01 44.824007
8 135 67.5 315 5e+05 1.255003e+02 70.428481
9 180 90.0 360 5e+05 0.000000e+00 85.515907
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 45 0 -180.00000 -90.00000
2 -135 -67.5 45 625000 -126.17124 -63.25135
3 -90 -45.0 45 1250000 -80.13712 -36.57743
4 -45 -22.5 45 1875000 -32.99689 -10.13013
5 0 0.0 45 2500000 16.28258 15.75991
6 45 22.5 45 3125000 70.80455 40.24084
7 90 45.0 45 3750000 141.53713 59.98943
8 135 67.5 45 4375000 239.64657 62.45299
9 180 90.0 45 5000000 315.00000 45.10506
lon1 lat1 bearing distance lon2 lat2
1 -180 -90.0 0 0 -1.800000e+02 -90.000000
2 -135 -67.5 45 625000 -1.261712e+02 -63.251354
3 -90 -45.0 90 1250000 -7.433028e+01 -43.911517
4 -45 -22.5 135 1875000 -3.074451e+01 -33.797267
5 0 0.0 180 2500000 2.896532e-15 -22.563681
6 45 22.5 225 3125000 2.557305e+01 1.623163
7 90 45.0 270 3750000 4.672582e+01 36.021757
8 135 67.5 315 4375000 3.035343e+01 62.452993
9 180 90.0 360 5000000 0.000000e+00 45.105056
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