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OCTAVE Mapping PackageDocumentation
Release 1.1.1
Alfredo Foltran
August 10, 2016
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Contents
1 Azimuth 31.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Reckon 52.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Distance 73.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Departure 94.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 Vincenty 115.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6 Vincenty (Direct Form) 136.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
7 Great-Circle to Small-Circle 157.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8 Degree to Kilometer 178.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
9 Kilometer to Degree 199.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
10 Degree to Radians 2110.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
11 Radians to Degree 2311.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
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12 Geocode 2512.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
13 Reverse 2713.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2713.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
14 nPI to PI 2914.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
15 ZERO to 2PI 3115.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
16 Reference Ellipsoid 3316.1 Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
17 Indices and tables 35
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OCTAVE Mapping Package Documentation, Release 1.1.1
This package implements simple mapping functions.
Mapping Functions:
Contents 1
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OCTAVE Mapping Package Documentation, Release 1.1.1
2 Contents
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CHAPTER 1
Azimuth
Calculates the great circle azimuth from a point 1 to a point 2. The latitude and longitude of these two points can eitherbe given independently or as columns of the matrices point 1 and point 2 in the form [latitude longitude].
1.1 Forms
az = azimuth(lat1, lon1, lat2, lon2)
az = azimuth(lat1, lon1, lat2, lon2, units)
az = azimuth(pt1, pt2)
az = azimuth(pt1, pt2, units)
Note: The units for the input coordinates and output angles can be degrees (the default) or radians.
1.2 Examples
Usages:
>> azimuth([10, 10], [10, 40])ans = 87.336>> azimuth([0, 10], [0, 40])ans = 90>> azimuth(pi / 4, 0, pi / 4, -pi / 2, "radians")ans = 5.3279
See also:
Reckon Distance
3
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OCTAVE Mapping Package Documentation, Release 1.1.1
4 Chapter 1. Azimuth
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CHAPTER 2
Reckon
Compute the coordinates of the end-point of a displacement on a sphere. lat e lon are the coordinates of the startingpoint, range is the covered distance of the displacements along a great circle and azimuth is the direction of thedisplacement relative to the North.
This function can also be used to define a spherical coordinate system with rotated poles.
2.1 Forms
[lato, lono] = reckon(lat, lon, range, azimuth)
[lato, lono] = reckon(lat, lon, range, azimuth, units)
Note: The units of all input and output parameters can be either degrees (default) or radians.
2.2 Examples
Usages:
>> [lato, lono] = reckon(0, 10, 30, 90)lato = 0lono = 40.000>> [lato, lono] = reckon(0, 0, pi, pi / 2, "radians")lato = 0lono = -3.1416
See also:
Azimuth
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OCTAVE Mapping Package Documentation, Release 1.1.1
6 Chapter 2. Reckon
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CHAPTER 3
Distance
Calculates the distance (in degrees) between point 1 and point 2.
3.1 Forms
dist = distance(pt1, pt2)
Note: pt1 and pt2 are two-column matrices of the form [latitude longitude].
3.2 Examples
Usages:
>> distance([37,-76], [37,-9])ans = 52.309>> distance([37,-76], [67,-76])ans = 30.000
See also:
Azimuth Vincenty
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OCTAVE Mapping Package Documentation, Release 1.1.1
8 Chapter 3. Distance
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CHAPTER 4
Departure
Calculates the distance in degrees between longitudes lon1 and lon2 at latitude defined by lat.
4.1 Forms
dist = departure(lon1, lon2, lat)
4.2 Examples
Usages:
>> departure(0, 10, 0)ans = 10>> departure(0, 10, 60)ans = 5
See also:
Distance
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OCTAVE Mapping Package Documentation, Release 1.1.1
10 Chapter 4. Departure
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CHAPTER 5
Vincenty
Calculates the distance (in kilometers) between point 1 and point 2 using the formula devised by Thaddeus Vincenty,with an accurate ellipsoidal model of the earth. The default ellipsoidal model is WGS-84, which is the most globallyaccurate model.
5.1 Forms
dist = vincenty(pt1, pt2)
dist = vincenty(pt1, pt2, ellipsoid)
[dist, az] = vincenty(pt1, pt2)
[dist, az] = vincenty(pt1, pt2, ellipsoid)
Note: pt1 and pt2 are two-column matrices of the form [latitude longitude]. The units for the inputcoordinates angles must be degrees. ellipsoid defines the reference ellipsoid to use.
Sample values for ellipsoid are the following:
• WGS_84 (default) - referenceEllipsoid(7030)
• GRS_80 - referenceEllipsoid(7019)
• Airy - referenceEllipsoid(7001)
• Intl - referenceEllipsoid(7022)
• Clarke - referenceEllipsoid(7012)
• GRS - referenceEllipsoid(7003)
The sample values are the following:
Model Major (km) Minor (km) 1 / fWGS 1984 6378.137 6356.7523142 298.257223563GRS 1980 6378.137 6356.7523141 298.257222101G.B. Airy 1830 6377.563396 6356.256909 299.3249646Internacional 1924 6378.388 6356.911946 297.0Clarke 1880 6378.249145 6356.51486955 293.465Australian Nat. 6378.1600 6356.774719 298.25
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OCTAVE Mapping Package Documentation, Release 1.1.1
5.2 Examples
Usages:
>> vincenty([37, -76], [37, -9])ans = 5830.081>> vincenty([37, -76], [67, -76], referenceEllipsoid(7019))ans = 3337.843
See also:
Distance Reference Ellipsoid
12 Chapter 5. Vincenty
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CHAPTER 6
Vincenty (Direct Form)
Compute the coordinates of the end-point of a displacement on a geodesic. The parameters lat and lon are thecoordinates of the starting point, The parameter range is the covered distance of the displacements along a specifiedgeodesic and azi is the direction of the displacement relative to the North.
6.1 Forms
[lato, lono] = vincentyDirect(lat, lon, range, azi)
[lato, lono, azo] = vincentyDirect(lat, lon, range, azi)
[lato, lono] = vincentyDirect(lat, lon, range, azi, dim)
[lato, lono, azo] = vincentyDirect(lat, lon, range, azi, dim)
[lato, lono] = vincentyDirect(lat, lon, range, azi}, dim, ellipsoid)
[lato, lono, azo] = vincentyDirect(lat, lon, range, azi, dim, ellipsoid)
Note: The units of all input and output parameters must be ‘radians’ and/or ‘kilometers’. dim defines the rangedimension to use. ellipsoid defines the reference ellipsoid to use.
The possible values for dim are ‘angle’ (default) or ‘length’.
Sample values for ellipsoid are the following:
• WGS_84 (default) - referenceEllipsoid(7030)
• GRS_80 - referenceEllipsoid(7019)
• Airy - referenceEllipsoid(7001)
• Intl - referenceEllipsoid(7022)
• Clarke - referenceEllipsoid(7012)
• GRS - referenceEllipsoid(7003)
The sample values are the following:
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OCTAVE Mapping Package Documentation, Release 1.1.1
Model Major (km) Minor (km) 1 / fWGS 1984 6378.137 6356.7523142 298.257223563GRS 1980 6378.137 6356.7523141 298.257222101G.B. Airy 1830 6377.563396 6356.256909 299.3249646Internacional 1924 6378.388 6356.911946 297.0Clarke 1880 6378.249145 6356.51486955 293.465Australian Nat. 6378.1600 6356.774719 298.25
6.2 Examples
Usages:
>> [lat, lon] = vincentyDirect(0, 0, pi, pi / 2)lat = 0lon = 3.1311>> [lat, lon, az] = vincentyDirect(0, 0, pi, pi / 2)lat = 0lon = 3.1311az = 1.5708
See also:
Vincenty Reference Ellipsoid
14 Chapter 6. Vincenty (Direct Form)
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CHAPTER 7
Great-Circle to Small-Circle
Converts a great circle to small circle notation.
7.1 Forms
[lato, lono, range] = gc2sc(lat, lon, azi)
[lato, lono] = gc2sc(lat, lon, azi, units)
mat = gc2sc(lat, lon, azi)
mat = gc2sc(lat, lon, azi, units)
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OCTAVE Mapping Package Documentation, Release 1.1.1
16 Chapter 7. Great-Circle to Small-Circle
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CHAPTER 8
Degree to Kilometer
Convert a distance along a great circle of the Earth from degrees to kilometer. Great-circle distance uses a sphericalmodel of the earth, using the average great-circle radius of 6372.795 kilometers, resulting in an error of up to about0.5%.
8.1 Forms
x = deg2km(a)
See also:
Kilometer to Degree
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OCTAVE Mapping Package Documentation, Release 1.1.1
18 Chapter 8. Degree to Kilometer
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CHAPTER 9
Kilometer to Degree
Convert a distance along a great circle of the Earth from kilometer to degrees. A radius Great-circle distance uses aspherical model of the earth, using the average great-circle radius of 6372.795 kilometers, resulting in an error of upto about 0.5%.
9.1 Forms
a = km2deg(x)
See also:
Degree to Kilometer
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OCTAVE Mapping Package Documentation, Release 1.1.1
20 Chapter 9. Kilometer to Degree
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CHAPTER 10
Degree to Radians
Converts angles input in degrees to the equivalent in radians.
10.1 Forms
anglout = deg2rad(anglin)
See also:
Radians to Degree
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OCTAVE Mapping Package Documentation, Release 1.1.1
22 Chapter 10. Degree to Radians
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CHAPTER 11
Radians to Degree
Converts angles input in radians to the equivalent in degrees.
11.1 Forms
anglout = rad2deg(anglin)
See also:
Degree to Radians
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OCTAVE Mapping Package Documentation, Release 1.1.1
24 Chapter 11. Radians to Degree
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CHAPTER 12
Geocode
Geolocation service from Google Maps API. Define a geocode method for resolving a location from a string.
Geocoding is the process of converting addresses (like “1600 Amphitheatre Parkway, Mountain View, CA”) intogeographic coordinates (like latitude 37.423021 and longitude -122.083739), which you can use to place markers orposition the map.
Reverse geocoding is the process of converting geographic coordinates into a human-readable address.
12.1 Forms
[lato, lono] = geocode(addr)
[lato, lono, xml] = geocode(addr)
12.2 Examples
Usages:
>> [lat, lon] = geocode('new york,ny')lat = 40.714lon = -74.006>> [lat, lon] = geocode('brasilia,df')lat = -15.827lon = -47.922
See also:
Reverse
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OCTAVE Mapping Package Documentation, Release 1.1.1
26 Chapter 12. Geocode
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CHAPTER 13
Reverse
Geolocation service from Google Maps API. Define a geocode method for resolving a address from a location.
The term geocoding generally refers to translating a human-readable address into a location on a map. The process ofdoing the converse, translating a location on the map into a human-readable address, is known as reverse geocoding.
13.1 Forms
addr = reverse([lat lon])
[addr, xml] = reverse([lat lon])
13.2 Examples
Usages:
>> reverse([40.714 -74.006])ans = '58-68 Chambers Street, Nova York, NY 10007, EUA'>> reverse([-15.827 -47.922])ans = 'Asa Sul, Brasília, DF, 70383-070, Brasil'
See also:
Geocode
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OCTAVE Mapping Package Documentation, Release 1.1.1
28 Chapter 13. Reverse
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CHAPTER 14
nPI to PI
This brings the angin into the [−𝑝𝑖𝑝𝑖] interval.
14.1 Forms
angout = npi2pi(angin)
See also:
ZERO to 2PI
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OCTAVE Mapping Package Documentation, Release 1.1.1
30 Chapter 14. nPI to PI
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CHAPTER 15
ZERO to 2PI
This brings the angin into the [02 * 𝑝𝑖[ interval.
15.1 Forms
angout = zero22pi(angin)
See also:
nPI to PI
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CHAPTER 16
Reference Ellipsoid
This function returns a reference ellipsoid object corresponding to the specified code (numerical EPSG). The val-ues of the SemimajorAxis and SemiminorAxis properties are in kilometers. The reference ellipsoid has fiveproperties: Code, Name, SemimajorAxis, SemiminorAxis and Flattening.
The form code can receive a valid EPSG code. 46 codes are currently implemented between 7001 and 7053 (exceptfor 7017, 7023, 7026 and 7037-7040).
The valid values for name form are as follows: sphere, unitsphere, earth, moon, mercury, venus, mars, jupiter, saturn,uranus, neptune and pluto.
16.1 Forms
ref = referenceEllipsoid(code)
ref = referenceEllipsoid(name)
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CHAPTER 17
Indices and tables
• genindex
• search
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Index
AAzimuth, 1
DDegree to Kilometer, 15Degree to Radian, 19Departure, 7Distance, 5
GGeocode, 23Great-Circle to Small-Circle, 14
KKilometer to Degree, 17
NnPI to PI, 27
RRadian to Degree, 21Reckon, 3Reference Ellipsoid, 31Reverse, 25
VVincenty, 9Vincenty (Direct Form), 12
ZZERO to 2PI, 29
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