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Projection Class Function Manual (SET) |
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Projection Class Function Manual (SET) |
Purpose
To set a projection object to the Albers Equal-Area Conic Projection.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Conic
Equal-Area
Parallels are unequally spaced arcs of concentric circles, more closely spaced at the north and south edges of the map.
Meridians are equally spaced radii of the same circles, cutting parallels at right angles.
There is no distortion in scale or shape along two standard parallel, normally, or along just one.
Poles are arcs of circles.
Used for equal-area maps of regions with predominant east-west expanse, especially the conterminous US.
Presented by Albers in 1805.
Class
Projection
Usage
{void} object.SETALBERS({double} argm1,{double} argm2,{double} argm3,{double} argm4,[{double} argm5,{double} argm6])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = latitude of the 1st standard parallel
argm4 = latitude of the 2nd standard parallel
argm5 = false origin X value (default = 0)
argm6 = false origin Y value (default = 0)
Example:
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->p = projection() ->p.setalbers(deg(31.4),deg(-98.3), deg(32.08), deg(33.58)) ->e.set("clarke66") ->p.ellipsoid() = e
->p.geo2xy(deg(32.15202345), deg(-99.40004567)) |
The above example set the Albers Equal-Area Conic projection's origin at latitude 31 deg 40 min. The central meridian is at longitude -98 deg 8 min. The two standard parallels are at latitudes 32 deg 8 min, and 33 deg 58 min. False origin is x = 0 and y = 0. The test data is at latitude 32 deg 15 min 20.2345 sec and longitude -99 deg 40 min 00.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Gnomonic Projection.
This projection is used only in the spherical form, hence the radius of the sphere will be taken from the value of the semi-major axis of the defined ellipsoid.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
It is the perspective projection of the globe from the center onto a plane tangent to the surface.
Azimuthal and perspective
All meridians and Equator are straight lines.
Neither conformal nor equal-area.
No distortion at the center only.
Used only in the spherical form.
Class
Projection
Usage
{void} object.SETGNOMONIC({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setGnomonic(-80,100) WARNING :
Gnomonic projection is available only in the spherical form ->dms(pt1.x(), 5) |
The above example set the Gnomonic projection's origin at latitude 80 deg 0 min. The central meridian is at longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Lambert Azimuthal Equal-Area Projection.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Azimuthal
Equal-Area
Scale decreases radially as the distance increases from the center, the only point without distortion.
Directions from the center are true for the sphere and the polar ellipsoidal forms.
Class
Projection
Usage
{void} object.SETLAEA({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setLAEA(-80,100)
->p1.geo2xy(deg(-80.15202345), deg(99.20124567))
->p1.xy2geo(pt.x(), pt.y()) ->dms(pt1.x(), 5) |
The above example set the Gnomonic projection's origin at latitude 80 deg 0 min. The central meridian is at longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Lambert Conformal Conic Projection.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Conic
Conformal
Parallels are unequally spaced arcs of concentric circles, more closely spaced at the north and south edges of the map.
Meridians are equally spaced radii of the same circles, cutting parallels at right angles.
Scale is true along two standard parallels, normally, or along just one.
Used for maps of countries and regions with predominant east-west expanse.
Presented by Lambert in 1772.
Class
Projection
Usage
{void} object.SETLCC({double} argm1,{double} argm2,{double} argm3,{double} argm4,[{double} argm5,{double} argm6])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = latitude of the 1st standard parallel
argm4 = latitude of the 2nd standard parallel
argm5 = false origin X value (default = 0)
argm6 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setLCC(deg(31.40), deg(-98.30), deg(32.08), deg(33.58), 600000,2000000) ->e = ellipsoid() ->e.set("GRS80") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(32.15207295), deg(-99.40000086)) ->print pt1 ( 490070.630 , 2065936.183) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) 32 15 20.72950 ->print dms(pt2.y(), 5) 260 19 59.99140 -> |
The above example set the Lambert Conformal Conic projection's origin at latitude 31 deg 40 min. The central meridian is at longitude -98 deg 30 min. The two standard parallels are at latitudes 32 deg 8 min, and 33 deg 58 min. False origin is x = 600000 and y = 2000000. The test data is at latitude 32 deg 15 min 20.7295 sec and longitude -99 deg 40 min 00.0086 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Lambert Conformal Conic Projection (one parallel). A scale factor at the central parallel has to be specified for this function.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Conic
Conformal
Parallels are unequally spaced arcs of concentric circles, more closely spaced at the north and south edges of the map.
Meridians are equally spaced radii of the same circles, cutting parallels at right angles.
Scale is true along two standard parallels, normally, or along just one.
Used for maps of countries and regions with predominant east-west expanse.
Presented by Lambert in 1772.
Class
Projection
Usage
{void} object.SETLCC({double} argm1,{double} argm2,{double} argm3,{double} argm4,[{double} argm5,{double} argm6])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = latitude of the 1st standard parallel
argm4 = scale factor at central parellel
argm5 = false origin X value (default = 0)
argm6 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setLCC1(deg(31.40), deg(-98.30), deg(32.08), 1.0000245, 600000,2000000) -> -> |
The above example set the Lambert Conformal Conic projection's origin at latitude 31 deg 40 min. The central meridian is at longitude -98 deg 30 min. The central parallels are at latitudes 32 deg 8 min, the scale factor is 1.0000245, False origin is x = 600000 and y = 2000000.
See also (class function)
geo2xy, xy2geo, setLCC
SETMERCATOR
Purpose
To set a projection object to the Mercator Projection.
All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Cylindrical
Conformal
Meridians are equally spaced straight lines.
Parallels are unequally spaced straight lines, closer near the Equator, cutting meridians at right angles.
Scale is true along the Equator, or along two parallels equidistant from the equator.
Presented by Mercator in 1569.
Class
Projection
Usage
{void} object.SETMERCATOR({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = longitude of central meridian (the Y-axis)
(Note the X-axis is the Equator)
argm2 = latitude of true scale (default = 0)
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setMERCATOR(100,20) ->e = ellipsoid() ->e.set("GRS80") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(21,99) ->print pt1 ( -104647.086 , 2234122.786) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) 21 00 00.00000 ->print dms(pt2.y(), 5) 99 00 00.00000 -> |
The above example set the Mercator projection's central meridian at longitude 100 deg 0 min. The latitude of true scale is at 20 deg. False origin is x = 0 and y = 0. The test data is at latitude 21deg and longitude 99 deg.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Oblique Mercator Projection.
Computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual, Hotine formulas.
The following is a summary of the projection.
Cylindrical (oblique)
Conformal
Two meridians 180 degrees apart are straight lines.
Other merdians and parallels are complex cueves.
Scale is true along chosen central line, if set =1, and becomes infinite 90 degrees from the central line.
Used for maps of areas with greater extent in an oblique direction.
Class
Projection
Usage
{void} object.SETOM({double} argm1,{double} argm2, {double} argm3,{double} argm4,[{double} argm5,{double} argm6])
argm1 = latitude of the projection center
argm2 = longitude of the projection center
argm3 = Azimuth of the central line passing through the projection center
argm4 = scale factor on the central line
argm5 = false origin X value (default = 0)
argm6 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setOM(deg(45.55), -123, 65, 1.000, 7000000, -3000000) ->e = ellipsoid() ->e.set("GRS80") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(46.121757866), deg(-123.572188345)) ->print pt1 ( 94514.720 , 218152.786) -> |
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Orthographic Projection.
This projection is used only in the spherical form, hence the radius of the sphere will be taken from the value of the semi-major axis of the defined ellipsoid.All angles are required and expressed in degrees.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Azimuthal
Neither conformal nor equal-area
Closely resembles a globe in appearance, since it is a perspective projectionfrom infinite distance.
ONly one hemisphere can be shown at a time.
No distortion at the center only.
Used only in the spherical form.
Class
Projection
Usage
{void} object.SETORTHGPH({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setORTHGPH(-80,100) WARNING :
Orthographic projection is available only in the spherical form ->e.set("CLARKE66") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(-80.15202345), deg(99.20124567)) ->print pt1 ( -12495.421 , -28527.001) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) -80 15 20.23450 ->print dms(pt2.y(), 5) 99 20 12.45670 -> |
The above example set the Orthographic projection's origin at latitude 80 deg 0 min. The central meridian is at longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Polar Stereographic Projection.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Azimuthal
Conformal
Scale increases away from the center of the projection.
Used for polar maps and miscellaneous special maps.
Class
Projection
Usage
{void} object.SETPLOSTRGPH({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = latitude of true scale
argm2 = longitude of central meridian (the Y-axis)
(Note X-axis is perpendicular to Y-axis and the origin is at the pole)
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setPOLSTRGPH(-80,100) ->e = ellipsoid() ->e.set("CLARKE66") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(-80.15202345), deg(99.20124567)) ->print pt1 ( -12531.874 , 1082606.147) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) -80 15 20.23450 ->print dms(pt2.y(), 5) 99 20 12.45670 -> |
The above example set the Polar Stereographic projection's origin at latitude 80 deg 0 min. The central meridian is at longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Stereographic Projection.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Azimuthal
Conformal
Scale increases away from the center of the projection.
Used for polar maps and miscellaneous special maps.
Class
Projection
Usage
{void} object.SETSTRGPH({double} argm1,{double} argm2,{double} argm3,[{double} argm4,{double} argm5])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = scale factor at the origin
argm4 = false origin X value (default = 0)
argm5 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setSTRGPH(-80,100,1.00) ->e = ellipsoid() ->e.set("CLARKE66") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(-80.15202345), deg(99.20124567)) ->print pt1 ( -12536.843 , -28615.685) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) -80 15 20.23450 ->print dms(pt2.y(), 5) 99 20 12.45670 -> |
The above example set the Stereographic projection's origin at latitude 80 deg 0 min. The central meridian is at longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Transverse Mercator Projection.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Cylindrical (transverse)
Conformal
Scale is true along central meridian, or along two straight lines equidistant from and parallel to central meridian.
Used extensively for map scale 1:24,000 to 1:250,000
Class
Projection
Usage
{void} object.SETTM({double} argm1,{double} argm2,{double} argm3,[{double} argm4,{double} argm5])
argm1 = latitude of origin
argm2 = longitude of central meridian (the Y-axis)
argm3 = scale factor along central meridian
argm4 = false origin X value (default = 0)
argm5 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setTM(31,-106,0.9999,500000,0) ->e = ellipsoid() ->e.set("CLARKE66") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(32.15207295), deg(-105.40000086)) ->print pt1 ( 531407.353 , 139269.107) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) 32 15 20.72950 ->print dms(pt2.y(), 5) 254 19 59.99140 -> |
The above example set the Transverse Mercator projection's origin at latitude 31 deg 0 min. The central meridian is at longitude -106 deg 0 min. Scale factor at central meridian is 0.9999. False origin is x = 500,000 and y = 0. The test data is at latitude 32 deg 15 min 20.7295 sec and longitude -105 deg 40 min 00.0086 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Topocentric Projection.
All angles are required and expressed in degrees.
This is in fact a 3D Cartesian coordinate, origin at a point on the earth surface, phe0 and rammda0. Its Y-axis point toward the north direction and the X-axis is perpendicular to the Y-axis. The utilization of this coordinate system is in Photogrammetry where aerial photos cover a very large area, hence error of the earth curvature is significant, and an intermediate true 3D Cartesian coordinate system is introduced.
The space rectangular coordinate system is used to bridge the geographic coordinate, latitude, and longitude, to X Y map projection coordinate and vice versa. However, the Z coordinate is dropped out when the computation is done. See more details in section Example (Geodesy and Surveying).
It is not recommended to use this coordinate system as a general map projection system, because it is not as accurate, due to lack of the third dimension information. The sole purpose of it is to used in orthophoto generation when an topocentric must be used as an intermediate coordinate system as mentioned above.
Class
Projection
Usage
{void} object.SETTOPOCTRC({double} argm1,{double} argm2,[{double} argm3,{double} argm4])
argm1 = latitude of origin
argm2 = longitude of origin
argm3 = false origin X value (default = 0)
argm4 = false origin Y value (default = 0)
Example:
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->p1 = projection() ->p1.setTOPOCTRC(-80,100) ->e = ellipsoid() ->e.set("CLARKE66") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(-80.15202345), deg(99.20124567)) ->print pt1 ( -12536.702 , -28615.454) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) -80 15 20.22356 ->print dms(pt2.y(), 5) 99 20 12.48590 -> |
The above example set the Topocentric origin at latitude 80 deg 0 min and longitude 100 deg 0 min. False origin is x = 0 and y = 0. The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Un-projected Projection.
The way the projection works is just simply to assign longitude to the y coordinate and latitude to x coordinate.
Class
Projection
Usage
{void} object.SETUNPROJ()
Example:
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->p1 = projection() ->p1.setUNPROJ() ->pt1 = p1.geo2xy(deg(-80.15202345), deg(99.20124567)) ->print pt1 ( 99.337 , -80.256) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) -80 15 20.23450 ->print dms(pt2.y(), 5) 99 20 12.45670 -> |
The test data is at latitude -80 deg 15 min 20.2345 sec and longitude 99 deg 20 min 12.4567 sec.
See also (class function)
geo2xy, xy2geo
Purpose
To set a projection object to the Universal Transverse Mercator (UTM) Projection.
Description and computation algorithms adopted from Snyder, J. P. (1987), Map Projections - A Working Manual.
The following is a summary of the projection.
Cylindrical (transverse)
Conformal
Scale at central meridian is 0.9996
mapping zone is 3 degrees from the left and right of the central meridian, hence 6 degree width.
Zone number 1 is at from longitudes 180 to 186.
False origin value for X is 500,000.
False origin value for Y is 0 for the northen hemisphere and ,1000,000 for the southern hemisphere.
Used extensively for map scale 1:24,000 to 1:250,000
Class
Projection
Usage
{void} object.SETUTM({int} argm1,[{String} argm2])
argm1 = zone number (must be 1 to 60)
argm2 = Northern or Southern hemisphere (must be either "N" or "S")
(default = "N")
Example:
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->p1 = projection() ->p1.setutm(48) ->e = ellipsoid() ->e.set("EVEREST") ->p1.ellipsoid() = e ->pt1 = p1.geo2xy(deg(13.47458745), deg(109.34545893)) ->print pt1 ( 995632.458 , 1529785.236) ->pt2 = p1.xy2geo(pt1.x(), pt1.y()) ->print dms(pt2.x(), 5) 13 47 45.87450 ->print dms(pt2.y(), 5) 109 34 54.58942 -> |
The above example set the Universal Transverse Mercator projection to zone 48 N . The test data is at latitude 13 deg 47 min 45.8745 sec and longitude 109 deg 34 min 54.5893 sec.
See also (class function)
geo2xy, xy2geo