GEOIDE SSII-109

GEOIDE SSII-109

M A P D I S T O R T I O N S

MAP DISTORTION

• No map projection maintains correct scale

throughout

• The intersection of any two lines on the Earth is

represented on the map at the same or different

angle

• Map projections aim to either minimize scale,

angular or area distortion

TISSOT'S THEOREM

At every point there are two orthogonal principal directions

which are perpendicular on both the Earth (u) and the map

(u')

Figure (A) displays a point on the Earth and (B) a point on the

projection

TISSOT'S INDICATRIX

• An infinitely small circle on the Earth will project

as an infinitely small ellipse on any map

projection (except conformal projections where

it is a circle)

• Major and minor axis of ellipse are directly related to the scale distortion and the

maximum angular deformation

SCALE DISTORTION

• The ratio of an infinitesimal linear distance in any

direction at any point on the projection and the

corresponding infinitesimal linear distance on the

Earth

• h – scale distortion along the meridians

• k – scale distortion along the parallels

MAXIMUM ANGULAR DEFORMATION AND AREAL SCALE FACTOR

• Maximum angular deformation, w is the biggest deviation from

principle directions define on the Earth to the principle directions

define on the map

• Occurs in each of the four quadrants

define by the principle directions

of Tissot's indicatrix

• Areal scale factor is the exaggeration

of an infinitesimally small area at a

particular point

NOTES

• Three tangent points are taken for a number of

different azimuthal projection:

(φ, λ)= (0°, 0°), (φ, λ)= (45° N, 0°), (φ, λ)= (80° N, 0°)

• Each projection covers a ‘square’ on the Earth, with

latitude and longitude increasing in increments of 1°

• Ellipsoidal (WGS84) equations are used for the

projections

AZIMUTHAL PROJECTIONS

• Direction or azimuth from the centre of the

projection to every other point on the map is show

correctly

• Scale and distortions change only with the distance

from the centre

• One standard point (centre of projection)

LAMBERT AZIMUTHAL EQUAL AREA

• Equal area

• Central meridian is a straight line on all aspects

• All other meridians and parallels are complex curves

• Not a perspective projection

• Scale increases radially as the distance increases

from the tangent point

• Scale increases in the direction perpendicular to

radii as the distance increases from the tangent

point


Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E

2 N 1.0000 0.9999 0.9998 0.9999 1.0000 2 N 1.0000 1.0001 1.0002 1.0001 1.0000

1 N 1.0001 1.0000 1.0000 1.0000 1.0001 1 N 0.9999 1.0000 1.0000 1.0000 0.9999

0 1.0002 1.0000 1.0000 1.0000 1.0002 0 0.9998 1.0000 1.0000 1.0000 0.9998

1 S 1.0001 1.0000 1.0000 1.0000 1.0001 1 S 0.9999 1.0000 1.0000 1.0000 0.9999

2 S 1.0000 0.9999 0.9998 0.9999 1.0000 2 S 1.0000 1.0001 1.0002 1.0001 1.0000


47 N 0.9999 0.9998 0.9998 0.9998 0.9999 47 N 1.0001 1.0002 1.0002 1.0002 1.0001

46 N 1.0000 1.0000 0.9999 1.0000 1.0000 46 N 1.0000 1.0000 1.0001 1.0000 1.0000

45 N 1.0001 1.0000 1.0000 1.0000 1.0001 45 N 0.9999 1.0000 1.0000 1.0000 0.9999

44 N 1.0001 1.0000 1.0000 1.0000 1.0001 44 N 0.9999 1.0000 1.0000 1.0000 0.9999

43 N 1.0000 0.9999 0.9999 0.9999 1.0000 43 N 1.0000 1.0001 1.0001 1.0001 1.0000


82 N 0.9998 0.9998 0.9998 0.9998 0.9998 82 N 1.0002 1.0002 1.0002 1.0002 1.0002

81 N 1.0000 1.0000 1.0000 1.0000 1.0000 81 N 1.0000 1.0000 1.0000 1.0000 1.0000

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0000 1.0000 1.0000 1.0000 1.0000 79 N 1.0000 1.0000 1.0000 1.0000 1.0000

78 N 0.9999 0.9999 0.9999 0.9999 0.9999 78 N 1.0001 1.0001 1.0001 1.0001 1.0001

Longitude (°) Longitude (°)


Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k)Longitude (°) Longitude (°)


Latitude (°) 2 W 1 W 0 1 E 2 E

2 N 2' 5.65'' 1' 18.54'' 1' 2.83'' 1' 18.54'' 2' 5.65''

1 N 1' 18.54'' 31.41'' 15.71'' 31.41'' 1' 18.54''

0 1' 2.84'' 15.71'' 0 15.71'' 1' 2.84''

1 S 1' 18.54'' 31.41'' 15.71'' 31.41'' 1' 18.54''

2 S 2' 5.65'' 1' 18.54'' 1' 2.83'' 1' 18.54'' 2' 5.65''


47 N 1' 49.95'' 1' 26.74'' 1' 18.95'' 1' 26.74'' 1' 49.95''

46 N 55.90'' 32.01'' 23.76'' 32.01'' 55.90''

45 N 33.55'' 9.73'' 0 9.73'' 33.55''

44 N 41.41'' 16.71'' 7.65'' 16.71'' 41.41''

43 N 1' 20.23'' 55.20'' 46.72'' 55.20'' 1' 20.23''


82 N 1' 9.91'' 1' 8.76'' 1' 8.37'' 1' 8.76'' 1' 49.95''

81 N 20.22'' 18.91'' 18.48'' 18.91'' 55.90''

80 N 2.14'' 0.68'' 0 0.68'' 33.55''

79 N 15.08'' 13.48'' 12.94'' 13.48'' 41.41''

78 N 59.60'' 57.87'' 57.30'' 57.87'' 1' 20.23''

Angular Deformation (w)

Longitude (°)

Longitude (°)

Longitude (°)

LAMBERT AZIMUTHAL EQUAL AREATISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (0°, 0°)

If |a – b| < 0.001 ellipse

is shown in green colour

otherwise it is red


Tangent Point: (φ, λ)= (45° N, 0°)



otherwise it is red





otherwise it is red


Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E

5N 1.0019 1.0016 1.0013 1.0011 1.0010 1.0010 1.0010 1.0011 1.0013 1.0016 1.0019

4 N 1.0016 1.0012 1.0010 1.0008 1.0006 1.0006 1.0006 1.0008 1.0010 1.0012 1.0016

3 N 1.0013 1.0010 1.0007 1.0005 1.0004 1.0003 1.0004 1.0005 1.0007 1.0010 1.0013

2 N 1.0011 1.0008 1.0005 1.0003 1.0002 1.0002 1.0002 1.0003 1.0005 1.0008 1.0011

1 N 1.0010 1.0006 1.0004 1.0002 1.0001 1.0000 1.0001 1.0002 1.0004 1.0006 1.0010

0 1.0010 1.0006 1.0003 1.0002 1.0000 1.0000 1.0000 1.0002 1.0003 1.0006 1.0010

1 S 1.0010 1.0006 1.0004 1.0002 1.0001 1.0000 1.0001 1.0002 1.0004 1.0006 1.0010

2 S 1.0011 1.0008 1.0005 1.0003 1.0002 1.0002 1.0002 1.0003 1.0005 1.0008 1.0011

3 S 1.0013 1.0010 1.0007 1.0005 1.0004 1.0003 1.0004 1.0005 1.0007 1.0010 1.0013

4S 1.0016 1.0012 1.0010 1.0008 1.0006 1.0006 1.0006 1.0008 1.0010 1.0012 1.0016

5 S 1.0019 1.0016 1.0013 1.0011 1.0010 1.0010 1.0010 1.0011 1.0013 1.0016 1.0019


50 N 1.0015 1.0013 1.0012 1.0011 1.0011 1.0011 1.0011 1.0011 1.0012 1.0013 1.0015

49 N 1.0011 1.0010 1.0008 1.0008 1.0007 1.0007 1.0007 1.0008 1.0008 1.0010 1.0011

48 N 1.0009 1.0007 1.0006 1.0005 1.0004 1.0004 1.0004 1.0005 1.0006 1.0007 1.0009

47 N 1.0007 1.0005 1.0004 1.0003 1.0002 1.0002 1.0002 1.0003 1.0004 1.0005 1.0007

46 N 1.0005 1.0004 1.0002 1.0001 1.0001 1.0001 1.0001 1.0001 1.0002 1.0004 1.0005

45 N 1.0005 1.0003 1.0002 1.0001 1.0000 1.0000 1.0000 1.0001 1.0002 1.0003 1.0005

44 N 1.0005 1.0003 1.0002 1.0001 1.0000 1.0000 1.0000 1.0001 1.0002 1.0003 1.0005

43 N 1.0006 1.0004 1.0003 1.0002 1.0001 1.0001 1.0001 1.0002 1.0003 1.0004 1.0006

42 N 1.0008 1.0006 1.0005 1.0004 1.0003 1.0003 1.0003 1.0004 1.0005 1.0006 1.0008

41 N 1.0010 1.0009 1.0007 1.0006 1.0006 1.0005 1.0006 1.0006 1.0007 1.0009 1.0010

40 N 1.0014 1.0012 1.0010 1.0009 1.0009 1.0009 1.0009 1.0009 1.0010 1.0012 1.0014


85N 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010 1.0010

84 N 1.0007 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0007

83 N 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004 1.0004

82 N 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002

81 N 1.0001 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0001

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

78 N 1.0002 1.0002 1.0002 1.0001 1.0001 1.0001 1.0001 1.0001 1.0002 1.0002 1.0002

77 N 1.0004 1.0003 1.0003 1.0003 1.0003 1.0003 1.0003 1.0003 1.0003 1.0003 1.0004

76 N 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006 1.0006

75 N 1.0010 1.0009 1.0009 1.0009 1.0009 1.0009 1.0009 1.0009 1.0009 1.0009 1.0010

Semi major - axis (a)

Longitude (°)

Longitude (°)

Longitude (°)



5N 0.9981 0.9984 0.9987 0.9989 0.9990 0.9990 0.9990 0.9989 0.9987 0.9984 0.9981

4 N 0.9984 0.9988 0.9990 0.9992 0.9994 0.9994 0.9994 0.9992 0.9990 0.9988 0.9984

3 N 0.9987 0.9990 0.9993 0.9995 0.9996 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987

2 N 0.9989 0.9992 0.9995 0.9997 0.9998 0.9998 0.9998 0.9997 0.9995 0.9992 0.9989

1 N 0.9990 0.9994 0.9996 0.9998 0.9999 1.0000 0.9999 0.9998 0.9996 0.9994 0.9990

0 0.9990 0.9994 0.9997 0.9998 1.0000 1.0000 1.0000 0.9998 0.9997 0.9994 0.9990

1 S 0.9990 0.9994 0.9996 0.9998 0.9999 1.0000 0.9999 0.9998 0.9996 0.9994 0.9990

2 S 0.9989 0.9992 0.9995 0.9997 0.9998 0.9998 0.9998 0.9997 0.9995 0.9992 0.9989

3 S 0.9987 0.9990 0.9993 0.9995 0.9996 0.9997 0.9996 0.9995 0.9993 0.9990 0.9987

4S 0.9984 0.9988 0.9990 0.9992 0.9994 0.9994 0.9994 0.9992 0.9990 0.9988 0.9984

5 S 0.9981 0.9984 0.9987 0.9989 0.9990 0.9990 0.9990 0.9989 0.9987 0.9984 0.9981


50 N 0.9985 0.9987 0.9988 0.9989 0.9989 0.9990 0.9989 0.9989 0.9988 0.9987 0.9985

49 N 0.9989 0.9990 0.9992 0.9992 0.9993 0.9993 0.9993 0.9992 0.9992 0.9990 0.9989

48 N 0.9991 0.9993 0.9994 0.9995 0.9996 0.9996 0.9996 0.9995 0.9994 0.9993 0.9991

47 N 0.9993 0.9995 0.9996 0.9997 0.9998 0.9998 0.9998 0.9997 0.9996 0.9995 0.9993

46 N 0.9995 0.9996 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9996 0.9995

45 N 0.9995 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995

44 N 0.9995 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995

43 N 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994

42 N 0.9992 0.9994 0.9995 0.9996 0.9997 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992

41 N 0.9990 0.9991 0.9993 0.9994 0.9994 0.9995 0.9994 0.9994 0.9993 0.9991 0.9990

40 N 0.9986 0.9988 0.9990 0.9991 0.9991 0.9991 0.9991 0.9991 0.9990 0.9988 0.9986


85N 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990 0.9990

84 N 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9993

83 N 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996

82 N 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998

81 N 0.9999 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 0.9999 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999

78 N 0.9998 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998

77 N 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9996

76 N 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994

75 N 0.9990 0.9991 0.9991 0.9991 0.9991 0.9991 0.9991 0.9991 0.9991 0.9991 0.9990

Longitude (°)

Longitude (°)

Longitude (°)

Semi minor - axis (b)

STEREOGRAPHIC

• Conformal

• Central meridian and a particular parallel (if shown)

are straight lines

• All other meridians and parallels are shown as arcs

of circles

• Scale increases away from the centre of the

projection

• Not truly perspective on a ellipsoid

STEREOGRAPHIC


2 N 1.0006 1.0004 1.0003 1.0004 1.0006 2 N 1.0006 1.0004 1.0003 1.0004 1.0006

1 N 1.0004 1.0002 1.0001 1.0002 1.0004 1 N 1.0004 1.0002 1.0001 1.0002 1.0004

0 1.0003 1.0001 1.0000 1.0001 1.0003 0 1.0003 1.0001 1.0000 1.0001 1.0003

1 S 1.0004 1.0002 1.0001 1.0002 1.0004 1 S 1.0004 1.0002 1.0001 1.0002 1.0004

2 S 1.0006 1.0004 1.0003 1.0004 1.0006 2 S 1.0006 1.0004 1.0003 1.0004 1.0006


47 N 1.0006 1.0005 1.0004 1.0005 1.0006 47 N 1.0006 1.0005 1.0004 1.0005 1.0006

46 N 1.0003 1.0002 1.0001 1.0002 1.0003 46 N 1.0003 1.0002 1.0001 1.0002 1.0003

45 N 1.0002 1.0000 1.0000 1.0000 1.0002 45 N 1.0002 1.0000 1.0000 1.0000 1.0002

44 N 1.0002 1.0001 1.0000 1.0001 1.0002 44 N 1.0002 1.0001 1.0000 1.0001 1.0002

43 N 1.0003 1.0002 1.0002 1.0002 1.0003 43 N 1.0003 1.0002 1.0002 1.0002 1.0003


82 N 1.0004 1.0003 1.0003 1.0003 1.0004 82 N 1.0004 1.0003 1.0003 1.0003 1.0004

81 N 1.0001 1.0001 1.0001 1.0001 1.0001 81 N 1.0001 1.0001 1.0001 1.0001 1.0001

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0001 1.0001 1.0001 1.0001 1.0001 79 N 1.0001 1.0001 1.0001 1.0001 1.0001

78 N 1.0003 1.0003 1.0003 1.0003 1.0003 78 N 1.0003 1.0003 1.0003 1.0003 1.0003




STEREOGRAPHIC


2 N 1.0012 1.0008 1.0006 1.0008 1.0012

1 N 1.0008 1.0003 1.0002 1.0003 1.0008

0 1.0006 1.0002 1 1.0002 1.0006

1 S 1.0008 1.0003 1.0002 1.0003 1.0008

2 S 1.0012 1.0008 1.0006 1.0008 1.0012


47 N 1.0011 1.0009 1.0008 1.0009 1.0011

46 N 1.0006 1.0003 1.0003 1.0003 1.0006

45 N 1.0003 1.0001 1 1.0001 1.0003

44 N 1.0003 1.0001 1.0000 1.0001 1.0003

43 N 1.0007 1.0005 1.0004 1.0005 1.0007


82 N 1.0007 1.0007 1.0007 1.0007 1.0007

81 N 1.0002 1.0002 1.0002 1.0002 1.0002

80 N 1.0000 1.0000 1 1.0000 1.0000

79 N 1.0001 1.0001 1.0001 1.0001 1.0001

78 N 1.0006 1.0005 1.0005 1.0005 1.0006

Longitude (°)

Longitude (°)

Area scale factor (s)Longitude (°)

STEREOGRAPHICTISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (0°, 0°)





STEREOGRAPHICTISSOT’S INDICATRIX


5N 1.003813 1.003126 1.002592 1.002211 1.001982 1.001906 1.001982 1.002211 1.002592 1.0031257 1.003813

4 N 1.003126 1.002439 1.001905 1.001524 1.001296 1.001219 1.001296 1.001524 1.001905 1.0024389 1.003126

3 N 1.002592 1.001905 1.001371 1.00099 1.000762 1.000686 1.000762 1.00099 1.001371 1.0019051 1.002592

2 N 1.002211 1.001524 1.00099 1.000609 1.000381 1.000305 1.000381 1.000609 1.00099 1.0015241 1.002211

1 N 1.001982 1.001296 1.000762 1.000381 1.000152 1.000076 1.000152 1.000381 1.000762 1.0012956 1.001982

0 1.001906 1.001219 1.000686 1.000305 1.000076 1 1.000076 1.000305 1.000686 1.0012195 1.001906

1 S 1.001982 1.001296 1.000762 1.000381 1.000152 1.000076 1.000152 1.000381 1.000762 1.0012956 1.001982

2 S 1.002211 1.001524 1.00099 1.000609 1.000381 1.000305 1.000381 1.000609 1.00099 1.0015241 1.002211

3 S 1.002592 1.001905 1.001371 1.00099 1.000762 1.000686 1.000762 1.00099 1.001371 1.0019051 1.002592

4S 1.003126 1.002439 1.001905 1.001524 1.001296 1.001219 1.001296 1.001524 1.001905 1.0024389 1.003126

5 S 1.003813 1.003126 1.002592 1.002211 1.001982 1.001906 1.001982 1.002211 1.002592 1.0031257 1.003813


50 N 1.003076 1.00276 1.002515 1.00234 1.002235 1.0022 1.002235 1.00234 1.002515 1.0027604 1.003076

49 N 1.002346 1.002025 1.001775 1.001597 1.00149 1.001454 1.00149 1.001597 1.001775 1.0020251 1.002346

48 N 1.00177 1.001443 1.001189 1.001007 1.000898 1.000861 1.000898 1.001007 1.001189 1.0014431 1.00177

47 N 1.001347 1.001014 1.000755 1.00057 1.000459 1.000422 1.000459 1.00057 1.000755 1.001014 1.001347

46 N 1.001077 1.000738 1.000474 1.000285 1.000172 1.000135 1.000172 1.000285 1.000474 1.0007375 1.001077

45 N 1.000959 1.000613 1.000345 1.000153 1.000038 1 1.000038 1.000153 1.000345 1.0006135 1.000959

44 N 1.000993 1.000642 1.000369 1.000174 1.000057 1.000018 1.000057 1.000174 1.000369 1.0006417 1.000993

43 N 1.001179 1.000822 1.000545 1.000346 1.000227 1.000188 1.000227 1.000346 1.000545 1.0008223 1.001179

42 N 1.001518 1.001155 1.000873 1.000671 1.00055 1.00051 1.00055 1.000671 1.000873 1.0011553 1.001518

41 N 1.00201 1.001641 1.001354 1.001149 1.001026 1.000985 1.001026 1.001149 1.001354 1.0016409 1.00201

40 N 1.002654 1.002279 1.001988 1.001779 1.001654 1.001613 1.001654 1.001779 1.001988 1.0022793 1.002654


85N 1.002037 1.002026 1.002018 1.002012 1.002009 1.002007 1.002009 1.002012 1.002018 1.0020262 1.002037

84 N 1.001335 1.001323 1.001313 1.001306 1.001302 1.0013 1.001302 1.001306 1.001313 1.0013227 1.001335

83 N 1.000787 1.000772 1.000761 1.000753 1.000748 1.000746 1.000748 1.000753 1.000761 1.0007724 1.000787

82 N 1.000392 1.000375 1.000362 1.000352 1.000347 1.000345 1.000347 1.000352 1.000362 1.0003749 1.000392

81 N 1.000149 1.00013 1.000115 1.000105 1.000098 1.000096 1.000098 1.000105 1.000115 1.0001298 1.000149

80 N 1.000058 1.000037 1.000021 1.000009 1.000002 1 1.000002 1.000009 1.000021 1.0000372 1.000058

79 N 1.00012 1.000097 1.000079 1.000066 1.000059 1.000056 1.000059 1.000066 1.000079 1.0000969 1.00012

78 N 1.000334 1.000309 1.000289 1.000275 1.000267 1.000264 1.000267 1.000275 1.000289 1.0003089 1.000334

77 N 1.000701 1.000673 1.000652 1.000637 1.000628 1.000625 1.000628 1.000637 1.000652 1.0006734 1.000701

76 N 1.00122 1.001191 1.001168 1.001152 1.001142 1.001139 1.001142 1.001152 1.001168 1.0011906 1.00122

75 N 1.001892 1.001861 1.001836 1.001819 1.001809 1.001805 1.001809 1.001819 1.001836 1.0018607 1.001892

Longitude (°)

Longitude (°)

Semi major - axis (a)Longitude (°)



5N 1.003813 1.003126 1.002592 1.002211 1.001982 1.001906 1.001982 1.002211 1.002592 1.003126 1.003813

4 N 1.003126 1.002439 1.001905 1.001524 1.001296 1.001219 1.001296 1.001524 1.001905 1.002439 1.003126

3 N 1.002592 1.001905 1.001371 1.00099 1.000762 1.000686 1.000762 1.00099 1.001371 1.001905 1.002592

2 N 1.002211 1.001524 1.00099 1.000609 1.000381 1.000305 1.000381 1.000609 1.00099 1.001524 1.002211

1 N 1.001982 1.001296 1.000762 1.000381 1.000152 1.000076 1.000152 1.000381 1.000762 1.001296 1.001982

0 1.001906 1.001219 1.000686 1.000305 1.000076 1 1.000076 1.000305 1.000686 1.001219 1.001906

1 S 1.001982 1.001296 1.000762 1.000381 1.000152 1.000076 1.000152 1.000381 1.000762 1.001296 1.001982

2 S 1.002211 1.001524 1.00099 1.000609 1.000381 1.000305 1.000381 1.000609 1.00099 1.001524 1.002211

3 S 1.002592 1.001905 1.001371 1.00099 1.000762 1.000686 1.000762 1.00099 1.001371 1.001905 1.002592

4S 1.003126 1.002439 1.001905 1.001524 1.001296 1.001219 1.001296 1.001524 1.001905 1.002439 1.003126

5 S 1.003813 1.003126 1.002592 1.002211 1.001982 1.001906 1.001982 1.002211 1.002592 1.003126 1.003813


50 N 1.003076 1.00276 1.002515 1.00234 1.002235 1.0022 1.002235 1.00234 1.002515 1.00276 1.003076

49 N 1.002346 1.002025 1.001775 1.001597 1.00149 1.001454 1.00149 1.001597 1.001775 1.002025 1.002346

48 N 1.00177 1.001443 1.001189 1.001007 1.000898 1.000861 1.000898 1.001007 1.001189 1.001443 1.00177

47 N 1.001347 1.001014 1.000755 1.00057 1.000459 1.000422 1.000459 1.00057 1.000755 1.001014 1.001347

46 N 1.001077 1.000738 1.000474 1.000285 1.000172 1.000135 1.000172 1.000285 1.000474 1.000738 1.001077

45 N 1.000959 1.000613 1.000345 1.000153 1.000038 1 1.000038 1.000153 1.000345 1.000613 1.000959

44 N 1.000993 1.000642 1.000369 1.000174 1.000057 1.000018 1.000057 1.000174 1.000369 1.000642 1.000993

43 N 1.001179 1.000822 1.000545 1.000346 1.000227 1.000188 1.000227 1.000346 1.000545 1.000822 1.001179

42 N 1.001518 1.001155 1.000873 1.000671 1.00055 1.00051 1.00055 1.000671 1.000873 1.001155 1.001518

41 N 1.00201 1.001641 1.001354 1.001149 1.001026 1.000985 1.001026 1.001149 1.001354 1.001641 1.00201

40 N 1.002654 1.002279 1.001988 1.001779 1.001654 1.001613 1.001654 1.001779 1.001988 1.002279 1.002654


85N 1.002037 1.002026 1.002018 1.002012 1.002009 1.002007 1.002009 1.002012 1.002018 1.002026 1.002037

84 N 1.001335 1.001323 1.001313 1.001306 1.001302 1.0013 1.001302 1.001306 1.001313 1.001323 1.001335

83 N 1.000787 1.000772 1.000761 1.000753 1.000748 1.000746 1.000748 1.000753 1.000761 1.000772 1.000787

82 N 1.000392 1.000375 1.000362 1.000352 1.000347 1.000345 1.000347 1.000352 1.000362 1.000375 1.000392

81 N 1.000149 1.00013 1.000115 1.000105 1.000098 1.000096 1.000098 1.000105 1.000115 1.00013 1.000149

80 N 1.000058 1.000037 1.000021 1.000009 1.000002 1 1.000002 1.000009 1.000021 1.000037 1.000058

79 N 1.00012 1.000097 1.000079 1.000066 1.000059 1.000056 1.000059 1.000066 1.000079 1.000097 1.00012

78 N 1.000334 1.000309 1.000289 1.000275 1.000267 1.000264 1.000267 1.000275 1.000289 1.000309 1.000334

77 N 1.000701 1.000673 1.000652 1.000637 1.000628 1.000625 1.000628 1.000637 1.000652 1.000673 1.000701

76 N 1.00122 1.001191 1.001168 1.001152 1.001142 1.001139 1.001142 1.001152 1.001168 1.001191 1.00122

75 N 1.001892 1.001861 1.001836 1.001819 1.001809 1.001805 1.001809 1.001819 1.001836 1.001861 1.001892

Longitude (°)

Longitude (°)

Longitude (°)


ORTHOGRAPHIC

• Perspective projection from infinite distance

• All meridians and parallels are ellipses, circles, or

straight lines

• Directions from the centre are true

• Radial scale factor decreases as distance increases

from the centre of projection

ORTHOGRAPHIC


2 N 0.9994 0.9994 0.9994 0.9994 0.9994 2 N 0.9994 0.9998 1.0000 0.9998 0.9994

1 N 0.9998 0.9998 0.9998 0.9998 0.9998 1 N 0.9994 0.9998 1.0000 0.9998 0.9994

0 1.0000 1.0000 1.0000 1.0000 1.0000 0 0.9994 0.9998 1.0000 0.9998 0.9994

1 S 0.9998 0.9998 0.9998 0.9998 0.9998 1 S 0.9994 0.9998 1.0000 0.9998 0.9994

2 S 0.9994 0.9994 0.9994 0.9994 0.9994 2 S 0.9994 0.9998 1.0000 0.9998 0.9994


47 N 0.9994 0.9994 0.9994 0.9994 0.9994 47 N 0.9997 0.9999 1.0000 0.9999 0.9997

46 N 0.9999 0.9998 0.9998 0.9998 0.9999 46 N 0.9997 0.9999 1.0000 0.9999 0.9997

45 N 1.0000 1.0000 1.0000 1.0000 1.0000 45 N 0.9997 0.9999 1.0000 0.9999 0.9997

44 N 0.9998 0.9998 0.9998 0.9998 0.9998 44 N 0.9997 0.9999 1.0000 0.9999 0.9997

43 N 0.9994 0.9994 0.9994 0.9994 0.9994 43 N 0.9997 0.9999 1.0000 0.9999 0.9997


82 N 0.9994 0.9994 0.9994 0.9994 0.9994 82 N 1.0000 1.0000 1.0000 1.0000 1.0000

81 N 0.9998 0.9998 0.9998 0.9998 0.9998 81 N 1.0000 1.0000 1.0000 1.0000 1.0000

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 0.9998 0.9998 0.9998 0.9998 0.9998 79 N 1.0000 1.0000 1.0000 1.0000 1.0000

78 N 0.9994 0.9994 0.9994 0.9994 0.9994 78 N 1.0000 1.0000 1.0000 1.0000 1.0000




ORTHOGRAPHIC


2 N 4' 11.38'' 2' 37.11'' 2' 5.69'' 2' 37.11'' 4' 11.38'' 2 N 0.9988 0.9992 0.9994 0.9992 0.9988

1 N 2' 37.11'' 1' 28.4'' 31.42'' 1' 28.4'' 2' 37.11'' 1 N 0.9992 0.9997 0.9998 0.9997 0.9992

0 2' 5.69'' 31.42'' 0 31.42'' 2' 5.69'' 0 0.9994 0.9998 1.0000 0.9998 0.9994

1 S 2' 37.11'' 1' 28.4'' 31.42'' 1' 28.4'' 2' 37.11'' 1 S 0.9992 0.9997 0.9998 0.9997 0.9992

2 S 4' 11.38'' 2' 37.11'' 2' 5.69'' 2' 37.11'' 4' 11.38'' 2 S 0.9988 0.9992 0.9994 0.9992 0.9988


47 N 3' 6.33'' 2' 20.85'' 2' 5.69'' 2' 20.85'' 3' 6.33'' 47 N 0.9991 0.9993 0.9994 0.9993 0.9991

46 N 1' 33.16'' 46.85'' 31.42'' 46.85'' 1' 33.16'' 46 N 0.9995 0.9998 0.9998 0.9998 0.9995

45 N 1' 2.84'' 15.71'' 0 15.71'' 1' 2.84'' 45 N 0.9997 0.9999 1 0.9999 0.9997

44 N 1' 35.35'' 47.4'' 31.42'' 47.4'' 1' 35.35'' 44 N 0.9995 0.9998 0.9998 0.9998 0.9995

43 N 3' 10.72'' 2' 21.95'' 2' 5.69'' 2' 21.95'' 3' 10.72'' 43 N 0.9991 0.9993 0.9994 0.9993 0.9991


82 N 2' 8.73'' 2' 6.45'' 2' 5.69'' 2' 6.45'' 2' 8.73'' 82 N 0.9994 0.9994 0.9994 0.9994 0.9994

81 N 34.83'' 32.27'' 31.42'' 32.27'' 34.83'' 81 N 0.9998 0.9998 0.9998 0.9998 0.9998

80 N 3.79'' .95'' 0 .95'' 3.79'' 80 N 1.0000 1.0000 1 1.0000 1.0000

79 N 35.58'' 32.46'' 31.42'' 32.46'' 35.58'' 79 N 0.9998 0.9998 0.9998 0.9998 0.9998

78 N 2' 10.23'' 2' 6.83'' 2' 5.69'' 2' 6.83'' 2' 10.23'' 78 N 0.9994 0.9994 0.9994 0.9994 0.9994




Angular Deformation (w) Area scale factor (s)

ORTHOGRAPHICTISSOT’S INDICATRICES



otherwise it is red




otherwise it is red




otherwise it is red



5N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

4 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

3 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

2 N 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

1 N 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

0 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

1 S 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

2 S 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

3 S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

4S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

5 S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038


50 N 1.0022 1.0014 1.0008 1.0004 1.0001 1.0000 1.0001 1.0004 1.0008 1.0014 1.0022

49 N 1.0022 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0022

48 N 1.0021 1.0013 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0013 1.0021

47 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

46 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

45 N 1.0019 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0019

44 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

43 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

42 N 1.0021 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0021

41 N 1.0022 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0022

40 N 1.0022 1.0014 1.0008 1.0004 1.0001 1.0000 1.0001 1.0004 1.0008 1.0014 1.0022


85N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

84 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

83 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

82 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

81 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

80 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

79 N 1.0037 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0037

78 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

77 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

76 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

75 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036


Longitude (°)

Longitude (°)

Longitude (°)



5N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

5 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


50 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016

49 N 1.0016 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0016

48 N 1.0017 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0017

47 N 1.0018 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0018

46 N 1.0018 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0018

45 N 1.0019 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0019

44 N 1.0018 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0018

43 N 1.0018 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0018

42 N 1.0017 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0017

41 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016

40 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016


85N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

84 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

83 N 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001

82 N 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001

81 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

80 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

79 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

78 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

77 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

76 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

75 N 1.0003 1.0002 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0002 1.0003

Longitude (°)

Longitude (°)

Longitude (°)


AZIMUTHAL EQUIDISTANT

• Distances measured from the tangent point are true

• Central meridian is a straight line

• All other meridians and parallels are complex curves

(with exceptions on polar aspect)

• Not a perspective projection

AZIMUTHAL EQUIDISTANT

Modified Azimuthal Equidistant:

•Developed by the US National Geodetic Survey to map

Micronesia

•Calculates distances from the origin along a normal section

rather than the geodesic

•For distances under 800 km no significant errors are introduced

GUAM Projection:

•Simplified form of the oblique aspect of the azimuthal

equidistant projection

MODIFIED AZIMUTHAL EQUIDISTANT


2 N 1.0002 1.0001 1.0000 1.0001 1.0002 2 N 1.0002 1.0002 1.0002 1.0002 1.0002

1 N 1.0002 1.0001 1.0000 1.0001 1.0002 1 N 1.0001 1.0001 1.0001 1.0001 1.0001

0 NaN NaN NaN NaN NaN 0 NaN NaN NaN NaN NaN

1 S 1.0002 1.0001 1.0000 1.0001 1.0002 1 S 1.0001 1.0001 1.0001 1.0001 1.0001

2 S 1.0002 1.0001 1.0000 1.0001 1.0002 2 S 1.0002 1.0002 1.0002 1.0002 1.0002


47 N 1.0001 1.0000 1.0000 1.0000 1.0001 47 N 1.0002 1.0002 1.0002 1.0002 1.0002

46 N 1.0001 1.0000 1.0000 1.0000 1.0001 46 N 1.0000 1.0001 1.0001 1.0001 1.0000

45 N 1.0001 1.0000 NaN 1.0000 1.0001 45 N 1.0000 1.0000 NaN 1.0000 1.0000

44 N 1.0001 1.0000 1.0000 1.0000 1.0001 44 N 1.0001 1.0001 1.0001 1.0001 1.0001

43 N 1.0001 1.0000 1.0000 1.0000 1.0001 43 N 1.0002 1.0002 1.0002 1.0002 1.0002


82 N 1.0000 1.0000 1.0000 1.0000 1.0000 82 N 1.0002 1.0002 1.0002 1.0002 1.0002

81 N 1.0000 1.0000 1.0000 1.0000 1.0000 81 N 1.0001 1.0001 1.0001 1.0001 1.0001

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0000 1.0000 4.3191 1.0000 1.0000

79 N 1.0000 1.0000 1.0000 1.0000 1.0000 79 N 1.0001 1.0001 1.0001 1.0001 1.0001

78 N 1.0000 1.0000 1.0000 1.0000 1.0000 78 N 1.0002 1.0002 1.0002 1.0002 1.0002




MODIFIED AZIMUTHAL EQUIDISTANT


2 N 1' 23.77'' 52.36'' 41.89'' 52.36'' 1' 23.77'' 2 N 1.0004 1.0003 1.0002 1.0003 1.0004

1 N 52.36'' 20.94'' 10.47'' 20.94'' 52.36'' 1 N 1.0003 1.0001 1.0001 1.0001 1.0003

0 NaN NaN NaN NaN NaN 0 NaN NaN NaN NaN NaN

1 S 52.36'' 20.94'' 10.47'' 20.94'' 52.36'' 1 S 1.0003 1.0001 1.0001 1.0001 1.0003

2 S 1' 23.77'' 52.36'' 41.88'' 52.36'' 1' 23.77'' 2 S 1.0004 1.0003 1.0002 1.0003 1.0004


47 N 1' 2.10'' 46.95'' 41.89'' 46.95'' 1' 2.10'' 47 N 1.0003 1.0002 1.0002 1.0002 1.0003

46 N 31.05'' 15.62'' 10.47'' 15.62'' 31.05'' 46 N 1.0002 1.0001 1.0001 1.0001 1.0002

45 N 20.94'' 5.24'' NaN 5.24'' 20.94'' 45 N 1.0001 1.0000 NaN 1.0000 1.0001

44 N 31.78'' 15.80'' 10.47'' 15.80'' 31.78'' 44 N 1.0002 1.0001 1.0001 1.0001 1.0002

43 N 1' 3.55'' 47.30'' 41.88'' 47.30'' 1' 3.55'' 43 N 1.0003 1.0002 1.0002 1.0002 1.0003


82 N 42.90'' 42.14'' 41.89'' 42.14'' 42.90'' 82 N 1.0002 1.0002 1.0002 1.0002 1.0002

81 N 11.61'' 10.76'' 10.47'' 10.76'' 11.61'' 81 N 1.0001 1.0001 1.0001 1.0001 1.0001

80 N 1.26'' 0.32'' NaN 0.32'' 1.26'' 80 N 1.0000 1.0000 NaN 1.0000 1.0000

79 N 11.86'' 10.82'' 10.47'' 10.82'' 11.86'' 79 N 1.0001 1.0001 1.0001 1.0001 1.0001

78 N 43.40'' 42.27'' 41.89'' 42.27'' 43.40'' 78 N 1.0002 1.0002 1.0002 1.0002 1.0002



Angular Deformation (w) Area scale factor (s)Longitude (°) Longitude (°)

MODIFIED AZIMUTHAL EQUIDISTANTTISSOT’S INDICATRICES



otherwise it is red




otherwise it is red




otherwise it is red



5N 1.0025 1.0021 1.0017 1.0015 1.0013 1.0013 1.0013 1.0015 1.0017 1.0021 1.0025

4 N 1.0021 1.0016 1.0013 1.0010 1.0009 1.0008 1.0009 1.0010 1.0013 1.0016 1.0021

3 N 1.0017 1.0013 1.0009 1.0007 1.0005 1.0005 1.0005 1.0007 1.0009 1.0013 1.0017

2 N 1.0015 1.0010 1.0007 1.0004 1.0003 1.0002 1.0003 1.0004 1.0007 1.0010 1.0015

1 N 1.0013 1.0009 1.0005 1.0003 1.0001 1.0001 1.0001 1.0003 1.0005 1.0009 1.0013

0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

1 S 1.0013 1.0009 1.0005 1.0003 1.0001 1.0001 1.0001 1.0003 1.0005 1.0009 1.0013

2 S 1.0015 1.0010 1.0007 1.0004 1.0003 1.0002 1.0003 1.0004 1.0007 1.0010 1.0015

3 S 1.0017 1.0013 1.0009 1.0007 1.0005 1.0005 1.0005 1.0007 1.0009 1.0013 1.0017

4S 1.0021 1.0016 1.0013 1.0010 1.0009 1.0008 1.0009 1.0010 1.0013 1.0016 1.0021

5 S 1.0025 1.0021 1.0017 1.0015 1.0013 1.0013 1.0013 1.0015 1.0017 1.0021 1.0025


50 N 1.0018 1.0016 1.0015 1.0014 1.0013 1.0013 1.0013 1.0014 1.0015 1.0016 1.0018

49 N 1.0014 1.0012 1.0010 1.0009 1.0008 1.0008 1.0008 1.0009 1.0010 1.0012 1.0014

48 N 1.0011 1.0008 1.0007 1.0006 1.0005 1.0005 1.0005 1.0006 1.0007 1.0008 1.0011

47 N 1.0008 1.0006 1.0004 1.0003 1.0002 1.0002 1.0002 1.0003 1.0004 1.0006 1.0008

46 N 1.0007 1.0004 1.0003 1.0002 1.0001 1.0001 1.0001 1.0002 1.0003 1.0004 1.0007

45 N 1.0006 1.0004 1.0002 1.0001 1.0000 NaN 1.0000 1.0001 1.0002 1.0004 1.0006

44 N 1.0007 1.0005 1.0003 1.0002 1.0001 1.0001 1.0001 1.0002 1.0003 1.0005 1.0007

43 N 1.0009 1.0006 1.0004 1.0003 1.0002 1.0002 1.0002 1.0003 1.0004 1.0006 1.0009

42 N 1.0011 1.0009 1.0007 1.0006 1.0005 1.0005 1.0005 1.0006 1.0007 1.0009 1.0011

41 N 1.0015 1.0012 1.0011 1.0009 1.0008 1.0008 1.0008 1.0009 1.0011 1.0012 1.0015

40 N 1.0020 1.0017 1.0015 1.0014 1.0013 1.0013 1.0013 1.0014 1.0015 1.0017 1.0020


85N 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013

84 N 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008

83 N 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005

82 N 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002

81 N 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 4.3191 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001 1.0001

78 N 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002 1.0002

77 N 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005 1.0005

76 N 1.0009 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0008 1.0009

75 N 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013 1.0013


Longitude (°)

Longitude (°)

Longitude (°)



5N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

1 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

5 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


50 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

49 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

48 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

47 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

46 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

45 N 1.0000 1.0000 1.0000 1.0000 1.0000 NaN 1.0000 1.0000 1.0000 1.0000 1.0000

44 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

43 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

42 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

41 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

40 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


85N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

84 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

83 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

82 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

81 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

78 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

77 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

76 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

75 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Longitude (°)

Longitude (°)

Longitude (°)


GUAM


2 N 1.0006 1.0002 1.0000 1.0002 1.0006 2 N 1.0000 1.0000 1.0000 1.0000 1.0000

1 N 1.0006 1.0002 1.0000 1.0002 1.0006 1 N 1.0000 1.0000 1.0000 1.0000 1.0000

0 1.0006 1.0002 1.0000 1.0002 1.0006 0 1.0000 1.0000 1.0000 1.0000 1.0000

1 S 1.0006 1.0002 1.0000 1.0002 1.0006 1 S 1.0000 1.0000 1.0000 1.0000 1.0000

2 S 1.0006 1.0002 1.0000 1.0002 1.0006 2 S 1.0000 1.0000 1.0000 1.0000 1.0000


47 N 1.0003 1.0001 1.0000 1.0001 1.0003 47 N 1.0003 1.0001 1.0000 1.0001 1.0003

46 N 1.0003 1.0001 1.0000 1.0001 1.0003 46 N 1.0003 1.0001 1.0000 1.0001 1.0003

45 N 1.0003 1.0001 1.0000 1.0001 1.0003 45 N 1.0003 1.0001 1.0000 1.0001 1.0003

44 N 1.0003 1.0001 1.0000 1.0001 1.0003 44 N 1.0003 1.0001 1.0000 1.0001 1.0003

43 N 1.0003 1.0001 1.0000 1.0001 1.0003 43 N 1.0003 1.0001 1.0000 1.0001 1.0003


82 N 1.0000 1.0000 1.0000 1.0000 1.0000 82 N 1.0006 1.0001 1.0000 1.0001 1.0006

81 N 1.0000 1.0000 1.0000 1.0000 1.0000 81 N 1.0006 1.0001 1.0000 1.0001 1.0006

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0006 1.0001 1.0000 1.0001 1.0006

79 N 1.0000 1.0000 1.0000 1.0000 1.0000 79 N 1.0006 1.0001 1.0000 1.0001 1.0006

78 N 1.0000 1.0000 1.0000 1.0000 1.0000 78 N 1.0006 1.0001 1.0000 1.0001 1.0006




GUAM


2 N 2' 6.16'' 31.55'' 0 31.55'' 2' 6.16'' 2 N 1.0006 1.0002 1 1.0002 1.0006

1 N 2' 6.39'' 31.61'' 0 31.61'' 2' 6.39'' 1 N 1.0006 1.0002 1 1.0002 1.0006

0 2' 6.47'' 31.63'' 0 31.63'' 2' 6.47'' 0 1.0006 1.0002 1 1.0002 1.0006

1 S 2' 6.39'' 31.61'' 0 31.61'' 2' 6.39'' 1 S 1.0006 1.0002 1 1.0002 1.0006

2 S 2' 6.16'' 31.55'' 0 31.55'' 2' 6.16'' 2 S 1.0006 1.0002 1 1.0002 1.0006


47 N 8.58'' 2.15'' 0 2.15'' 8.58'' 47 N 1.0006 1.0002 1 1.0002 1.0006

46 N 4.19'' 1.05'' 0 1.05'' 4.19'' 46 N 1.0006 1.0002 1 1.0002 1.0006

45 N .0.21'' 0.05'' 0 0.05'' .0.21'' 45 N 1.0006 1.0002 1 1.0002 1.0006

44 N 4.61'' 1.15'' 0 1.15'' 4.61'' 44 N 1.0006 1.0002 1 1.0002 1.0006

43 N 9.01'' 2.25'' 0 2.25'' 9.01'' 43 N 1.0006 1.0002 1 1.0002 1.0006


82 N 2' 0.76'' 30.20'' 0 30.20'' 2' 0.76'' 82 N 1.0006 1.0002 1 1.0002 1.0006

81 N 1' 59.48'' 29.88'' 0 29.88'' 1' 59.48'' 81 N 1.0006 1.0002 1 1.0002 1.0006

80 N 1' 58.05'' 29.52'' 0 29.52'' 1' 58.05'' 80 N 1.0006 1.0002 1 1.0002 1.0006

79 N 1' 56.48'' 29.13'' 0 29.13'' 1' 56.48'' 79 N 1.0006 1.0002 1 1.0002 1.0006

78 N 1' 54.76'' 28.70'' 0 28.70'' 1' 54.76'' 78 N 1.0006 1.0002 1 1.0002 1.0006




GUAMTISSOT’S INDICATRICES



otherwise it is red




otherwise it is red




otherwise it is red



5N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

4 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

3 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

2 N 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

1 N 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

0 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

1 S 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

2 S 1.0038 1.0025 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0025 1.0038

3 S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

4S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

5 S 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038


50 N 1.0022 1.0014 1.0008 1.0004 1.0001 1.0000 1.0001 1.0004 1.0008 1.0014 1.0022

49 N 1.0022 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0022

48 N 1.0021 1.0013 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0013 1.0021

47 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

46 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

45 N 1.0019 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0019

44 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

43 N 1.0020 1.0013 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0013 1.0020

42 N 1.0021 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0021

41 N 1.0022 1.0014 1.0008 1.0003 1.0001 1.0000 1.0001 1.0003 1.0008 1.0014 1.0022

40 N 1.0022 1.0014 1.0008 1.0004 1.0001 1.0000 1.0001 1.0004 1.0008 1.0014 1.0022


85N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

84 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

83 N 1.0038 1.0024 1.0014 1.0006 1.0002 1.0000 1.0002 1.0006 1.0014 1.0024 1.0038

82 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

81 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

80 N 1.0037 1.0024 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0024 1.0037

79 N 1.0037 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0037

78 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

77 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

76 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036

75 N 1.0036 1.0023 1.0013 1.0006 1.0001 1.0000 1.0001 1.0006 1.0013 1.0023 1.0036


Longitude (°)

Longitude (°)

Longitude (°)



5N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

2 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

4S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

5 S 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000


50 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016

49 N 1.0016 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0016

48 N 1.0017 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0017

47 N 1.0018 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0018

46 N 1.0018 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0018

45 N 1.0019 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0019

44 N 1.0018 1.0012 1.0007 1.0003 1.0001 1.0000 1.0001 1.0003 1.0007 1.0012 1.0018

43 N 1.0018 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0018

42 N 1.0017 1.0011 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0011 1.0017

41 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016

40 N 1.0016 1.0010 1.0006 1.0003 1.0001 1.0000 1.0001 1.0003 1.0006 1.0010 1.0016


85N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

84 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

83 N 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001

82 N 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001

81 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

80 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

79 N 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001

78 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

77 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

76 N 1.0002 1.0001 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0001 1.0002

75 N 1.0003 1.0002 1.0001 1.0000 1.0000 1.0000 1.0000 1.0000 1.0001 1.0002 1.0003

Longitude (°)

Longitude (°)

Longitude (°)


GENERAL PERSPECTIVE PROJECTION

• Orthographic, stereographic and gnomonic are

special forms of vertical perspective

• View of the Earth from space

• Central meridian and a particular parallel are

shown as straight lines

• Other meridians and parallels are arcs of circles or

ellipses (some might be parabolas or hyperbolas)



2 N 0.9991 0.9991 0.9992 0.9991 0.9991 2 N 0.9991 0.9997 0.9999 0.9997 0.9991

1 N 0.9997 0.9998 0.9998 0.9998 0.9997 1 N 0.9991 0.9998 1.0000 0.9998 0.9991

0 0.9999 1.0000 1.0000 1.0000 0.9999 0 0.9992 0.9998 1.0000 0.9998 0.9992

1 S 0.9997 0.9998 0.9998 0.9998 0.9997 1 S 0.9991 0.9998 1.0000 0.9998 0.9991

2 S 0.9991 0.9991 0.9992 0.9991 0.9991 2 S 0.9991 0.9997 0.9999 0.9997 0.9991


47 N 0.9991 0.9992 0.9992 0.9992 0.9991 47 N 0.9995 0.9998 0.9999 0.9998 0.9995

46 N 0.9998 0.9998 0.9998 0.9998 0.9998 46 N 0.9996 0.9999 1.0000 0.9999 0.9996

45 N 1.0000 1.0000 1.0000 1.0000 1.0000 45 N 0.9996 0.9999 1.0000 0.9999 0.9996

44 N 0.9997 0.9998 0.9998 0.9998 0.9997 44 N 0.9996 0.9999 1.0000 0.9999 0.9996

43 N 0.9991 0.9991 0.9992 0.9991 0.9991 43 N 0.9995 0.9998 0.9999 0.9998 0.9995


82 N 0.9992 0.9992 0.9992 0.9992 0.9992 82 N 0.9999 0.9999 0.9999 0.9999 0.9999

81 N 0.9998 0.9998 0.9998 0.9998 0.9998 81 N 1.0000 1.0000 1.0000 1.0000 1.0000

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 80 N 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 0.9998 0.9998 0.9998 0.9998 0.9998 79 N 1.0000 1.0000 1.0000 1.0000 1.0000

78 N 0.9991 0.9992 0.9992 0.9992 0.9991 78 N 0.9999 0.9999 0.9999 0.9999 0.9999




Height of perspective : 50 000 km



2 N 5`15.30`` 3`16.97`` 2`37.54`` 3`16.97`` 5`15.30`` 2 N 0.9982 0.9989 0.9991 0.9989 0.9982

1 N 3`17.14`` 1`18.81`` 39.38`` 1`18.81`` 3`17.14`` 1 N 0.9989 0.9995 0.9998 0.9995 0.9989

0 2`37.76`` 39.43`` 0 39.43`` 2`37.76`` 0 0.9991 0.9998 1.0000 0.9998 0.9991

1 S 3`17.14`` 1`18.81`` 39.38`` 1`18.81`` 3`17.14`` 1 S 0.9989 0.9995 0.9998 0.9995 0.9989

2 S 5`15.30`` 3`16.97`` 2`37.54`` 3`16.97`` 5`15.30`` 2 S 0.9982 0.9989 0.9991 0.9989 0.9982


47 N 3`53.85`` 2`56.74`` 2`37.71`` 2`56.74`` 3`53.85`` 47 N 0.9986 0.9990 0.9991 0.9990 0.9986

46 N 1`56.94`` 58.80`` 39.42`` 58.80`` 1`56.94`` 46 N 0.9993 0.9997 0.9998 0.9997 0.9993

45 N 1`18.89`` 19.725`` 0 19.725`` 1`18.89`` 45 N 0.9995 0.9999 1.0000 0.9999 0.9995

44 N 1`59.39`` 59.49`` 39.42`` 59.49`` 1`59.39`` 44 N 0.9993 0.9997 0.9998 0.9997 0.9993

43 N 3`59.34`` 2`58.11`` 2`37.70`` 2`58.11`` 3`59.34`` 43 N 0.9986 0.9990 0.9991 0.9990 0.9986


82 N 2`41.67`` 2`38.81`` 2`37.86 2`38.81`` 2`41.67`` 82 N 0.9991 0.9991 0.9991 0.9991 0.9991

81 N 43.75`` 40.53`` 39.46`` 40.53`` 43.75`` 81 N 0.9997 0.9998 0.9998 0.9998 0.9997

80 N 4.76`` 1.19`` 0 1.19`` 4.76`` 80 N 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 44.69`` 40.76`` 39.46`` 40.76`` 44.69`` 79 N 0.9997 0.9998 0.9998 0.9998 0.9997

78 N 2`43.55`` 2`39.28`` 2`37.85`` 2`39.28`` 2`43.55`` 78 N 0.9990 0.9991 0.9991 0.9991 0.9990




Height of perspective : 50 000 km

GENERAL PERSPECTIVE PROJECTIONTISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (0°, 0°) Height of perspective : 50 000 km



otherwise it is red


Tangent Point: (φ, λ)= (45° N, 0°) Height of perspective : 50 000 km



otherwise it is red


Tangent Point: (φ, λ)= (80° N, 0°) Height of perspective : 50 000 km



otherwise it is red



5N 0.9990 0.9992 0.9993 0.9994 0.9995 0.9995 0.9995 0.9994 0.9993 0.9992 0.9990

4 N 0.9992 0.9994 0.9995 0.9996 0.9997 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992

3 N 0.9993 0.9995 0.9997 0.9997 0.9998 0.9998 0.9998 0.9997 0.9997 0.9995 0.9993

2 N 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994

1 N 0.9995 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995

0 0.9995 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995

1 S 0.9995 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 0.9995

2 S 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 0.9998 0.9997 0.9996 0.9994

3 S 0.9993 0.9995 0.9997 0.9997 0.9998 0.9998 0.9998 0.9997 0.9997 0.9995 0.9993

4S 0.9992 0.9994 0.9995 0.9996 0.9997 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992

5 S 0.9990 0.9992 0.9993 0.9994 0.9995 0.9995 0.9995 0.9994 0.9993 0.9992 0.9990

Latitude (°) 5 W 4 W 3 W 2 W 1 W 0.0000 1 E 2 E 3 E 4 E 5 E

50 N 0.9993 0.9994 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9994 0.9994 0.9993

49 N 0.9995 0.9995 0.9996 0.9997 0.9997 0.9997 0.9997 0.9997 0.9996 0.9995 0.9995

48 N 0.9996 0.9997 0.9997 0.9998 0.9998 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996

47 N 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997

46 N 0.9997 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997

45 N 0.9998 0.9998 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.9998

44 N 0.9997 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9997

43 N 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997

42 N 0.9996 0.9997 0.9997 0.9998 0.9998 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996

41 N 0.9994 0.9995 0.9996 0.9996 0.9997 0.9997 0.9997 0.9996 0.9996 0.9995 0.9994

40 N 0.9993 0.9993 0.9994 0.9995 0.9995 0.9995 0.9995 0.9995 0.9994 0.9993 0.9993

Latitude (°) 5 W 4 W 3 W 2 W 1 W 0.0000 1 E 2 E 3 E 4 E 5 E

85N 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995

84 N 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997

83 N 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998

82 N 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

81 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

80 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

79 N 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

78 N 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

77 N 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998

76 N 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997

75 N 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995 0.9995

Longitude (°)

Longitude (°)

Semi major - axis (a)Longitude (°)

Height of

perspective :

50 000 km



5N 0.989526 0.991406 0.992869 0.993916 0.994544 0.994753 0.994544 0.993916 0.992869 0.991406 0.989526

4 N 0.991402 0.993286 0.994753 0.995801 0.99643 0.99664 0.99643 0.995801 0.994753 0.993286 0.991402

3 N 0.992863 0.99475 0.996219 0.997269 0.997899 0.998109 0.997899 0.997269 0.996219 0.99475 0.992863

2 N 0.993907 0.995796 0.997267 0.998318 0.998949 0.999159 0.998949 0.998318 0.997267 0.995796 0.993907

1 N 0.994534 0.996424 0.997896 0.998948 0.999579 0.99979 0.999579 0.998948 0.997896 0.996424 0.994534

0 0.994743 0.996634 0.998106 0.999158 0.999789 1 0.999789 0.999158 0.998106 0.996634 0.994743

1 S 0.994534 0.996424 0.997896 0.998948 0.999579 0.99979 0.999579 0.998948 0.997896 0.996424 0.994534

2 S 0.993907 0.995796 0.997267 0.998318 0.998949 0.999159 0.998949 0.998318 0.997267 0.995796 0.993907

3 S 0.992863 0.99475 0.996219 0.997269 0.997899 0.998109 0.997899 0.997269 0.996219 0.99475 0.992863

4S 0.991402 0.993286 0.994753 0.995801 0.99643 0.99664 0.99643 0.995801 0.994753 0.993286 0.991402

5 S 0.989526 0.991406 0.992869 0.993916 0.994544 0.994753 0.994544 0.993916 0.992869 0.991406 0.989526


50 N 0.992358 0.993217 0.993885 0.994363 0.994649 0.994745 0.994649 0.994363 0.993885 0.993217 0.992358

49 N 0.994197 0.995074 0.995757 0.996245 0.996537 0.996635 0.996537 0.996245 0.995757 0.995074 0.994197

48 N 0.995618 0.996514 0.99721 0.997708 0.998007 0.998106 0.998007 0.997708 0.99721 0.996514 0.995618

47 N 0.996621 0.997534 0.998244 0.998752 0.999057 0.999158 0.999057 0.998752 0.998244 0.997534 0.996621

46 N 0.997205 0.998135 0.998859 0.999376 0.999686 0.99979 0.999686 0.999376 0.998859 0.998135 0.997205

45 N 0.997369 0.998316 0.999052 0.999579 0.999895 1 0.999895 0.999579 0.999052 0.998316 0.997369

44 N 0.997113 0.998076 0.998825 0.999361 0.999682 0.99979 0.999682 0.999361 0.998825 0.998076 0.997113

43 N 0.996438 0.997417 0.998178 0.998723 0.999049 0.999158 0.999049 0.998723 0.998178 0.997417 0.996438

42 N 0.995344 0.996338 0.997111 0.997664 0.997996 0.998107 0.997996 0.997664 0.997111 0.996338 0.995344

41 N 0.993831 0.99484 0.995625 0.996187 0.996523 0.996636 0.996523 0.996187 0.995625 0.99484 0.993831

40 N 0.991902 0.992925 0.993722 0.994291 0.994633 0.994746 0.994633 0.994291 0.993722 0.992925 0.991902


85N 0.994659 0.994688 0.99471 0.994726 0.994736 0.994739 0.994736 0.994726 0.99471 0.994688 0.994659

84 N 0.996535 0.99657 0.996596 0.996616 0.996627 0.996631 0.996627 0.996616 0.996596 0.99657 0.996535

83 N 0.997993 0.998033 0.998064 0.998086 0.9981 0.998104 0.9981 0.998086 0.998064 0.998033 0.997993

82 N 0.99903 0.999076 0.999111 0.999137 0.999152 0.999157 0.999152 0.999137 0.999111 0.999076 0.99903

81 N 0.999646 0.999698 0.999738 0.999766 0.999784 0.999789 0.999784 0.999766 0.999738 0.999698 0.999646

80 N 0.999841 0.999898 0.999943 0.999975 0.999994 1 0.999994 0.999975 0.999943 0.999898 0.999841

79 N 0.999615 0.999678 0.999726 0.999761 0.999782 0.999789 0.999782 0.999761 0.999726 0.999678 0.999615

78 N 0.998967 0.999035 0.999089 0.999127 0.99915 0.999157 0.99915 0.999127 0.999089 0.999035 0.998967

77 N 0.997899 0.997973 0.99803 0.998071 0.998096 0.998104 0.998096 0.998071 0.99803 0.997973 0.997899

76 N 0.99641 0.99649 0.996552 0.996596 0.996622 0.996631 0.996622 0.996596 0.996552 0.99649 0.99641

75 N 0.994503 0.994588 0.994654 0.994701 0.99473 0.994739 0.99473 0.994701 0.994654 0.994588 0.994503

Longitude (°)

Longitude (°)

Semi minor - axis (b)Longitude (°)

Height of

perspective :

50 000 km

Documents

GEOIDE SSII-109