Geoide Ssii-109

GEOIDE SSII-109

• 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 LAMBERT AZIMUTHAL EQUAL AREA

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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 LAMBERT AZIMUTHAL EQUAL AREA

Angular Deformation (w) 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''

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

Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E 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'' LAMBERT AZIMUTHAL EQUAL AREA TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (0°, 0°) LAMBERT AZIMUTHAL EQUAL AREA TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (45° N, 0°) LAMBERT AZIMUTHAL EQUAL AREA TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (80° N, 0°) LAMBERT AZIMUTHAL EQUAL AREA TISSOT’S INDICATRICES

Semi major - axis (a) Longitude (°) 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

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

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

LAMBERT AZIMUTHAL EQUAL AREA TISSOT’S INDICATRICES

Semi minor - axis (b) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

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

Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

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

Area scale factor (s) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E 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 STEREOGRAPHIC TISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (0°, 0°) STEREOGRAPHIC TISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (45° N, 0°) STEREOGRAPHIC TISSOT’S INDICATRICES

Tangent Point: (φ, λ)= (80° N, 0°) STEREOGRAPHIC TISSOT’S INDICATRIX

Semi major - axis (a) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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 STEREOGRAPHIC TISSOT’S INDICATRICES

Semi minor - axis (b) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

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

Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

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

Angular Deformation (w) Area scale factor (s) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 ORTHOGRAPHIC TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red ORTHOGRAPHIC TISSOT’S INDICATRICES

Semi major - axis (a) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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 ORTHOGRAPHIC TISSOT’S INDICATRICES

Semi minor - axis (b) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

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

Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

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

Angular Deformation (w) Area scale factor (s) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 MODIFIED AZIMUTHAL EQUIDISTANT TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red MODIFIED AZIMUTHAL EQUIDISTANT TISSOT’S INDICATRICES

Semi major - axis (a) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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 MODIFIED AZIMUTHAL EQUIDISTANT TISSOT’S INDICATRICES

Semi minor - axis (b) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

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

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

Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

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

Angular Deformation (w) Area scale factor (s) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 GUAM TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red GUAM TISSOT’S INDICATRICES

• 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) GENERAL PERSPECTIVE PROJECTION

Scale Distortion Along Meridians (h) Scale Distortion Along Parallels (k) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 GENERAL PERSPECTIVE PROJECTION

Angular Deformation (w) Area scale factor (s) Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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

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

Longitude (°) Longitude (°) Latitude (°) 2 W 1 W 0 1 E 2 E Latitude (°) 2 W 1 W 0 1 E 2 E 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 PROJECTION TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (0°, 0°) Height of perspective : 50 000 km GENERAL PERSPECTIVE PROJECTION TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (45° N, 0°) Height of perspective : 50 000 km GENERAL PERSPECTIVE PROJECTION TISSOT’S INDICATRICES

If |a – b| < 0.001 ellipse is shown in green colour otherwise it is red

Tangent Point: (φ, λ)= (80° N, 0°) Height of perspective : 50 000 km GENERAL PERSPECTIVE PROJECTION TISSOT’S INDICATRICES

Semi major - axis (a) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

Longitude (°) 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 Height of 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 perspective : 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 50 000 km 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

Longitude (°) 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 GENERAL PERSPECTIVE PROJECTION TISSOT’S INDICATRICES

Semi minor - axis (b) Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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

Longitude (°) Latitude (°) 5 W 4 W 3 W 2 W 1 W 0 1 E 2 E 3 E 4 E 5 E 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 Height of 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 perspective : 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 50 000 km 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

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