Cartography Basics

*Map Projections

*Datums

*Coordinate Conversion

*Modtran

*Resampling

Map Projections

* Spherical earth model

Latitude, Longitude, Altitude

* Meracator Projection

*Universal Transverse Mercator (UTM)Projection

zone, easting, northing, altitude

* UTM Military Grid

* Global Coordinate System (GCS)

a

b

DATUM WGS 84

Semi-major axis = a = 6378137.000m

Semi-minor axis = b= 6356752.314m

Flattening =f

1/f = (a-b)/a = 1/298.257223563

Geodetic latitude

DATUMS

DATUM TRANSFORM

Lat/long/altin datum 1

Same Lat/long/altin differentDatum

The same lat/long/alt numbers in two different datums refer to two different points on the earth. A Datum Transform converts the same point on the earth from lat/long/alt in one datum to lat’/long’/alt’ in second datum.

Same earth point has different lat’/long’/alt’ in a different datum

a=semi-major axis

1/f = reciprocal of flattening

Coordinate Conversion

Projection 1

Datum 1

Projection 2

Datum 2

Easting = E(lat,long,alt,datum_parameters)

Zone = Z (lat,long,alt,datum_parameters)

Northing = N(lat,long,alt,datum_parameters)

Alt = A(lat,long,alt,datum_parameters)

long

lat

Zone, Easting

Modtran execution

EXAMPLE

Resampling

Projection 1

Datum 1

Projection 2

Datum 2

V(Easting,Zone, T(V(lat,long,alt,datum_parameters),

Northing, Alt V(lat,long,alt,datum_parameters),

datum_parameters) V(lat,long,alt,datum_parameters),

V(lat,long,alt,datum_parameters))

long

lat

Zone, Easting

Resampling Algorithm

1) Get point of interest P

2) Transform to coordinates P’ =T(P) in which data is available

3) Find surrounding data Values V(P’+1),V(P’-1)

4) Interpolate from surrounding values to the Value at the transformed point

V(P’) = I(V(P’+1),V(P’-1),…)

5) Assign the interpolated value to the point of interest V(P) = V(P’)

Interpolation*Nearest neighbor

*Truncate

*Bilinear Interpolation

X X+1

Y

Y+1X’,Y’

V(x’,y) =V(x,y) + {V(x+x,y) - V(x,y)}(x’-x)/((x+ x)-x)

V(x’,y+1) =V(x,y+ y) + {V(x+ x,y+ y) - V(x,y+ y)}(x’-x)/(x)

V(x’,y’) = V(x’,y) + {V(x’,y+ y) - V(x’,y’)} (y’-y)/(y)