356 15 “Ellipsoid-of-revolution to cylinder”: transverse aspect
Example 15.9 (WGS84 reference ellipsoid, strip transformation x 2 (x 1 , y 1 ) and y 2 (x 1 , y 1 ) of conformal
coordinates of UTM type versus direct transformations {L, B} → {x 1 , y 1 } with respect to L 01 = 9
◦ and
{L, B} → {x 2 , y 2 } with respect to L 02 = 1 5
◦ , B = 4 9
◦ , and L = 1 2
◦ 0
3 6
).
{L, B} → {x 1 , y 1 }:
L 01 = 9
◦ ,
dilatation factor ρ = 0 .9 9 9 5 7 8
,
B 0 = 4 8
◦
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
x 1 = ρ × 2 2 0 2 3 3
.0 8 0 3 3 m
,
y 1 = ρ × 1 1 5 5 6 7
.8 3 9 9 1 m
,
y 0 = ρ × 5 3 1 8 4 2 7
.5 9 5 4 9 m
,
B 0 = 4 8 .8
◦
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
x 1 = ρ × 2 2 0 2 3 3
.0 8 0 3 3 m
,
y 1 = ρ × 2 6 6 0 9
.3 6 3 1 4 m
,
y 0 = ρ × 5 4 0 7 3 8 6
.0 7 2 2 6 m
.
C onventional UT M coordinates:
N orthing y UTM = y 0 + y 1 = 5 4 3 1 7 0 2
.2 8 9 3 3 m
,
F
alse E asting
x UTM = 5 0 0 0 0 0 m +
x 1 = 7 2 0 1 4 0
.1 4 2 0 0 m
, z one
L 01 +3
◦
6 ◦
+ 3 0= 3 2
.
{L, B} → {x 2 , y 2 }:
L 02 = 1 5
◦ ,
dilatation factor ρ = 0 .9 9 9 5 7 8
,
B 0 = 4 8
◦
x 2 = −ρ × 2 1 8 7 6 9
.9 2 2 6 4 m
,
y 2 = ρ × 1 1 5 5 0 9
.9 6 7 9 4 m
,
B 0 = 4 8 .8
◦
x 2 = −ρ × 2 1 8 7 6 9
.9 2 2 6 4 m
,
y 2 = ρ × 2 6 5 5 1
.4 9 1 1 7 m
.
C onventional UT M coordinates:
N orthing y UTM = 5 4 3 1 6 4 4
.4 4 1 7 8 m
,
F
alse E asting
x UTM = 2 8 1 3 2 2
.3 9 8 2 7 m, z one
L 02 +3
◦
6 ◦
+ 3 0= 3 3
,
{x 1 , y 1 } → {x 2 , y 2 }:
B 0 = 4 8
◦
{x 2 = −ρ × 2 1 8 7 6 9
.9 1 9 7 9 m
, y 2 = ρ × 1 1 5 5 0 9
.9 6 8 2 6 m
,
B 0 = 4 8 .8
◦
{x 2 = −ρ × 2 1 8 7 6 9
.9 2 1 9 3 m
, y 2 = ρ × 2 6 5 5 1
.4 9 1 4 6 m
.
End of Example.