Map Projections of Alternative Structures: Torus, Hyperboloid, Paraboloid, Onion Shape and Others - Map Projections: Cartographic Information Systems - page 628

(ii) equiareal:

a
√ n +1 (

n

n +1 ) n/ 2 U
y= ( n +1) ( n +1)

x =

V

cos 2 n− 1 V ∗ sin V ∗
(n + 1) 2 cos 2 V ∗ sin 2 V ∗ +a 2 [ cos 2 V ∗ (n + 1)

√ n n

V

n] 2 dV ∗

−

Λ 1 = [n / (n + 1)] n / 2

1
cos n V sin V

(n + 1)

(n + 1)

[n / (n + 1)] n / 2 cos n V sin V

Λ 2 =

(iii) equidistant:

a
√ n +1 (

n

n +1 ) n/ 2 U

x =

y= V
V

(cos V ∗ ) n − 1 .
(n + 1) 2 cos 2 V ∗ sin 2 V ∗ +a 2 [ cos 2 V ∗ (n + 1)

n] 2 dV ∗

−

Λ 1 = [n(n + 1)] n / 2

1
cos n V sin V

(n + 1)

Λ 2 =1

23-5 Mapping the Clothoid: Projection Geometry
for High-Speed-Railways

High-speed-railways also called bullet trains or Transrapid need ext reme reli a ble control sy stems
(“ extasy ”) to avoid catastrophic events. Here we consequently focus on two sensitive problems
related to extasy:
• a local high resolution of the track design (clothoid, circle, straight line) in UTM map matching

coordinates is given.

• the Mixed Model ( universal Kriging ) is used to discriminate measurement errors from track

displacement.
In this first part we develop the local high resolution representation of the clothoid (special
case: circle, straight line) which is needed for creating an expert base of extasy.

Local representation of the clothoid