Azimuthal Family·Inventor: Hipparchus (c. 150 BCE) / Classical Antiquity·Year: -150

Orthographic Projection

"Perspective view of the globe from an infinite distance in space (The Spacecraft Gaze)"

A perspective azimuthal projection where light rays originate from infinity. It portrays the Earth exactly as it appears from deep space, displaying exactly one hemisphere at a time with foreshortening increasing toward the horizon limb.

Forward Mathematical Formulation

X-COORDINATE:

x = R \cos \phi \sin(\lambda - \lambda_0)

Y-COORDINATE:

y = R [\cos \phi_1 \sin \phi - \sin \phi_1 \cos \phi \cos(\lambda - \lambda_0)]

DIFFERENTIAL METRIC:

h = 1, \quad k = \cos c, \quad hk = \cos c

Cartographic Application & Critique

Primary Applications: 3D Digital Earth globes, Satellite coverage footprint planning, Astronomical illustrations of celestial bodies.

Critical Analysis: Provides unmatched intuitive 3D spherical realism, though extreme radial compression eliminates metric measurements near the planetary limb.

TISSOT INDICATRIX (Lat: 60°N)Area: 1.02×

MERIDIAN (h)

1.13

PARALLEL (k)

0.90

ANGULAR (2θ')

13.2°

Tissot Profile Across Latitudes

LATITUDE	SCALE h	SCALE k	AREA hk	2θ' DEFORM
90°N	1.00	1.00	1.00×	0.0°
60°N	1.00	0.87	0.87×	8.2°
30°N	1.00	0.50	0.50×	38.9°
0°N	1.00	0.00	0.00×	90.0°

Interdisciplinary Geometric Links

LunologiumCORRESPONDS_TO

Lunar Disc Observation

MorphologiumCOMPUTES

Orthographic Camera Rendering

Academic Provenance: Snyder, J. P. (1987)