1

Types of Operations (4.7/4.9)

Operations on coordinates– Validation (move to clause 5?)– Conversions– Transformations

• Horizontal• Vertical (especially gravity models)

Operations on coordinates for compensating projection-based distortions– Point scale– Convergence of the meridian– Vector (bound)

Operations on directions (one or more SRF?)– Radii of curvature (and mean radius)– Azimuth (forward/backward), Bearing– "Euclidean Distance": Minimum length path (geodesics)– "3D" Distance in Augmented SRF– Vector (cross-product, dot-product ???)

Operations on scalar measures– Othometric height (and for other vertical datums?)– Distance

2

Organize Operations by SRF Type

• Celestiocentric (centric J2000 inertial)– Kinematic formulations (time; no forces)– Rotating body (vs. revolving vs. inertial orientation)

• Celestiodetic (detic centric)• Projected (detic projected)

– M/AM, TM/ATM, UTM/AUTM (Earth-specific; zones)– OM/AOM, LCC/ALCC (treat LCC1 as special case)– PS/APS, UPS/AUPS (Earth-specific), EC/AEC

• Topocentric (topo centric)– LTP, GCS (Earth-specific case)

• Celestiomagnetic (magnetic centric)• Celestiocentric non-fixed (CNF centric)• Heliocentric non-fixed (HNF centric)• Artificial body-centric (ABC centric)• Non-tied ( detic, projected, topo)

– Requires additional parameters

3

Celestiodetic

• Celestiodetic– Celestiodetic 2D SRF to Celestiocentric SRF

• Conversion– Formulation– Applicable domain

» 40 km central ball excluded; maximum radius/distance …– Accuracy

• Radius of curvature– Formulation– Applicable domain– Accuracy

– Celestiocentric SRF to Celestiodetic 2D SRF (exclude?)• …

– Celestiodetic 3D SRF to Celestiocentric SRF• …

– Celestiocentric SRF to Celestiodetic 3D SRF• …

Spherical cases in AnnexSpherical cases in Annex

4

Example of a Projected SRF

• Mercator– Celestiodetic 2D SRF to Mercator 2D SRF

• Coordinate conversion– Formulation– Applicable domain– Accuracy

• Point scale– Formulation– Applicable domain– Accuracy

• Convergence of the meridian– Formulation– Applicable domain– Accuracy

– Mercator 2D SRF to Celestiodetic 2D SRF• ...

– Celestiodetic 3D SRF to Augmented Mercator SRF• …

– Augmented Mercator SRF to Celestiodetic 3D SRF• …

Spherical cases in AnnexSpherical cases in Annex

5

Transformation

• Shifting between two local horizontal datums• Seven-parameter ellipsoid of revolution ORS

transformations– Transformation to coordinates based on the WGS 84 global

datum– Transformation to coordinates based on a local datum– Parameter values– Accuracy

• Three-parameter ellipsoid of revolution ORS transformations– Transformation to coordinates based on the WGS 84 global

datum– Transformation to coordinates based on a local datum– Molodensky single-step transformations– Local datum distortion

Note that these are all Earth-specificNote that these are all Earth-specific