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 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 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 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-specific