Presentation Index

Presentation Index

1 SEDRIS Spatial Reference Model	2 SRM Tutorial	3 Outline	4 Section I
5 In the Beginning ...	6 Simulation Interfaces	7 A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis	8 A Spectrum of Constructive, Live and Virtual Capabilities Support Training, Planning & Analysis
9 The Interface Canyons	10 Why is a Spatial Reference Model (SRM) Needed?	11 SRM Requirements	12 Location is Not Enough
13 A Shared Solution is Required!	14 Section II	15 It’s a Loooong Way Up	16 Here’s an Interesting Perspective
17 Not All Projections are Geodetic!	18 More Familiar?	19 Spatial, the Final Frontier	20 Coordinates
21 DRM <Location> (Page 15)	22 Spatial Reference Frames	23 SRF Example	24 Named SRFs in SEDRIS
25 Named SRFs in SEDRIS	26 Coordinates & Coordinate Systems	27 ERMs	28 Standard Ellipsoids
29 Standard Spheres	30 Standard Horizontal Datums	31 Standard Vertical Datums	32 ORMs
33 Many SRFs	34 Spatial Reference Model	35 Operations on Coordinates	36 Types of Operation Errors
37 Section IIB	38 Ellipsoidal Earth Reference Model (ERM) Geometry & Notation	39 Latitude, Longitude and Height for Ellipsoids & Spheres	40 Cross-Section of the Geoid, Ellipsoid and Earth Surface
41 Gravitational Field and the Geoid, Ellipsoid & Earth Surface	42 SRM Refresher	43 Section III	44 Development of Surfaces to Generate Maps
45 Map Projections	46 Projecting from 2D to 1D	47 Cylindrical Projections	48 Planar Projections
49 A Stereographic Projection	50 Conic Projections	51 Mercator Projection	52 Oblique Mercator Projection*
53 Transverse Mercator Map of the Western Hemisphere*	54 Universal Transverse Mercator (60)	55 Lines of Constant Heading*	56 Great Circle Arc between Moscow and Washington D.C.*
57 Many Map Projections are Conformal	58 Section IV	59 Augmented Projection-Based SRFs	60 “3D” Projection-based SRFs
61 Coordinate Operations affect Geometrical Relationships	62 SRF Operation Relationships	63 Geometric Distortions	64 Distance and Elevation Angle
65 Distance Distortion Can Be Mitigated, Somewhat	66 Azimuth	67 How Much Azimuth Distortion?	68 Flattening the ERM: Distance and Geometry
69 Section V	70 Modelers Often Prefer Cartesian Coordinate Frameworks	71 Non-real World 3-D Systems are often Used. Why ?	72 Relationships Between Coordinate Systems and Simulations
73 MCG&I and Dynamics Modeling	74 MCG&I	75 Dynamics Modeling	76 Section VI
77 Euclidean Distance in a Rectangular Framework	78 Defining Geometrical Concepts	79 The Traditional Surveying Process	80 Surveying is a Complex Process
81 Traditional Distance Determination in Surveys	82 Surveying on a Flat ERM	83 Surveying on a Flat ERM with a Terrain Model Added	84 Surveying on a Spherical ERM
85 Chaining on a Spherical ERM with a Terrain Model Added	86 Surveying on an Ellipsoidal ERM	87 Normal Section of an Ellipsoid	88 Distance on an Ellipsoidal ERM
89 Bearing Angles (Ellipsoidal ERM)	90 Bearing when a Point P is above the ERM Surface (Ellipsoid)	91 Once the Environment is Included, There are Many Feasible Paths	92 Placing a Solid Cube on an ERM
93 Doing the Math ...	94 Placing a Cube on the Terrain Skin Model	95 Long Linear Structures	96 Vectors in Augmented Projection-based SRFs
97 Vectors in a Curvilinear System	98 Defining a Canonical Local Tangent Plane SRF	99 A LTP Embedded in a GD SRF	100 Defining a CLTP Embedded in a GD SRF
101 Reference Vectors	102 Reference Vector Transformations	103 SRF “North” may not be True North	104 Convergence of the Meridian
105 Representing a Projection-based SRF Vector in Terms of a CLTP	106 TM series for X and Y (from P. D. Thomas)	107 Computing the Convergence of the Meridian (COM)	108 Second Method for Computing the COM
109 Computing the Sine and Cosine of the COM	110 Observations	111 Section VII	112 Why is Accuracy Needed for Coordinate Transformations?
113 Shooting at a Target in the Real World (Relative Coordinate System)	114 Simulation of Shooting at a Target (Simulation of a Relative Coordinate System)	115 Error Sources in Coordinate Transformation Software	116 Definition of Error
117 Numerical methods	118 Efficient Evaluation of Special Functions Common to Coordinate Transformations	119 Analytic (closed form) Solutions	120 Taylor/Maclaurin Series Methods
121 Iterative Methods	122 Direct Approximation of a Function or its Inverse	123 Error in Power Series Expansions	124 Authoritative Sources Sometimes Appear to Disagree
125 Error Analysis and Resolution of Disagreements	126 Effect of Small Errors	127 Fuzzy Creep/Coordinate Drift	128 Bounds Checking
129 What to Do?	130 Distortion and Computation Error Tradeoff	131 Distortion in Projection-based SRFs	132 Distortion-Accuracy Trades for UTM
133 Point Scale Equations	134 UTM Point Scale Equations	135 Linear Distortion Error For UTM	136 Difference between SR-7 & Extended Formulas for Transverse Mercator
137 Conclusions of Experiment	138 The Chaining Problem	139 Section VIII	140 SRFs
141 DRM <Location> (Page 15)	142 SRFs Supported	143 SRFs with CS Origin Offsets*	144 Local Space Rectangular
145 Local Space Rectangular (2D)	146 Geocentric	147 Geodetic	148 Geodetic (2D)
149 Local Tangent Plane	150 Local Tangent Plane (2D)	151 GCS	152 Mercator
153 Augmented Mercator	154 Oblique Mercator	155 Augm. Oblique Mercator	156 Transverse Mercator
157 Augm. Transverse Mercator	158 Universal Transverse Mercator	159 Augm. Univ. Transverse Mercator	160 Lambert Conformal Conic
161 Augm. Lambert Conformal Conic	162 Polar Stereographic	163 Augm. Polar Stereographic	164 Universal Polar Stereographic
165 Augm. Univ. Polar Stereographic	166 Equidistant Cylindrical	167 Augm. Equidistant Cylindrical	168 Geocentric Equatorial Inertial
169 Geomagnetic	170 Geocentric Solar Ecliptic	171 Geocentric Solar Magnetic	172 Solar Magnetic
173 Section IX	174 PPT Slide	175 ERM Datum Transformations	176 Init WGS84 Geoidal Separation
177 Get WGS84 Geoidal Separation	178 PPT Slide	179 Types of Operation Errors	180 “Valid” Coordinates
181 Coordinate Validity	182 Implementation Details (1 of 2)	183 Implementation Details (2 of 2)	184 Range Extension (1 of 2)
185 Range Extension (2 of 2)	186 PPT Slide	187 Op Support	188 Coordinate Operation Chains
189 Status Codes (1 of 3)	190 Status Codes (2 of 3)	191 Status Codes (3 of 3)	192 Interface Specification(s)
193 Operation Setup	194 Conversion Operation	195 Multi-conversion Operation	196 Boundary Checking
197 Operation Teardown	198 Vector Operation	199 Matrix Operation*	200 Transformation Operation
201 Convergence of Meridian Operation	202 “SRM Check Utility”*	203 Further Reading	.