1
PPT Slide |
2
SRM Tutorial |
3
Prerequisite |
4
PPT Slide |
5
PPT Slide |
6
Section I |
7
In the Beginning ... |
8
PPT Slide |
9
Simulation Interfaces |
10
Other Interoperability Examples |
11
SRM Requirements |
12
The Meaning Of Accuracy Is Context Dependent |
13
Why is Accuracy Needed
for Coordinate Transformations? |
14
PPT Slide |
15
It’s a Loooong Way Up |
16
The SRM Encompasses More Than The Earth |
17
The Scope Of The SRM |
18
The SRM Requires a Shared Solution |
19
Structure of the SRM ISO Standard |
20
Structure of the SRM ISO Standard |
21
Section II |
22
So How Will We Get There? |
23
Coordinates |
24
2-D Rectilinear Coordinate Systems |
25
Curvilinear Coordinate Systems(1 of 2) |
26
Curvilinear Coordinate Systems (2 of 2) |
27
Projection-based Coordinate Systems |
28
Spatial Referencing |
29
Indirect Embeddings |
30
Example: Vancouver_2002 |
31
Example: Vancouver_2002 Cont’d |
32
Example: Vancouver_2002 Cont’d |
33
Spatial Reference Frame |
34
Reference Datums (1 of 4) |
35
Reference Datums (2 of 4) |
36
Reference Datums (3 of 4) |
37
Reference Datums (4 of 4) |
38
Reference Datum Set |
39
Orthonormal RDS Class |
40
Oblate Spheroid RDS Class |
41
Infrastructure Review |
42
Section III |
43
Development of Surfaces
to Generate Maps |
44
Projecting from 2D to 1D |
45
Distance Distortion
Can Be Mitigated, Somewhat |
46
Cylindrical Map Projections |
47
Planar Map Projections |
48
A Stereographic Map Projection |
49
Conic Map Projections |
50
Mercator Map Projection |
51
Oblique Mercator Map Projection* |
52
The Grid for Transverse Mercator* |
53
Universal Transverse Mercator (60) |
54
Lines of Constant Heading* |
55
Great Circle Arc between Moscow
and Washington D.C.* |
56
Augmented Projection-Based SRFs |
57
Projection-based “3D” SRFs |
58
The Use of Augmented Systems Changes
Geometrical Relationships |
59
SRF Operation Relationships |
60
Geometric Distortions |
61
Augmented map projection
vertical distortion |
62
Flattening the ORM:
Distance and Geometry |
63
Placing a Solid Cube on an OBS |
64
Doing the Math ... |
65
Placing a Cube on the
Topographic Surface Model |
66
Long Linear Structures |
67
Vectors in Augmented
Projection-based SRFs |
68
Vectors in a Curvilinear System |
69
Defining a Canonical
Local Tangent Plane SRF |
70
A LTP Coordinate System
Embedded in a Celestiodetic SRF |
71
Defining a CLTP
Embedded in a Celestiodetic SRF |
72
Reference Vectors |
73
Reference Vector Transformations |
74
Convergence of the Meridian |
75
SRF “North” may not be True North |
76
Convergence of the Meridian |
77
Section IV |
78
ORMs vs. Object Models |
79
Celestial Object Models |
80
Example: Earth |
81
Earth Surface Model Terminology |
82
Section V |
83
Spatial Operations |
84
Spatial Operations |
85
Coordinate Conversion |
86
Coordinate Transformation |
87
Spatial Reference Model |
88
Quality Assurance
for Spatial Operations |
89
Conformance Verification for the SEDRIS Implementation |
90
Acceptance Testing Methodology |
91
SRM Concept Management |
92
SRF Relationships |
93
Section VI |
94
Why is Accuracy Needed
for Coordinate Operations? |
95
Shooting at a Visible Target
in the Real World |
96
Simulation of Shooting
at a Visible Target |
97
Servicing a Non-visible Target
in the Real World |
98
Error Sources in Coordinate Operations Software |
99
Definition of Computational Error |
100
Numerical Methods |
101
Analytic (closed form) Solutions |
102
Taylor/Maclaurin Series Methods |
103
Iterative Methods |
104
Direct Approximation
of a Function or Its Inverse |
105
Direct Approximation of a
Function or Its Inverse (cont) |
106
Error in Power Series Expansions |
107
Error Analysis and
Resolution of Disagreements |
108
Effect of Small Errors |
109
Fuzzy Creep/Coordinate Drift |
110
Bounds Checking |
111
Distortion in
Map Projection-based SRFs |
112
Treatment of Point Scale |
113
Distortion and Computation
Error Tradeoff |
114
Distortion-Accuracy Tradeoff Experiment for TM |
115
Authoritative Sources Sometimes
Appear to Disagree |
116
Difference between SR-7 & Extended
Formulas for Transverse Mercator |
117
Transverse Mercator Map Projection Point Scale Equations |
118
Linear Distortion Error For TM |
119
Conclusions of Experiment |
120
What to Do? |
121
The Chaining Problem |
122
Section VII |
123
Modelers Often Prefer
Orthonormal Coordinate Systems |
124
Euclidean Distance
for an Orthonormal System |
125
Once the Environment is Included,
there are Many Feasible Paths |
126
Geometry Distorting 3-D SRFs
are often Used – Why ? |
127
Section VIII |
128
SRFs in the DRM |
129
DRM <Location> (Sheet 15) |
130
SRFs Supported |
131
Section IX |
132
PPT Slide |
133
ERM Datum Transformations |
134
WGS84 Geoidal Separation |
135
PPT Slide |
136
Types of Operation Errors |
137
“Valid” Coordinates |
138
Coordinate Validity |
139
Implementation Details (1 of 2) |
140
Implementation Details (2 of 2) |
141
Range Extension (1 of 2) |
142
Range Extension (2 of 2) |
143
PPT Slide |
144
Operation Implementation Status |
145
Coordinate Operation Chains |
146
Interface Specification(s) |
147
Status Codes (1 of 3) |
148
Status Codes (2 of 3) |
149
Status Codes (3 of 3) |
150
Operation Setup |
151
Change SRF Operation |
152
Multi-change SRF Operation |
153
Boundary Checking |
154
Operation Teardown |
155
Vector Operation |
156
Matrix Operation |
157
Convergence of the Meridian |
158
Further Reading |
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