Lecture 4: Coordinate systems 2 Flashcards
(84 cards)
1
Q
The problem with mapping…
A
You can’t make a round object flat
2
Q
Projection conversion process
A
- The ellipsoid - Survey measurements are reduced to the ellipsoid (in terms of a datum) e.g distances and bearings
- The plane surface - coordinate conversion using projection formula
- The map - Scale change e.g 1:50,000 onto i.e a cadastral plan
3
Q
The ideal map or projection is characterized as follows
A
- It should not change the shape of countries/objects
- Countries/objects should maintain their true relative sizes
- The distance of every place from every other place should be proportional to the true distance, i.e scale factor
- Places lying on a straight line on the earths surface (on a geodesic should lie on a straight line on the map
4
Q
Is it possible to achieve all the criteria for an ideal map or projection
A
No
5
Q
A mapping or projection surface is a systematic method of representing
A
The curved surface of the earth as a plane surface
6
Q
A mapping and projection surface can be defined as a mathematical transformation of
A
3D objects to a 2D space with minimal distortions
7
Q
Four components ideally mapping and projection surfaces should have
A
- Distances and areas have the correct relative magnitude
- Azimuths and angles are correctly shown
- Great circles on Earth would be shown as straight lines
- Geodetic latitude and longitude are shown correctly
8
Q
A measured straight line on the earths surface projects as a ____ line on a projection
A
Curved
9
Q
Mapping/projection surfaces have ____ change to observed angles
A
Minimal
10
Q
The measured distances in mapping/projection surfaces changed ____ in all directions
A
Changed equally, i.e point scale factor is independent of direction
11
Q
Types of projections - categories
A
- Azimuthal
- Cylindrical
- Conic
12
Q
Azimuthal projections usage
A
- Useful for showing polar regions
- Distorts direction and distance
13
Q
Cylindrical projections usage
A
- Easy to use
- Latitude and longitude are at right angles
- Shows true direction
- Distorts high latitudes
14
Q
Conic projections usage
A
Good for showing a small area accurately
15
Q
Types of projections - common
A
- Conformal
- Equal area
- Equidistant
- Azimuthal
16
Q
Conformal projections preserve
A
Angles (and thus shapes), at least over small distances
17
Q
Equal area projections preserve
A
Size or area such that the area of all features on the map have the same relative size as on the globe
18
Q
Equidistant projections preserve
A
Distances (but usually only in certain directions)
19
Q
Azimuthal projections preserve
A
Directions such that a direction on the globe is the same as the direction on the map
20
Q
The mercator projection has its central meridian
A
Selected (arbitrary)
21
Q
In the mercator projection, the largest distortions occur at ____ latitudes
A
High latitudes
22
Q
Mercator projections are unsuitable at latitudes greater than
A
+-70
23
Q
Mercator projections have reasonably true shapes and distances within ____ of the equator
A
15 degrees
24
Q
The cylinder tangent, in which the mercator projection is based on, touches
A
The equator (true scale on the equator)
25
Mercator projected meridians and parallels intersect at ____ angles
Right angles
26
The mercator projection is conformal, meaning
The shapes of small elements are well preserved
27
The convergence in the mercator projection is zero, meaning
Grid north and true north coincide
28
A transveres mercator projection has its central meridian
Selected (arbitrary)
29
Transverse mercator projections are suitable for what regions
North-South regions (large distortions at East-west extents)
30
In transverse mercator projections, the cylinder tangent touches
The central meridian (true scale at CM)
31
Transverse Mercator projected meridians and parallels intersect at ____ angles
Right angles
32
Like the mercator projection, is the transvere mercator projection also conformal
Yes
33
In the transverse mercator projection, the convergence is zero at ____ and Non zero ____
Zero at the equator and CM, non-zero everywhere else (Grid north and true north do not coincide)
34
In transverse mercator projections, rhumblines are projected as
Complex curves
35
Equal area projections are aimed at
Preserving area and scale
36
The Dymaxion map (fuller) is what type of map projection
Polyhedral map projection
37
The dymaxion map is a projection onto the surface of an
Icosahedron - a polygon with 20 faces
38
Dymaxion map properties
1. Neither conformal or equal area
2. Less distortion of the relative sizes of areas
3. No "right way up" - universe has no up or down, north or south, onky in and out (gravitational attraction)
39
Surveying projections are always
Conformal
40
Why are surveying projections always conformal
1. They correctly represent angles - an angle observed on the ground can be plotted directly on the map (ease of use for navigation, calculation)
2. Shapes are preserved - The shape of an object on the ground will be the same asits shape on the map
41
Examples of conformal projections
1. Mercator projection
2. Transverse mercator
3. Lambert conic conformal
4. Stereographic projection
42
Mercator projection usage
Navigation purposes
43
Transverse mercator usage
1. Universally for most surveying and mapping applications, from which we get the universal trnasverse mercator (UTM) projection
2. Originally designed for military mapping purposes
44
Lambert conic conformal usage
State plane coordinate systems and national mapping
45
Stereographic projection usage
Polar mapping, from which we get the universal polar stereographic (UPS) projection
46
When a measured line or a measured angle is projected, what may happen to the length of the line
Change or the size of the angle might change, depending on the projection
47
The ratio of a differentially small line on the projection surface and the same differentially small line on the ellipsoid is known as
The scale coeefiecient, or (point) scale factor
48
Scale coefficient is given by:
k = grid distance (dS) / ellipsoid distance (ds)
49
All conformal projections have a true
True origin with respect to which the mapping coordinates are calculated
50
In order for all map coordinates to remain positive, the true origin is often
Given values other than (0 mE, 0 mN).
51
The non-zero origin coordinates are known as
False origin coordinates
52
Conformal projections always have a
Central meridian
53
A central meridian is a meridian that
Has respect to which longitudes are measured when calculating E, N grid coordinates
54
The origin of projection lies on
The central meridian
55
True north definition
The direction of the tangent to the meridian at a point
56
Grid north definition
The direction parallel to the north axis of a north-east grid. It is parallel to the central meridian of the projection
57
Meridian convergence
The angle between grid north (northern grid axis) and the true north (tangent to the projected meridian)
58
In the southern hemisphere, positive convergence occurs when grid north is
West of true north
59
Magnetic north
The direction that a compass needle points to align with the earths magnetic field
60
Earths magnetic poles are fixed. True or false
False
61
Magnetic north deviates from true north over time. True or false
True
62
True north and grid north only coincide along
The central meridian
63
Azimuth definition
The angle measured clockwise from true north and the projected geodesic
64
Ellipsoidal bearing definition
The angle measured clockwise from grid north and the projected geodesic (arc)
65
Grid bearing definition
The angle measured clockwise from grid north and the projection bearing
66
Arc to chord definition
The angle between the grid and ellipsoid bearing
67
Arc to chrod correction can be generally ignored unless the line being observed is
1. Long, i.e > 10 km
2. A long way from the central meridian i.e > 200km
68
Geodesic definition
The geodesic is the curved line that represents the shortest distance between two points on the ellipsoid.
69
The geodesic projects as a ____ on a conformal projection
Curved line
70
Ellipsoid distance definition
The projected geodesic is the arc between A and B (see slides)
71
What is the scale factor
A dimensionless ratio (unitless)
72
What does the scale factor account for
The difference between a distance on the ellipsoid (curved surface) and that same distance when projected onto a mapping plane, grid or projection.
73
What does the scale factor transform
A (measured) distance on the ellipsoid to the projection distance
74
Point scale factor is the scale factor at a pojnt, and changes East-West away from
The central meridian
75
The line scale factor is
The integrated scale factor along a line on the projection
76
Old cadastral surveys use what type of coordinates
Plane coordinates
77
Old cadastral is based on ____ generally close to the centres of settlements
Local origins
78
Discrepancies arose in old surveying when
Surveys based on different origins merged
79
Who recommended the use of triangulation methods in 1874
Major H. S. Palmer
80
What did Palmer insist for triangulation methods
A general triangulation of the colony is necessary for systematic development rather than the current scattered nature of surveys
81
Triangulation methods were deemed impractical to implement because
1. Settlement and land ownership was being established at the time of colonisation (unlike UK)
2. Dispersed nature of settlement
3. Rugged topography that had to be surveyed
82
Three coordinate systems history in NZ
1. Datum pre 1949 - None
2. Geodetic datum 1949 - NZGD1949
3. Geodetic datum 2000 - NZGD2000
83
What was used before the geodetic datums in 1949 as a datum
Old cadastral plane coordinates
84
How many meridional circuits are there
28
