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Map Projections > Map > Flashcards

Map Flashcards

1
Q

Mercator Projection

A
  • Cylindrical Conformal
  • Poles are infinite in size and distance from the equator (distortion at poles)
  • Good for mapping equatorial regions
  • Distance correct at equator
  • Straight like of constant bearing - loxodrome/rhumb line
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2
Q

Transverse Mercator

A
  • Cylindrical conformal
  • Central meridian and meridians 90 degrees from central meridian are straight lines
  • all other meridians and parallels are curved
  • widely used: UTM, UK national grid
  • Scale factor is the same in any direction m=secO
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3
Q

Lambert Conformal conical

A
  • Widely used with TM
  • Meridians are straight lines deriving from a common centre point
  • parallels are arcs of circles gathering at a central point
  • normal aspect good for mapping mid latitudes
  • projection errors vary increasingly N/S of standard parallels
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4
Q

Stereo graphic azimuthal

A
  • Perspective point lies on the datum surface, diametrically opposed to the central point
  • Conformal projection
  • Central meridian is a straight line
  • no distortion at centre
  • scale factor increases with distance from centre
  • good for minimising distortion in circular regions
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5
Q

Orthographic azimuthal

A
  • perspective point lies at infinity
  • used only in spherical form
  • all meridians and parallels are straight lines, circles or ellipses
  • no distortion at centre
  • scale factor rapidly decreases away from centre
  • only one hemisphere can be shown
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6
Q

Gnomonic azimuthal

A
  • perspective point lies at the centre of the datum surface
  • only used in spherical form
  • all meridians and equator are straight lines
  • no distortion at centre
  • scale factor rapidly increases from centre
  • less than one hemisphere can be shown
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7
Q

Equidistant azimuthal

A
  • non perspective projection
  • mathematically derived
  • meridians are straight lines
  • no distortion at centre
  • Suitable for mapping polar regions
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8
Q

Winkel Trippel

A
  • Oswald Winkel 1921
  • Central Meridian and Equator are straight lines
  • adaption of azimuthal projection
  • poles are shown as lines
  • parallels are curves
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9
Q

Datum surface

A

Is an ellipsoid of revolution obtained by rotating an ellipse around it’s minor axis

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10
Q

Projection/Developable Surface

A
  • The ellipsoidal earth can be projected onto an intermediate BLANK developable surface. As the curvature of the developable surface is only 1D, the projection can be unravelled to a plane without further distortion.
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11
Q

Normal, transverse and oblique position

A
  • Normal: Axis of symmetry of BLANK, parallel to the polar direction
  • Transverse: Axis of symmetry in equatorial plane
  • Oblique: otherwise
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12
Q

Tangent & Secant

A

Tangent - BLANK surface touches ellipsoid along parallel

Secant: BLANK cuts ellipsoid

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13
Q

Equidistant, Equal Area and Conformal

A

Equidistant - Preserves distances along the meridian
Equal area - preserves areas (mphi mldr = 1)
Conformal - preserves angles (mphi = mldr)

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14
Q

Grid & Graticule

A

Grid: lines on a projection which run N-S and E-W

Graticule: the projection of meridians and parallels. The size of the graticule depends on the projection formulae.

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15
Q

False coordinates

A
  • offsets added to eastings and northungs to ensure both are positive and not too large
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16
Q

Tissots Indicatrix

A

Tissots indicatrix is a mathematical tool devised by the french mathematician, Nicolas Tissot in 1859. It describes local distortion on a map via an ellipse of revolution in 2 principal directions orthogonal to each other on the datum surface and on the projection plane. It can be constructed anywhere on the map to show distortion in that location. Distortion pattern is shown by a regular spread of tissots indicatricies and circular indicatrices are indicative of conformality.

17
Q

Molleweide

A
  • Pseudocylindrical equal area projection
  • uses several cylinders to minimise distortion
  • meridians lie 90 degrees east and west from perfect circle
  • derives by Karl Brandon mollweide in 1805
  • parallels condensed at the poles
18
Q

Datum

A

A datum is the information required to attach a coordinate system to an object. Namely the location of origin, scale and orientation of the axis of the coordinate system. A datum turns a coordinate system into a coordinate reference system.

19
Q

Geodetic Datum

A

A geodetic datum describes the relationship between a 2D/3D coordinate system and the earth. A geodetic datum can turn a coordinate system into a geodetic coordinate system: WGS84

20
Q

Map scale

A

The ratio between the distance on the reduced scale datum surface and the corresponding distance on the datum surface

21
Q

Scale factor

A

The ratio between the distance on the map and the corresponding distance on the reduced scale datum surface.

Only the concept of scale factor is associated with map projections

22
Q

How to project the earth onto a map?

A
  1. the earths figure is approximated by a datum surface; sphere or ellipsoid of revolution
  2. The datum surface must be reduced in order to be represented on a map.
  3. The reduced scale datum surface is then projected onto a plane or a developable surface.
  4. If the projection is a cylinder or cone, it must be developed into a plane.
  5. If the projection is mathematically derived, steps 3 and 4 are skipped
23
Q

Describe using the forward geodetic problem and describe how to use a map projection with associated scale factor, convergence and arc to chord correction

A
  1. Project the geodetic last/long onto a plane using a map projection
  2. Find an approximation of t ignoring arc to chord correction
  3. Find the line scale factor along line at grid azimuth t
  4. Estimate the projected distance using line scale factor and ground distance
  5. Estimate EB and NB and iterate with t using the arc to chord correction for EA NA and EB NB
    - if converged, go to step 6. If not, got to step 3
  6. Use the inverse projection formulae to find the grid lat/long of B using Eb and Nb
24
Q

OSTN15

A
  • OSTN15 is an upgrade of OSTN02 due to an improvement in the realisation of ETRS89 in the UK
  • Resolution is 1km by 1km with 1250km by 700km area
  • obtained using thousands of ETRS89 coordinates and primary and secondary OSGB36 trig points
  • uses bilinneal interpolation of values at corner of grid Cell
  • 1cm agreement with OSTN02
25
Q

OSGM15

A
  • OSGM15 is an update of OSGM02 incorporating gravity data from from GRACE
  • Contains a single grid of height shifts with ERTS89 heights and ODN
  • same resolution
  • uses bilinneal interpolation of values at corner grid cell
  • 2.5 height shift between 15 and 02
26
Q

GNSS

A
  • GNSS derived lat and long expressed via ETRS89 are projected to eastings and northings via standard national grid mapping.
  • Eastings and northings shifts are calculated via OSTM15 and applied to determine OSGB36 national grid eastings and northings
  • OSGM15 is used to convert ETRS89 ellipsoidal heights into ODN orthometric heights.
27
Q

Lambert equal area

A
  • Cylinder in normal aspect tangent to sphere
  • Meridians are equal spaces vertical straight lines
  • parallels are unequally spaced horizontal lines of equal length
  • equator is a standard parallel
  • origin at 0 degrees, lldr 0
28
Q

Peters

A
  • adaption of lamberts equal area
  • equal area proj
  • normal cylindrical projection
  • further scaling of 0.5 and 2 along m/p
  • shapes of features correct at mid-lat

Map Projections (1 decks)

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