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Mathematical Cartography > Midterm 2 > Flashcards

Midterm 2 Flashcards

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1
Q

What is the direct problem?

A

Transferring all points on the datum surface onto a projection surface one to one correspondence.

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2
Q

What is the inverse problem?

A

Transferring all points on the plane surface onto the datum surface in a one to one correspondence.

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3
Q

What are the general distortion properties?

A
  1. Area distortion
  2. Angular distortion
  3. Direction distortion
  4. Scale distortion
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4
Q

What is a Standard Line?

A

a line or point that is transferred from the earth to a map free of distortion.

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5
Q

What is an earth model?

A

A scaled down replica of the earth

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6
Q

What is Map Scale

A

relates the map to the earth

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7
Q

What is Scale Factor

A

relates the earth model alone with a map

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8
Q

What is Scale Distortion

A

the difference of the scale factor value from 1.00

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9
Q

What is a Tissot Indicatrix

A

an ellipse of distortion with semi-major and semi-minor axis parameters.

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10
Q

What is an advantage of a Tissot Indicatrix

A

Gives a general visual representation of variations of distortions around any projected point. Convenient way of displaying distorting effects of projections.

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11
Q

What is Tissots Theorum

A

For any projection, at least one pair directions (principle points) remain orthogonal.

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12
Q

What are the parameters of a Conformal Projection in terms of Tissots Indicatrix

A

a=b at all points

indicatrix is circular

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13
Q

What are the parameters of a Equal-Area Projection in terms of Tissots Indicatrix

A

a*b=1

a=b only at 1 or 2 points or on a standard line

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14
Q

What the 3 traditional bases of projection classification?

A
  1. Distortion Property (relationship between sem-axis of tissot indicatrix)
  2. Appearance of the Graticule (type of projection surface used ie cylinder, conic, etc.)
  3. Aspect (viewpoints)
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15
Q

What are the properties of Conformality distortion?

A
  • Local angles in original feature are preserved
  • Over small areas shapes are preserved
  • Specific only to Mercator
  • Scale factor at points are same in every direction, varying point to point
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16
Q

What are the properties of Equal Area distortion?

A
  • No area distortion
  • Tissot Indicatrix has same area everywhere, always elliptical, never circle
  • Will strongly distort shape & angles
17
Q

What are the properties of Equidistant distortion?

A
  • Preserves relative distance from one or two points only

- No projection in which all distance are preserved

18
Q

What are the 3 classes of projections according to base 2?

A
  1. Conic
  2. Cylindrical
  3. Planar
19
Q

Describe tangent as secant cases relating to base 2.

A
  • Tangent: when a developable shape touching the earth creates a line/point/region
  • Secant: line or lines created when the earth & developable shape cut through each other
20
Q

What are the properties of the Conic Projection?

A

Conic projection can only represent one hemisphere

21
Q

What are the properties of the Cylindrical Projection?

A

-Typical grid shows parallels and meridians forming straight perpendicular lines.

22
Q

What are the properties of the Planar projection?

A
  • Usually placed above a pole, can only represent 1 hemisphere.
  • Also called azimuthal, stereographic
23
Q

What are the 3 Aspects of base 3?

A

-Direct or Normal Aspect
The long axis is parallel to or along N/S pole
-Oblique Aspect
Projection is placed above or on any postion between but not on, the pole and the equator
-Transverse Aspect
The long axis is parallel to or along the E/W of the equator

24
Q

What are the parameters of Edge Matching?

A
  • Map must be same scale
  • Map must be same projection
  • Maps must have same standard parallels
  • Maps should be based on same ellipsoid
25
Q

What do Grids and Graticules do?

A

Serve as a framework on which the map is based

26
Q

What are the advantages of the Grid?

A
  • usually shown @ regular intervals and usually in meters

- allows coords. to be read off map easily, points easy to plot

27
Q

What are disadvantages graticules?

A
  • Measured in DMS

- Parallels and meridians are curved lines and are difficult to use in reading and plotting points

28
Q

What is a Mercator Projection?

A

a conformal cylindrical, normal aspect, projection mainly for equatorial regions and hydrography.

  • distances only true along equator
  • areas and large shape distortion increase away from equator
29
Q

Advantages of Mercator?

A
  • two neighboring mercator maps of same scale can be easily put together
  • only mercator can produce rhumb line as straight line for use in navigation
30
Q

Explain principle directions, max and min scale factors with respect to Tissot indicatrix

A

-Principles directions are direction of (a) semi major axis and (b) semi minor axis
a=max scale factor
b=min scale factor

31
Q

Name 8 quantities of distortions in mapping:

A
  1. scale factor
  2. scale along meta meridian
  3. scale along meta parallel
  4. max angular distortion
  5. semi major axis of tissot
  6. semi minor axis of tissot
  7. maximum direction distortion
  8. scale of area
32
Q

Different countries use different projections. How does this relate to position and shape of country?

A
  • local datums are different depending on position of country
  • tropical regions use cylindrical (normal)
  • temperature regions use conic (oblique aspect)
  • polar regions use planar (polar aspect)
  • countries with large EW extent use conic projection
  • countries with large NS extent use tranverse mercator
  • countries that equal area or circular use stereographic
33
Q

what is foot latitude

A

latitude of the reflection of the y-coordinate value of a point on the central meridian

34
Q

What is grid convergence?

A

the angular difference at a point between the grid north and the true north defined by the projected meridian

Mathematical Cartography (1 decks)

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