学步园

From http://maps.unomaha.edu:16080/Peterson/gis/notes/MapProjCoord.html

Outline

1. Map Projections

• Basic Principles
  • Earth’s Shape and Vertical Datums
  • Geographic Coordinate System (latitude and longitude)
  • Map Projections Defined
  • Types of Projections.
    • Azimuthal
    • Cylindrical
    • Conic
    • Mathematical
  • Projection distance, area and shape
    • Equal Area
    • Conformal
    • Distance
    • Compromise
  • Common GIS Projections
    • Mercator
    • Lambert Conformal Conic
    • State Plane
    • Lambert Equal Area

1. Coordinate Systems

• General
• State Plane Coordinates
  • Every State has at least one
  • Based on origins identified by each state
  • Identified on US Quadrangle maps
  • Universal Transverse Mercator
    • Transverse (uses longitude as standard line) cylindrical projection
    • 60 Zones
  • United States Public Land Survey System

1. GIS Capabilities

• Basic Concepts
• Selecting the proper projection

1. Questions

1. Map Projections

Basic Principles

• Although for many mapping applications the earth
  can be assumed to be a perfect sphere, there is a difference between the distance around the earth between the poles versus the
  equator.  The circumference of the earth
  is about 1/300th smaller around the poles. This type of figure is termed an
  oblate ellipsoid or spheroid, and is the three-dimensional shape obtained by
  rotating an ellipse about its shorter axis. An estimate of the earth’s surface
  based on an ellipsoid provides a determination of the elevation of every point
  on the earth’s surface, including sea level, and is often called a datum. Over
  time, and in different countries, many datums have
  been developed and used. With more accurate means of measurement today (i.e.
  satellite and GPS), recent datums are referenced from
  the center of the earth rather than a theoretical surface.  The resulting North American Datum of 1983
  (NAD83)and the slightly refined World Geodetic System (WGS84), from the U.S.
  Military in 1984, are internationally accepted as the geodetic reference system
  (GRS 80).
• Geographic Coordinates simply refers to the
  system of latitude and longitude. This coordinate system is formed by creating
  a grid using the equator as 0 degrees and forming parallels of latitude to the
  north and south (90 degrees N is the North Pole, 90 degrees S is the South
  Pole), and meridians of longitude east and west (which meet at 180 degrees,
  commonly called the International Date Line) of the "Prime Meridian"
  which passes through Greenwich, England.

• Map projections are used to transfer or
  “project” geographical coordinates onto a flat surface.

The easiest way to try to transfer the information onto a flat
surface is to convert the geographic coordinates into an X and Y coordinate
system, where x is longitude and y is latitude. This is an example of
“projecting” onto a plane.  Coordinates
can also be "projected" onto two other flat surfaces, a cylinder or
cone, and then unfolded into a map. The grid formed by the latitude and
longitude on a map is called the graticule.  There are thousands of different map
projections all depending on how they intersect earth’s surface and how they
are oriented.  For example, the line of
latitude or longitude where a projection intersects or “cuts” the earth’s
surface is called the point of contact, or standard line, where distortion is
minimized.  Orientations of the three
shapes can also vary between equatorial (standard lines of latitude),
transverse (standard lines of longitude), and oblique (standard line other than
latitude or longitude).  In addition,
each projection effects the distance, area, and angle
relationships of the earth surface as portrayed on the map. Ideally, these
factors would be consistent to the relationships on the real earth.
Unfortunately, some relationships are always distorted.

Types of Projections

• An azimuthal or planar
  projection is usually tangent to a specific point on earth’s
  surface, but may also be secant. This point, or focus, may be a pole, the
  equator, or other oblique point. 
  Normally though, the azimuthal projection is
  used for polar charts due to distortion at other latitudes.

• A cylindrical projection usually places the
  earth inside a cylinder with the equator tangent or secant to the inside of the
  cylinder.  If the cylinder is placed
  perpendicular to the axis of the earth, the resulting projection is called a
  transverse projection.

• In a conic projection, a cone is placed over the
  earth, normally tangent to one or more lines of latitude. This tangent line is
  called a standard parallel and, in general, distortion increases the further
  away you get from this line.  A conic projection
  works best over mid latitudes for this reason.
• Mathematical map projections are not based on
  developable surface, but often specify a direct mathematical projection from a
  spheroid onto a flat surface.  These types
  of map projections can change for different parts or regions of the world in
  order to reduce certain distortions. 
  They can also be formed by merging other projections in order to get the
  “best” of each.

Projection Distance, Area, and Shape

• Equal area projections preserve the property of
  area. On an equivalent projection all parts of the earth's surface are shown
  with the correct area. However, latitudinal distances are never accurate.

• Conformal projections preserve right angles
  between lines of latitude and longitude and are primarily used because they
  preserve direction. Area is always distorted on conformal maps. Because of
  GIS’s emphasis on cartographic shapes, GIS systems often use conformal
  projections.

• Some projections only preserve correct distance
  relationships along a few lines on the map. For example, an Equidistant
  azimuthal projection has the distance to the outside
  of the map portrayed correctly. These are seldom used in GIS.

• A final category is compromise maps. They may be
  the average of two or more projections or interrupted or broken in order to
  minimize certain distortions.

Common GIS Projections

• Mercator- A conformal,
  cylindrical projection tangent to the equator. 
  Originally created to display accurate
  compass bearings for sea travel. An additional feature of this projection is
  that all local shapes are accurate and clearly defined.

• Transverse Mercator - Similar to the Mercator
  except that the cylinder is tangent along a meridian instead of the equator. The
  result is a conformal projection that minimizes distortion along a north-south
  line, but does not maintain true directions.

• Universal Transverse Mercator (UTM) – Based on a Transverse Mercator
  projection centered in the middle of zones that are 6 degrees in longitude
  wide.  These zones have been created
  throughout the world.

• Lambert Conformal
  Conic – A conic, confromal projection typically
  intersecting parallels of latitude, standard parallels, in the northern
  hemisphere.  This projection is one of
  the best for middle latitudes because distortion is lowest in the band between
  the standard parallels. It is similar to the Albers Conic Equal Area projection
  except that the Lambert Conformal Conic projection portrays shape more
  accurately than area.

• State Plane – A
  standard set of projections for the

  United States

  • based on either the Lambert Conformal Conic or
    transverse mercator
    projection, depending on the orientation of each state.  Large states commonly require several state
    plane zones.

• Lambert Equal Area - An equidistant, conic
  projection similar to the Lambert Conformal Conic that preserves areas.

• Albers Equal Area
  Conic - This conic projection uses two standard parallels to reduce some of the
  distortion of a projection with one standard parallel. Shape and linear scale
  distortion are minimized between standard parallels.

2. Coordinate Systems

General.

As described under map projections, traditional coordinate
systems are based on a flat coordinate system. They are almost always a
positive quadrant coordinate system, and are easier to develop and use over a
small area. Recently, with improvements in computer processing capabilities,
GIS and GPS systems are migrating toward using the spherical coordinate system
of longitude and latitude.

State Plane Coordinate System (SPCS).

• The SPCS is primarily used in engineering
  applications by utility companies and local governments for doing accurate
  surveys. The SPCS is based on Transverse Mercator or
  Lambert Conformal conic projections with units in feet. States that elongate
  north to south normally use the Lambert Conformal. Those that are elongated
  east to west normally use the Transverse Mercator.

• Every State has at least one SPCS zone, some as many
  as five. Because they are so localized and tailored for the specific geographic
  area, distortion is very small.

• Nebraskahas two zones. There are between 100 and 150 zones in the US.

• Each zone is based on origins identified by each
  state. Each zone will have its on origin identified by some given number west
  and south of the south-western-most corner of the map. This means that
  positional numbers from the origin are expressed in positive terms. Normally
  locations are expressed in feet east and north of the origin. This can become
  difficult when areas may need to be identified across two zones.

• SPCS is identified on US Quadrangle maps by
  black graticule marks.

Universal Transverse Mercator
(UTM).

• The UTM coordinate system is commonly used in
  GIS for larger scale areas within a certain UTM zone. The UTM projection is
  formed by using a transverse cylindrical projection, i.e., the standard line
  runs along a meridian of longitude. The effect is to minimize distortion in a
  narrow strip running pole to pole.

• UTM divides the earth into pole-to-pole zones 6
  degrees of longitude wide. The first zone starts at the International Date Line
  (180 degrees east) and the last zone, 60, starts at 174 degrees east. Northings are determined separately for the areas north and
  south of the equator. Because distortion becomes extreme at northern latitudes,
  UTM is not normally used above 80 degrees North or South.

United States Public Land Survey System.

The US Public Land Survey System is a grid
system based on a set of selected meridians, termed "principal
meridians," and parallels, called "baselines." Distances are
measured in the four cardinal directions from the initial point and are formed
into townships, ranges, and sections. This system is primarily used for legal
land description west of Ohio.

3. GIS Capabilities

Basic Concepts.

All GIS systems must be capable of converting projections
and converting coordinates. This involves a lot of computer programming and
computational power. At a minimum, a GIS must be able to convert digitized
coordinates to latitude and longitude and reproject
them on to a flat surface.

Selecting the proper projection.

In order to select the correct projection to use, we must analyze the object
of our project. A projection should be selected which has a standard line which
is centered on the area of focus. You must also determine if correct depiction
of area, angle relationships, or distance accuracy is important. Distance may
be especially difficult if correct depiction is required over a large area.

4. Questions for Map Projections, Coordinate Systems, and GIS Capabilities

1. Describe the difference between a sphere and spheriod.
2. Describe the four basic types of projections. When is
   each type normally used?
3. Name an example of a conformal, equal area, and
   compromise map.
4. Describe the State Plane Coordinate System using Nebraska
   as an example.
5. Why is the UTM system not used North or South of 80
   degrees latitude?
6. Explain the key elements in selecting a projection to
   use in a GIS project.

Submitted by Dave Gay on
16 February 98.

Updated by Paul Woodward on December 6, 2004