Teaching:TUW - UE InfoVis WS 2008/09 - Gruppe 08 - Aufgabe 1 - Contour Plot/Map: Difference between revisions

From InfoVis:Wiki
Jump to navigation Jump to search
mNo edit summary
(properties of contour lines, applications (former types) updated)
Line 3: Line 3:
{{Quotation|A '''contour plot''' (also '''contour map''') is a graphic representation of the relationships among three numeric variables in two dimensions. Two variables are for X and Y axes, and a third variable Z is for contour levels. The contour levels are plotted as curves (also lines); the area between curves can be color coded to indicate interpolated values.|[SAS, 2008]}}
{{Quotation|A '''contour plot''' (also '''contour map''') is a graphic representation of the relationships among three numeric variables in two dimensions. Two variables are for X and Y axes, and a third variable Z is for contour levels. The contour levels are plotted as curves (also lines); the area between curves can be color coded to indicate interpolated values.|[SAS, 2008]}}


{{Quotation|A '''contour line''' for a function of two variables is a curve connecting points where the function has a same particular value. ... The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone.|[AbAs, 2008]}}
{{Quotation|A '''contour line''' (also '''isoline''') for a function of two variables is a curve connecting points where the function has a same particular value. ... The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone.|[AbAs, 2008]}}


----
----


==Types of contour plots==
==Properties of contour lines==


Contour plots are used for a wide range of applications.
[[image:Contour_map.png|thumb|A contour map with contour lines.]]
 
* Isolines have to be closed. They can only end at the map edge. Therefore they must be somewhere outside of the viewing area to connect itself, but then again they are closed.
* They may not touch nor cross nor run into each other. If there is no possibility to avoid this cause of reasons of scale or pressure, they should interrupt at such a bottleneck.
* The continuity of the values shown by the presence of isolines is in no way modified or restricted. A contour line never shows an edge, a step or a bend.
* The gap value depends on the distance from the isolines: The closer the isolines are the more rapid the continuum changes.
* Between any pair of points, whose imaginary line doesn't lie parallel to the neighboring isolines, there is a difference of the represented value, whether between the two points runs a contour line or not.
* Widely spaced points, between which no isoline runs, have a greater value difference than closely spaced points, between which a Contour line is located.
* The locations of the lines are actually random in the sense that they depend on the attributed values.
 
----


===Meteorology===
==Applications==


[[image:Weather_map.jpg|thumb|The map shows the analysis of the weather condition. The isobars represent lines of constant barometric pressure.]]
[[image:Weather_map.jpg|thumb|The map shows the analysis of the weather condition. The isobars represent lines of constant barometric pressure.]]
[[Image:Bathymetry.jpg|thumb|Ocean bottom topography, also known as bathymetry, is the measurement of the depth of large bodies of water.]]
[[Image:Topographic_map.jpg|thumb|Topographic maps are maps that show topography, or land contours, by means of contour lines. Contour lines are curves that connect contiguous points of the same altitude.]]
Data that can be displayed by a contour map is found in many applications. Any piecewise continuous, single-valued function of two continuous independent variables can be represented in the form of a contour map.
===Meteorology===


Numerous weather stations measure different meteorological properties. The collected data just represent the local situation at the weather stations. Therefore contour lines are drawn to best approximate the locations of exact values, based on the scattered information points available.
Numerous weather stations measure different meteorological properties. The collected data just represent the local situation at the weather stations. Therefore contour lines are drawn to best approximate the locations of exact values, based on the scattered information points available.


Contour lines in meteorological maps:
Contour lines in meteorological maps (and types of isolines):
* '''Barometric pressure''' (isobar)
* '''Barometric pressure''' (isobar)
* '''Temperature''' (isotherm)
* '''Temperature''' (isotherm)
Line 26: Line 42:
=== Physical geography and oceanography ===
=== Physical geography and oceanography ===


* '''Elevation and depth''' (topographic maps, bathymetric maps) [[Image:Topographic_map.jpg|thumb]]
* '''Elevation and depth''' (topographic maps, bathymetric maps)
[[Image:Bathymetry.jpg|thumb|Ocean bottom topography, also known as bathymetry, is the measurement of the depth of large bodies of water.]]
* '''Magnetism'''
* '''Magnetism'''
* '''Oceanography'''
* '''Oceanography'''
Line 36: Line 51:
* '''Thermodynamics, engineering, and other sciences'''
* '''Thermodynamics, engineering, and other sciences'''
* '''Other phenomena'''
* '''Other phenomena'''
[[image:Contour_map.png|thumb|A contour map with contour lines.]]


----
----
Line 45: Line 58:
* [SAS, 2008] SAS OnlineDoc, SAS. Retrieved at: October 29, 2008. [http://support.sas.com/onlinedoc/913/getDoc/de/sgug.hlp/ctr_index.htm http://support.sas.com/onlinedoc/913/getDoc/de/sgug.hlp/ctr_index.htm]
* [SAS, 2008] SAS OnlineDoc, SAS. Retrieved at: October 29, 2008. [http://support.sas.com/onlinedoc/913/getDoc/de/sgug.hlp/ctr_index.htm http://support.sas.com/onlinedoc/913/getDoc/de/sgug.hlp/ctr_index.htm]
* [AbAs, 2008] Absolute Astronomy. Retrieved at: October 31, 2008. [http://www.absoluteastronomy.com/ http://www.absoluteastronomy.com/]
* [AbAs, 2008] Absolute Astronomy. Retrieved at: October 31, 2008. [http://www.absoluteastronomy.com/ http://www.absoluteastronomy.com/]
* [Wiki, 2008] Contour line, Wikipedia. Retrieved at: October 30, 2008. [http://en.wikipedia.org/wiki/Contour_map http://en.wikipedia.org/wiki/Contour_map]
* [Wakonigg, 2001] Herwig Wakonigg, Struktur und Wesen von Isolinienkarten. Institut für Geographie und Raumforschung. Created at: October 1, 2001. Retrieved at: November 6, 2008. [http://www.uni-graz.at/geowww/geo/geoweb_magazin_artikel_detail.php?recordID=54 http://www.uni-graz.at/geowww/geo/geoweb_magazin_artikel_detail.php?recordID=54]
* [Morse, 1969] Stephen P. Morse. Concepts of Use in Contour Map Processing. ''Communications of the ACM'', 12(3):147-152, March 1969
* [Wikipedia, 2008] Contour line, Wikipedia. Retrieved at: October 30, 2008. [http://en.wikipedia.org/wiki/Contour_map http://en.wikipedia.org/wiki/Contour_map]


----
----

Revision as of 12:49, 6 November 2008

Definitions

A contour plot (also contour map) is a graphic representation of the relationships among three numeric variables in two dimensions. Two variables are for X and Y axes, and a third variable Z is for contour levels. The contour levels are plotted as curves (also lines); the area between curves can be color coded to indicate interpolated values.
[SAS, 2008]


A contour line (also isoline) for a function of two variables is a curve connecting points where the function has a same particular value. ... The gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone.
[AbAs, 2008]


Properties of contour lines

A contour map with contour lines.
  • Isolines have to be closed. They can only end at the map edge. Therefore they must be somewhere outside of the viewing area to connect itself, but then again they are closed.
  • They may not touch nor cross nor run into each other. If there is no possibility to avoid this cause of reasons of scale or pressure, they should interrupt at such a bottleneck.
  • The continuity of the values shown by the presence of isolines is in no way modified or restricted. A contour line never shows an edge, a step or a bend.
  • The gap value depends on the distance from the isolines: The closer the isolines are the more rapid the continuum changes.
  • Between any pair of points, whose imaginary line doesn't lie parallel to the neighboring isolines, there is a difference of the represented value, whether between the two points runs a contour line or not.
  • Widely spaced points, between which no isoline runs, have a greater value difference than closely spaced points, between which a Contour line is located.
  • The locations of the lines are actually random in the sense that they depend on the attributed values.

Applications

The map shows the analysis of the weather condition. The isobars represent lines of constant barometric pressure.
Ocean bottom topography, also known as bathymetry, is the measurement of the depth of large bodies of water.
Topographic maps are maps that show topography, or land contours, by means of contour lines. Contour lines are curves that connect contiguous points of the same altitude.

Data that can be displayed by a contour map is found in many applications. Any piecewise continuous, single-valued function of two continuous independent variables can be represented in the form of a contour map.

Meteorology

Numerous weather stations measure different meteorological properties. The collected data just represent the local situation at the weather stations. Therefore contour lines are drawn to best approximate the locations of exact values, based on the scattered information points available.

Contour lines in meteorological maps (and types of isolines):

  • Barometric pressure (isobar)
  • Temperature (isotherm)
  • Precipitation and air moisture (isohyet and isohume)
  • Wind speed and direction (isotach and isogon)
  • Freeze and thaw (isotac)

Physical geography and oceanography

  • Elevation and depth (topographic maps, bathymetric maps)
  • Magnetism
  • Oceanography

Environmental science

  • Social sciences
  • Thermodynamics, engineering, and other sciences
  • Other phenomena

References

External links

Retrieved from "https://infovis-wiki.net/w/index.php?title=Teaching:TUW_-_UE_InfoVis_WS_2008/09_-_Gruppe_08_-_Aufgabe_1_-_Contour_Plot/Map&oldid=20018"