User manual MATLAB MAPPING TOOLBOX 3

[. . . ] Mapping ToolboxTM 3 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Mapping ToolboxTM User's Guide © COPYRIGHT 1997­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] This is not the case for the skew-oblique aspect; however, scale is true along the paths of the transformed parallels and meridian. 8-17 8 Using Map Projections and Coordinate Systems Projection Parameters Every projection has at least one parameter that controls how it transforms geographic coordinates into planar coordinates. Some projections are rather fixed, and aside from the orientation vector and nominal scale factor, have no parameters that the user should vary, as to do so would violate the definition of the projection. For example, the Robinson projection has one standard parallel that is fixed by definition at 38º North and South; the Cassini and Wetch projections cannot be constructed in other than Normal aspect. In general, however, projections have several variable parameters. The following section discusses map projection parameters and provides guidance for setting them. Projection Characteristics Maps Can Have In addition to the name of the projection itself, the parameters that a map projection can have are · Aspect -- Orientation of the projection on the display surface · Center or Origin -- Latitude and longitude of the midpoint of the display · Scale Factor -- Ratio of distance on the map to distance on the ground · Standard Parallel(s) -- Chosen latitude(s) where scale distortion is zero · False Northing -- Planar offset for coordinates on the vertical map axis · False Easting -- Planar offset for coordinates on the horizontal map axis · Zone -- Designated latitude-longitude quadrangle used to systematically partition the planet for certain classes of projections While not all projections require all these parameters, there will always be a projection aspect, origin, and scale. Other parameters are associated with the graphic expression of a projection, but do not define its mathematical outcome. These include · Map latitude and longitude limits · Frame latitude and longitude limits 8-18 Projection Parameters However, as certain projections are unable to map an entire planet, or become very distorted over large regions, these limits are sometimes a necessary part of setting up a projection. Determining Projection Parameters In the following exercise, you define a map axes and examine default parameters for a cylindrical, a conic, and an azimuthal projection. 1 Set up a default Mercator projection (which is cylindrical) and pass its handle to the getm function to query projection parameters: figure; h=axesm('Mapprojection', 'mercator', 'Grid', 'on', 'Frame', 'on', . . . 'MlabelParallel', 0, 'PlabelMeridian', 0, 'mlabellocation', 60, . . . 'meridianlabel', 'on', 'parallellabel', 'on') The graticule and frame for the default map projection are shown below. 75 N ° 60 N ° 180° W 120° W 60° W 45 N 30° N 15° N 0°° 0 15° S ° 30 S ° 45 S 60 S 75° S ° ° 60° E 120° E 180° E 8-19 8 Using Map Projections and Coordinate Systems 2 Query the map axes handle using getm to inspect the properties that pertain to map projection parameters. The principal ones are aspect, origin, scalefactor, nparallels, mapparallels, falsenorthing, falseeasting, zone, maplatlimit, maplonlimit, rlatlimit, and flonlimit: getm(h, 'aspect') ans = normal getm(h, 'origin') ans = 0 0 0 getm(h, 'scalefactor') ans = 1 getm(h, 'nparallels') ans = 1 getm(h, 'mapparallels') ans = 0 getm(h, 'falsenorthing') ans = 0 getm(h, 'falseeasting') ans = 0 8-20 Projection Parameters getm(h, 'zone') ans = [] getm(h, 'maplatlimit') ans = -86 86 getm(h, 'maplonlimit') ans = -180 180 getm(h, 'Flatlimit') ans = -86 86 getm(h, 'Flonlimit') ans = -180 180 For more information on these and other map axes properties, see the reference page for axesm. 3 Reset the projection type to equal-area conic ('eqaconic'). The figure is redrawn to reflect the change. Determine the parameters that the toolbox changes in response: setm(h, 'Mapprojection', 'eqaconic') getm(h, 'aspect') ans = normal getm(h, 'origin') 8-21 8 Using Map Projections and Coordinate Systems ans = 0 0 0 getm(h, 'scalefactor') ans = 1 getm(h, 'nparallels') ans = 2 getm(h, 'mapparallels') ans = 15 75 getm(h, 'falsenorthing') ans = 0 getm(h, 'falseeasting') ans = 0 getm(h, 'zone') ans = [] getm(h, 'maplatlimit') ans = -86 86 getm(h, 'maplonlimit') 8-22 Projection Parameters ans = -135 135 getm(h, 'Flatlimit') ans = -86 86 getm(h, 'Flonlimit') ans = -135 135 The eqaconic projection has two standard parallels, at 15º and 75º. It also has reduced longitude limits (covering 270º rather than 360º). The resulting eqaconic graticule is shown below. 4 Now set the projection type to Stereographic ('stereo') and examine the same properties as you did for the previous projections: setm(h, 'Mapprojection', 'stereo') setm(gca, 'MLabelParallel', 0, 'PLabelMeridian', 0) getm(h, 'aspect') ans = normal 8-23 8 Using Map Projections and Coordinate Systems getm(h, 'origin') ans = 0 0 0 getm(h, 'scalefactor') ans = 1 getm(h, 'nparallels') ans = 0 getm(h, 'mapparallels') ans = [] getm(h, 'falsenorthing') ans = 0 getm(h, 'falseeasting') ans = 0 getm(h, 'zone') ans = [] getm(h, 'maplatlimit') ans = -90 90 8-24 Projection Parameters getm(h, 'maplonlimit') ans = -180 180 getm(h, 'Flatlimit') ans = -Inf 90 getm(h, 'Flonlimit') ans = -180 180 The stereographic projection, being azimuthal, does not have standard parallels, so none are indicated. The map limits do not change from the previous projection. The map figure is shown below. 8-25 8 Using Map Projections and Coordinate Systems Chapter 11, "Map Projections Reference" (available online and in the PDF version of this document) lists and illustrates all supported Mapping Toolbox map projections, including suggestions for parameter usage. 8-26 Visualizing and Quantifying Projection Distortions Visualizing and Quantifying Projection Distortions In this section. . . "Displays of Spatial Error in Maps" on page 8-27 "Quantifying Map Distortions at Point Locations" on page 8-31 Displays of Spatial Error in Maps Because no projection can preserve all directional and nondirectional geographic characteristics, it is useful to be able to estimate the degree of error in direction, area, and scale for a particular projection type and parameters used. Several Mapping Toolbox functions display projection distortions, and one computes distortion metrics for specified locations. A standard method of visualizing the distortions introduced by the map projection is to display small circles at regular intervals across the globe. After projection, the small circles appear as ellipses of various sizes, elongations, and orientations. The sizes and shapes of the ellipses reflect the projection distortions. Conformal projections have circular ellipses, while equal-area projections have ellipses of the same area. [. . . ] See rhumb lines ltln2val example 2-46 M makesymbolspec setting patch colors 6-8 map definition 2-2 map axes accessing default property values 4-16 accessing properties 4-14 Cartesian data and 4-45 changing projection of 4-46 example of properties 4-15 inset maps 6-2 resetting to default properties 4-35 setting properties 4-14 use of userdata 4-3 map display 3-D globes 12-63 map frame adjusting for a new projection 4-34 controlling appearance 4-53 defined 4-48 full-world 4-48 resetting altitude 4-54 setting limits 4-48 map grid controlling appearance 4-55 defined 4-55 displaying 4-55 resetting altitude 4-56 map legend deprecated term 2-39 . See referencing vector map limits adjusting for a new projection 4-34 setting 4-53 map objects mobjects GUI 4-83 map origin 8-10 See also orientation vectors map projections 2-D vs. 3-D 5-49 area 8-4 azimuthal 8-8 base 8-16 changing with geoshow 4-42 choosing 8-63 classifying distortion 8-3 computations 8-37 conformality 8-3 conic 8-7 cylindrical 8-5 defined 8-2 developable surface 8-3 distance 8-3 equidistance 8-3 equivalence 8-4 general properties 3-29 polyconic 8-7 pseudocylindrical projection examples 8-6 shape 8-3 switching with setm 4-34 table of properties 8-63 vectors 8-43 visualizing distortions 8-27 map scale between axes 6-2 when printing 6-38 map viewer using 1-9 mapped objects manipulating by name 4-83 Index-8 Index reprojecting 4-39 Mapping Toolbox help for 1-26 mapprofile Mercator, Gerardus 12-93 Equidistant Conic projection 12-49 12-52 MeridianLabel example 7-42 maps printing 6-38 mapstructs for polygons 2-30 maptriml use of 4-58 meridians controlling display 4-55 defined 3-12 meshgrat discussion 7-22 maptrimp 3-D example 4-74 example 2-55 use of 4-73 meshlsrm discussion 7-22 mapview coloring and shading terrain maps 5-33 miller 12-95 example 1-9 Marinus of Tyre 12-105 Equidistant Cylindrical projection 12-53 McBryde, F. Webster and McBryde-Thomas Flat-Polar Parabolic projection 12-87 and McBryde-Thomas Flat-Polar Quartic projection 12-89 and McBryde-Thomas Flat-Polar Sinusoidal projection 12-91 McBryde-Thomas Flat-Polar Parabolic projection 12-87 McBryde-Thomas Flat-Polar Quartic projection 12-89 McBryde-Thomas Flat-Polar Sinusoidal projection 12-91 mean geographic location example 10-2 meanm Miller Cylindrical projection 12-95 and Mercator projection 12-95 Miller, Osborn Maitland 12-95 minaxis example 3-6 MLineException usage 4-57 MLineLimit usage 4-57 modsine 12-121 mollweid 12-97 example 10-4 mercator 12-93 Mercator Equal-Area projection 12-117 Mercator projection 12-93 bearings on 10-13 in navigational tracking 10-29 transverse aspect 8-16 Mollweide projection 12-97 and Goode Homolosine projection 12-97 and Sinusoidal projection 12-97 Mollweide, Carl B. [. . . ]