Projections and Coordinates
description
Transcript of Projections and Coordinates
![Page 1: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/1.jpg)
Projections and Coordinates
![Page 2: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/2.jpg)
Vital Resources
• John P. Snyder, 1987, Map Projections – A Working Manual, USGS Professional Paper 1395
• To deal with the mathematics of map projections, you need to know trigonometry, logarithms, and radian angle measure
• Advanced projection methods involve calculus
![Page 3: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/3.jpg)
Shape of the World
• The earth is flattened along its polar axis by 1/298
• We approximate the shape of the earth as an ellipsoid
• Ellipsoid used for a given map is called a datum
• Ideal sea-level shape of world is called the geoid
![Page 4: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/4.jpg)
Shape of the World• Earth with topography• Geoid: Ideal sea-level shape of the earth– Eliminate topography but keep the gravity– Gravity is what determines orbits and leveling of
survey instruments– How do we know where the sea would be at some
point inland?• Datum: Ellipsoid that best fits the geoid• Sphere: Globes and simple projections
![Page 5: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/5.jpg)
The Datum
![Page 6: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/6.jpg)
Datums• In mapping, datums is the plural (bad Latin)• Regional datums are used to fit the regional
curve of the earth– May not be useful for whole earth
• Obsolete datums often needed to work with older maps or maintain continuity
![Page 7: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/7.jpg)
Regional Datum
![Page 8: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/8.jpg)
The Geoid
![Page 9: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/9.jpg)
Distortion• You cannot project a curved earth onto a flat
surface without distortion• You can project the earth so that certain
properties are projected without distortion– Local shapes and angles– Distance along selected directions– Direction from a central point– Area
• A property projected without distortion is preserved
![Page 10: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/10.jpg)
Preservation
• Local Shape or Angles: Conformal• Direction from central point: Azimuthal• Area: Equal Area• The price you pay is distortion of other
quantities• Compromise projections don’t preserve any
quantities exactly but they present several reasonably well
![Page 11: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/11.jpg)
Projections• Very few map “projections” are true projections
that can be made by shining a light through a globe (Mercator is not)
• Projection = Mathematical transformation• Many projections approximate earth with a
surface that can be flattened– Plane– Cone– Cylinder
• Complex projections not based on simple surfaces
![Page 12: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/12.jpg)
Choice of Projections
• For small areas almost all projections are pretty accurate
• Principal issues– Optimizing accuracy for legal uses– Fitting sheets for larger coverage
• Many projections are suitable only for global use
![Page 13: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/13.jpg)
Projection Surfaces
![Page 14: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/14.jpg)
Simple Projection Methods
![Page 15: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/15.jpg)
Orthographic Projection
![Page 16: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/16.jpg)
Gnomonic
![Page 17: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/17.jpg)
Butterfly Projection
![Page 18: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/18.jpg)
Dymaxion Projection
![Page 19: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/19.jpg)
Azimuthal Equal Area
![Page 20: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/20.jpg)
Azimuthal Equal Area
![Page 21: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/21.jpg)
Azimuthal Equidistant
![Page 22: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/22.jpg)
Stereographic
![Page 23: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/23.jpg)
Equirectangular (Geographic)
![Page 24: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/24.jpg)
Equirectangular Projection
![Page 25: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/25.jpg)
Mercator
![Page 26: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/26.jpg)
Transverse Mercator
![Page 27: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/27.jpg)
Oblique Mercator
![Page 28: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/28.jpg)
Lambert Equal Area Cylindrical
![Page 29: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/29.jpg)
Peters Projection
![Page 30: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/30.jpg)
Ptolemy’s Conic
![Page 31: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/31.jpg)
Lambert Conformal Conic
![Page 32: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/32.jpg)
Albers Equal Area Conic
![Page 33: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/33.jpg)
Polyconic Projection
![Page 34: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/34.jpg)
Bipolar Oblique Conic
![Page 35: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/35.jpg)
Mollweide
![Page 36: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/36.jpg)
Aitoff Projection
![Page 37: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/37.jpg)
Sinusoidal
![Page 38: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/38.jpg)
Robinson
![Page 39: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/39.jpg)
Mollweide Interrupted
![Page 40: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/40.jpg)
Mollweide Interrupted
![Page 41: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/41.jpg)
Homolosine Projection
![Page 42: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/42.jpg)
Van der Grinten
![Page 43: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/43.jpg)
Bonne
![Page 44: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/44.jpg)
Specialized Projection
![Page 45: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/45.jpg)
Specialized Projection
![Page 46: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/46.jpg)
Transverse Mercator Projection
![Page 47: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/47.jpg)
UTM Zones
![Page 48: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/48.jpg)
UTM Pole to Pole
![Page 49: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/49.jpg)
Halfway to the Pole
![Page 50: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/50.jpg)
USA Congressional Surveys
![Page 51: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/51.jpg)
Grid vs. No Grid
![Page 52: Projections and Coordinates](https://reader035.fdocuments.us/reader035/viewer/2022062501/568167f0550346895ddd5ff6/html5/thumbnails/52.jpg)
Wisconsin Grid
Systems