Location Reference Systems GTECH 201 Lecture 06 Flattening

Location Reference Systems GTECH 201 Lecture 06

Flattening the Earth

Historical Projections n Marinus n Ptolemy n Mercator

Distortions n Shape n Area n Distance n Direction

Preserving Properties n n If two properties are to be preserved then one is always direction These properties are incompatible:

Shape Property n n Conformal Non-conformal

Area Property

Distance Property

Direction Property

Direction Property n Mercator with rhumb line or loxodrome n Azimuthal map with shortest distance

Tissot Indicatrices

Distortions n Mercator n Sinusoidal n Equal-area cylindrical n Robinson

Cylindrical Projections

Conic Projections

Planar Projections

Refining Map Projections n n Transverse Mercator Albers equal area conic n n Lambert conformal conic Lambert azimuthal equal area

Equatorial (normal) Aspect

Transverse Aspect

Oblique Aspect

Aspects for Planar Projections n Polar Gnomic Stereographic Orthographic

Aspects for Planar Projections n Equatorial Aspect Gnomic Stereographic Orthographic

Aspects for Planar Projections n Oblique Aspect Gnomic Stereographic Orthographic

Aspects for Conic Projections n Normal aspect

Polyconic Projection n Hassler, 1820 s US Coastal Survey

Perspective n Position of the light source

Perspectives

Other Perspective Projections Lambert cylindrical equal area

Classifying Projections n Cylindrical and pseudo-cylindrical

Classifying Projections n Conic and pseudo-conic

Classifying Projections n Planar and modified planar

Classifying Projections

Classifying Projections Cylindrical straight parallels; straight meridians Pseudo-cylindrical straight parallels, curved meridians Conic partial concentric circles for parallels; straight meridians Pseudo-conic Planar Modified planar partial concentric circles for parallels; curved meridians Concentric circles for parallels; straight meridians No common appearance of parallels and meridians

Projections Parameters n Angular parameters n n n Central meridian Latitude of origin Standard parallel Latitude of center Central parallel n Linear parameters n n n False easting False northing Scale factor

Origin of X, Y Coordinates

Central Parallel

False Easting/northing

Scale n Mercator n UTM

Choosing a Map Projection n Conformal (shape-preserving) maps n n Topographic and cadastral Navigation Civil engineering Weather

Choosing a Map Projection n Area-preserving maps n n n Population density Land use Quantitative attributes

Choosing a Map Projection n Scale-preserving maps no map preserves true distance for all measurements n n n Airline distances Distance from epicenter of an earthquake Cost calculations

Rules of Thumb

Rules of Thumb

Rules of Thumb

Coordinate Systems n Two ways to identify a position on a plane

Coordinate Systems n . . and on a sphere

Geographic Coordinate Systems Latitude and longitude defined on a sphere

Geographic Coordinate Systems n Latitude defined on a spheroid (longitude is as on a sphere)

Components of a GCS n An angular unit of measure n A prime meridian n A datum, which includes a spheroid

Planar Coordinate Systems

Cartesian Coordinates n Calculate distance A-B

Universal Transverse Mercator n UTM zones

UTM Zones n . . as seen from the North Pole

UTM Projections n Each zone uses a custom Transverse Mercator projection with its own central meridian

Universal Polar Stereographic n Fills the holes of UTM in polar regions

State Plane Coordinate System

SPC n n N-S zones use Transverse Mercator E-W zones use Lambert Conformal Conic Maximal scale error is 1: 10, 000 NAD 27 or NAD 83 datum

Public Land Survey System PLS are shown in purple

PLS n n n It is used to locate areas, not points It is not rigorous enough for spatial analysis like the calculation of distance or direction It is not a grid imposed on a map projection (a system invented in a room), but lines measured on the ground by surveyors

PLS Meridians and Baselines

PLS Area Unit Hierarchy

PLS Township Sections A township is divided into 36 sections, each a square mile (640 acres) A section is divided into 160 -acre quarters, which can be further divided into halves, quarters, and so on