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Introduction to CartographyGEOG 2016 E

Lecture-3Scale, Reference and Coordinate

Systems

What is Scale

• Ratio between distances on a map and the corresponding distances on the earth’s surface.

• Example:– 1:100,000 means that 1 cm on the map

corresponds to 100,000 cm (or 1 km) on earth.– 1:50,000 means that 1 cm on the map

corresponds to 50,000 cm (or 0.5 km) on earth.

Scale and Features

• Showing features on a map depends on the scale chosen.

• The larger the scale of the map, the more details it shows.– A map with a scale of 1:10,000 will show a lot

more details than a map with a scale of 1:100,000.– The scale of 1:10,000 is larger than the scale of

1:100,000.

Scale and Features

• A map with a scale of 1:10,000 can be used to show individual houses or buildings.

• However, a map with a scale of 1:100,000 can show those houses or buildings only as points.

• Choosing the right scale is very important in cartography.

• The choice depends on the area to be covered and the features to be shown.

Reference Systems• A reference system is needed to locate a point

on earth’s surface.• Latitude and longitude comprise a reference

system.• A coordinate system is needed for referencing.

Coordinate Systems

• A coordinate system is needed for positioning and navigation.

• For example, global positioning systems use coordinate system for precise location of points in space.

• Different coordinate systems have been constructed and are used in cartography.

• Cartesian, polar and spherical are three most commonly used coordinate systems.

Cartesian Plane Coordinate System

• A plane or two-dimensional coordinate system can be defined with respect to a single plane.

Plane Polar Coordinate System• Points on a two-dimensional surface can also

be represented by radius-angle pairs.

Polar - Cartesian Conversion• Plane polar coordinates can be converted into

plane Cartesian coordinates.

Exercise

• Convert the following Cartesian coordinates into their polar equivalents:– (1.245, -2.769)– (0.673, 1.999)– (-9.999, 4.531)

• Convert the following polar coordinates into their Cartesian equivalents:– (1.296, 36.7)– (4.555, 0)– (6.782, 173.8)

ݔ = ݎ cosߠݕ = ݎ sinߠ

ݎ = ଶݔ + ଶݕ

ߠ = tanିଵݕݔ

Answers

• Cartesian to polar:– (1.245, -2.769) (3.04, -65.79) – (0.673, 1.999) (2.109, 71.39)– (-9.999, 4.531) (10.98, 155.6)

• Polar to Cartesian:– (1.296, 36.7) (1.039, 0.774)– (4.555, 0) (4.555, 0)– (6.782, 173.8) (-6.742, 0.732)

Three-Dimensional Cartesian System

Longitude, Latitude, Height• Most commonly used global coordinate

system in cartography• Reference planes for latitude and longitude

are defined by prime meridian and equator

Geodetic Latitude• Angle from the equatorial plane to vertical

direction of a line normal to the reference ellipsoid.

Geodetic Longitude• Angle between the reference plane and a plane

passing through the point. Both planes must be perpendicular to the equatorial plane.

Geodetic Height• Distance from the reference ellipsoid to the

point in the direction normal to the ellipsoid.

Earth-Centered Earth-Fixed X,Y,Z• Generally called ECEF XYZ• Three-dimensional Cartesian coordinate system• Centered at the center of mass of reference

ellipsoid

Universal Transverse Mercator (UTM)

• Recall that Mercator is a cylindrical projection.• UTM coordinates define two-dimensional

positions.• Dimensions are defined by zone numbers and

zone characters.– Zone numbers designate 6-degree longitudinal strips.

Extend from 80 degrees South latitude to 84 degrees North latitude

– Zone characters designate 8-degree zones. Extend North and South from equator.

UTM

World Geographic Reference System Index (GEOREF)

• Based on latitude and longitude• Earth’s sphere is divided into:

– 12 bands of latitude– 24 zones of longitude

• Used in aircraft navigation