Module II Map Projections

MAPS Definitions "A representation, usually on a plane surface, of all or part of the earth or some other body showing a group of features in terms of their relative size and position." Norman Thrower

MAPS Definitions A map is a selective, symbolized, generalized and planimetric picture of spatial distribution of the earths surface on a definite scale with annotations

Map Types It is not possible to represent all features of earth on maps, since they are numerous. Classification on the basis of Scale Usage

Map Types 1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps) 2.Topographic maps2.Topographic maps2.Topographic maps2.Topographic maps 3.Thematic maps3.Thematic maps3.Thematic maps3.Thematic maps 4.Remotely sensed images4.Remotely sensed images4.Remotely sensed images4.Remotely sensed images

Cadastral maps A map which provides detailed information about real property within a specific area Used to demarcate boundaries of fields and buildings and for registering ownership of landed properties Prepared and compiled by government agencies and used for revenue and tax purposes Examples. Village maps or city plan maps

Cadastral map

Topographic maps A topographic map is a detailed and accurate graphic representation of cultural and natural features on the ground. Shows the shape and elevation of the terrain Used for designing gardens, parks, buildings, roads and pipelines Examples. Flood control maps and engineering maps

Topographic map

Thematic maps A thematic map is a type of map or chart especially designed to show a particular theme connected with a specific geographic area. These maps "can portray physical, social, political, cultural, economic, sociological, agricultural, or any other aspects of a city, state, region, nation , or continent

Thematic map

Remotely sensed images These are geographic information gathered by means of a sensor which include aerial photographs, radar images and satellite images These are important sources for producing digital maps and are useful for monitoring environmental changes and human activities

Remotely sensed image

MAP PROJECTION

Geodesy and Map Projections Geodesy - the shape of the earth and definition of earth datums Map Projection - the transformation of a curved earth to a flat map Coordinate systems - (x,y) coordinate systems for map data

Coordinate System (o,o) (xo,yo) X Y Origin A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin

Map Projections Map projection: a system of parallels and meridians representing the Earths curved surface drawn on a flat surface Curved surface cannot be projected onto a flat sheet without distortion Each map projection has a specific purpose Each projection has advantages and drawbacks

MAPPROJECTIONSMAPPROJECTIONS Map projection is a systematic transformation of a spatial surface to a surface that is convenient to work with. A spherical co-ordinate system (like latitude and longitude) works well only if one is using a globe but not if one has to display the data on a flat surface like a map .

Latitude and Longitude on a Sphere Meridian of longitude Parallel of latitude X Y Z N EW =0-90S P O R =0-180E =0-90N Greenwich meridian =0 Equator =0 =0-180W - Geographic longitude - Geographic latitude R - Mean earth radius O - Geocenter

In practice map projections use mathematical formulae to convert from one coordinate system to the other. Where f and g are transformation functions for a particular projection. example relations for Mercator projection are: ( ) ( ) , , gy fx = = ,=x ( )4/2/tanln +=y

Geographic and Projected Coordinates (, ) (x, y) Map Projection

Transformation functionsTransformation functions 1.1. UniquenessUniqueness - The functions should be unique so that a point on the surface of earth will appear at only one position of the map. 2.2. FinitenessFiniteness The function should be finite so that a point will not appear at an infinite distance and hence remain unplotted. There are exceptions. 3.3. ContinuousContinuous There should not be gaps on the projected surface

Map Characteristics Map Scale: Map distance to Real distance- Expressed as a ratio or fraction The unit on the left indicates distance on the map and the number on the right indicates distance on the ground. Eg 1:1000, 1/100,000 Small-Scale , Medium-Scale and Large-Scale < 1 : 1,000,000 >1 : 75,000 Large scale maps have more details

Map scale Representing the Scale of a Map Bar Scale A bar scale shows a graphic representation, where the actual distance on the map is measured and compared it to the bar scale

Map scale (Contd) Representing the Scale of a Map Representative fraction gives a number scale represented by a fraction or a ratio

Map scale (Contd) Representing the Scale of a Map Textual scale describes the scale in words A representative fraction of 1:1,00,000 may be expressed as 1 cm on the map equals to 1 kilometer on the ground

Scale factor It is the ratio of the map distance to the globe distance Scale factor on a map is generally not constant for various points, thus scale of a map is not uniform for the entire map. This is in contrast to a plan which has a uniform scale.

Earth to Globe to Map Representative Fraction Globe distance Earth distance = Map Scale: Map Projection: Scale Factor Map distance Globe distance = (e.g. 1:24,000) (e.g. 0.9996)

Ideal Map Projection An ideal map projection is that in which there is no distortion and all the lines and angles are represented correctly. An ideal map projection should satisfy the following conditions 1.All distances and areas on the map should have correct relative magnitude as those on the surface of the earth. 2. All angles and azimuths on the map should be the same as those on the surface of the earth.

Ideal Map Projection (Contd) 3. All great circles on the earth should appear as straight lines on the map. 4. Longitudes and latitudes of all points should be shown correctly on the map. It is not possible to satisfy all these in the same map. Only one or two conditions are satisfied in a particular projection and selection for a particular purpose and area made according to suitability.