RASTER ENCODING METHODS
Step 2: Eliminate unwanted units by multiplication
Example: One inch = two miles. Convert it into RF scale.
Solution: 1 mile = 52,800 ft
= 2 miles × (52,800 ft/1 mile) = 105,600 ft
1 ft = 12 inches
105,600 ft = 12 inches × (105,600 ft/1 ft) Figure 2.7 A scale bar
= 1,267,200 inches 1 inch = 1,267,200 inches
= 1:1,267,200
• Representative fraction to verbal scale: RF to verbal scale conversion is an easier process. A verbal scale may have same or different units on both sides of the mathematical expression. Both 1 cm = 10 miles and 1 cm = 10 cm are correct for a verbal scale representation. RF uses only one unit for representation.
Example: 1:65,000. Convert it into a verbal scale
Solution: As RF uses only one unit for representation, let it be in cm.
Hence, verbal scale is 1 cm = 65,000 cm
= 65 km on ground
Large Scale and Small Scale
A large scale represents a small area in great detail. A map that depicts small territories in great detail is called a large-scale map. A small scale represents large features. A map depicting a large area, such as a country, is called a small-scale map. Small-scale maps show more territory but are less detailed. To understand the difference between large scale and small scale, let us consider the following two representations with the ratio method.
1. The ratio 1:25,000 means that the size of objects on the map is 1/25,000 of their size on the ground. For example, 1 cm on a map is equal to 25,000 cm or 25 km on the earth’s surface.
2. The ratio 1:250,000 means that the size of objects on the map is 1/250,000 of their size on the ground.
It is now clear from the aforementioned representations that 1/25,000 is a larger fraction than 1/250,000 (same as half a mango is a larger than one-eighth of a mango). Hence, 1/25,000 represents a large-scale map.
Therefore, large-scale maps show a small territory in greater detail, and they are guide maps or topo graphic maps that show details of cities, towns, and villages. On the other hand, small-scale maps show a larger area in less detail (Figure 2.8). They are wall maps or atlas maps that show important features such as mountains, plateaus, con tinents, and countries.
Types of Maps
A map helps to represent real-world scenarios. Based on the purpose, there are different types of maps: thematic maps, topographic maps, and general-purpose maps.
Thematic maps
Thematic maps are used to depict information about a particular topic or theme. The information depicted on a thematic map may be substantial, statistical, and precise. Sometimes, the map user requires domain-specific knowledge to read the map. Population maps, forest coverage maps, and maps showing the watershed of a river are different types of thematic maps (Figure 2.9). Thematic map’s data have to be accurate. There are various ways to use the data, and each way must be considered with the map’s theme. The sources of a thematic map’s data are also important and should be carefully considered. Cartographers must find accurate, recent, and reliable sources of information in a wide range of subjects—from environmental features to demographic data—to make the best possible maps.
Topographic maps
Topographic maps are used to depict extensive graphical details of objects present on the earth’s surface providing preliminary information about terrain details (Figure 2.10). They use a wide variety of symbols to represent human and physical features. Among the most striking features of topographic maps are contour lines, which are used to represent elevation by connecting points of equal elevation. These imaginary lines nicely represent a terrain.
Figure 2.8 Large- and small-scale maps
Figure 2.10 Geologic map of the Mexico Valley Basin Source <http://grass.osgeo.org/screenshots/cartography>
Figure 2.9 A thematic map
General-purpose maps
General-purpose maps show a variety of information about a place. These maps are used to represent almost all physical features at a location and summarize the properties of the landscape, for example, a city map or a street map. They are a conglomerate of all the characteristics that depict the presence of all objects in a particular location. When cartography was in its infancy, almost all maps were general-purpose maps. These maps were also called reference maps. They represent both natural and human-made features such as coastlines, lakes, rivers, boundaries, settlements, roads, rail lines, and others (Figure 2.11). General-purpose maps focus on location. Wall maps, most maps found in atlases, and road maps are of this category.
Maps are two-dimensional representations of the earth’s surface;
therefore, location is another important aspect of maps. Primarily, location is the place of an object, which may be physical or abstract, or a phenomenon on the earth’s surface. A huge amount of information is associated with place. Name, geographical attributes, statistical variables such as population or density, physical attributes, and many other information sets can be linked to a place. Usually, the phenomena that affect places are comparatively slow; hence, they are considered static, while place is a dynamic identity. It is difficult to represent changes such as erosion of soil, changes in population density or vegetation pattern of any place over time; however, it is not wise to avoid such information from our representation. Location on any map also gives the idea of
Figure 2.11 Ageneral-purpose map
distance and direction. Hence, it is an essential requirement to address the formal definition of location, which can be mathematically defined and manipulated. A coordinate system is a reference system that uses coordinates (set of values that show the exact position of an object along and up or down the defined origin) to define the unique position of an object on the earth’s surface.
A coordinate system is a mathematical system used to define and analyse spatial objects geometrically. It is easier to numerically determine the relationships and properties of a set of points with known coordinates. The most familiar spaces are planes and three-dimensional spaces where a point P is determined by (x, y) and (x, y, z) coordinates, respectively. Every coordinate system is defined by its origin (datum, meridian), units (for example, metre, radian), and coordinate axes (for example, x, y, z). The common types of coordinate systems used in GIS are as follows.
1. Two-dimensional coordinate system: In a two-dimensional coordinate system, the location of a point is given by coordinates that represent the point’s distance from two perpendicular lines intersecting at the origin (Figure 2.12). There are four subcategories of a two-dimensional coordinate system.
Plane Cartesian system—x-axis and y-axis
Polar coordinates—r, q(theta)
Raster grid—easting, northing
Map projection
Figure 2.12 A coordinate system
Note O is the origin of the reference system. The point at (12, 5) is 12 units along the x-axis and 5 units along the y-axis.
A projected coordinate system is based on map projections and designed for a flat surface. A mathematical transformation is carried out to convert spherical coordinates on a globe to the planar coordinates on a flat surface.
2. Three-dimensional coordinate system: In a three-dimensional coordinate system, the location of a point is given by three real values (coordinates) that represent the point’s distance from perpendicular projections on fixed perpendicular lines, called axes, intersecting at the origin. The common three-dimensional coordinate systems used in GIS are as follows.
Three-dimensional Cartesian coordinates
Geographical coordinate system (latitude and longitude)
A geographical coordinate system (GCS) uses three-dimensional spherical surfaces to define the location on the earth’s surface. A GCS uses a datum, an angular unit of measure, and a meridian to define the locations. A point on the earth’s surface is referenced by its lat–long values. Latitude and longitude are the angles measured, usually in degree or grad, from the earth’s centre to the point on the earth’s surface.
These are global or specific coordinate systems.
A coordinate system, either GCS or projected, provides a framework to define the location on the earth’s surface. All spatial information must be referenced by a coordinate system having an associated coordinate value.