Map

Antiquity to 14th century

It is unknown when or where humans created the first maps. Their appearance in the records of numerous ancient cultures suggests that mapmaking originated in prehistory.^[32] One of the earliest preserved maps is inscribed on a clay tablet, dated to 2300 BCE, and found in Nuzi, within the Akkadian Empire (in modern Iraq).^[33][h] Egyptian maps on papyrus from 1300 BCE show the location of gold mines.^[35] A document from China dated 1020 BCE describes maps used for town planning.^[36] Early Chinese maps that are still preserved include one from the 4th century BCE engraved on a large bronze sheet, showing the location of five mausoleums,^[37] and a set of maps drawn on silk from the 2nd century BCE, which showed more sophistication than contemporary maps originating in Europe.^[38]

Around 490 BCE, Greek geographer Hecataeus created a map of his known world, encompassing the Mediterranean Sea and most of Europe, North Africa, and the Middle East.^[39][i] One of the most influential early maps was a world map prepared around 150 CE by the Greco-Roman geographer and scientist Ptolemy.^[30][g] Maps created by the Romans – in contrast to the Greek emphasis on science – were used for political and administrative purposes: in 44 BCE Julius Caesar commissioned a map of the known world, which was prepared by Agrippa.^[42] The Romans also produced the Tabula Peutingeriana, which diagrammed most major roads of their empire. Like many modern transit maps, it is schematic in nature and is not drawn to scale.^[43][j]

A notable set of maps from the Islamic world was the Nuzhat al-Mushtaq ('The Book of Pleasant Journeys into Faraway Lands')^[k] – an atlas created in 1154 by Muhammad al-Idrisi, an Arab geographer, at the request of Norman King Roger II.^[31][l] Within medieval Europe, a large number of mappae mundi ('maps of the world') were created^[46] and – as Christianity dominated medieval European society – many incorporated religious themes.^[47][m] Scholars refer to some of the mappae mundi as T-O maps because they depicted the Earth as an "O" shape, containing three continents (Europe, Asia, and Africa) separated by waters in a "T" shape.^[49][n]

15th to 19th centuries

Maps played a major role in the Age of Discovery.^[51] On his first voyage in 1492, Christopher Columbus carried a world map created by Paolo dal Pozzo Toscanelli. The map did not include the Americas and greatly underestimated the distance from Europe westward to Asia.^[52] That year, Martin Behaim created the Erdapfel (lit. 'Earth apple') – one of the earliest extant globes.^[53]

In the 16th century, map accuracy^[o] improved with the development of triangulation (initially described by Gemma Frisius in 1533), which advanced surveying techniques by using devices such as plane tables and theodolites to precisely measure angles between lines of sight to landmarks.^[54][p] During this era, cartographers also advanced the study of map projections; notably Gerardus Mercator, who created the Mercator projection in 1569, which proved valuable to navigators because it allowed them to draw a straight line on the map pointing to their destination and reach it by following the indicated compass direction.^[56] When Europeans encountered indigenous peoples in Central and South America and in Oceania, they found maps already in use for navigation, administration, and commerce.^[57][q]

The applications of cartography expanded in the late 17th century with the invention of thematic maps that focused on portraying a specific kind of data – such as rainfall or population density.^[58][r] In the late 18th century, the accuracy of maps increased dramatically with the perfection of clocks that could keep accurate time for extended periods and withstand the violent motions of a ship and the temperature changes of different climates. These chronometers enabled longitude to be computed accurately at any point on Earth. For example, a voyager could sail to Easter Island and use a chronometer (in conjunction with other equipment, such as a sextant) to determine the precise latitude and longitude of the island. Cartographers could use such positions to prepare accurate maps.^[61]

Military applications led to innovations in cartography. In the late 18th century, Napoleon created a corps of geographic engineers [fr] to produce topographic maps for military use.^[62] The rise of nationalism in the 19th century was reinforced by maps,^[63] as noted by the French historian Christian Jacob [fr], who wrote that maps focused on individual nations were "the visual glue of a sense of national identity".^[64]

20th century to present

During World War I (WWI), cameras were mounted in airplanes that flew over battlefields and took photographs that were later analyzed for reconnaissance purposes.^[65] Some photos were used to update trench maps at scales up to 1:10,000.^[62] In the early 20th century, maps were widely used for propaganda by nations such as Soviet Russia and Nazi Germany to promote territorial claims and to exaggerate threats from perceived enemies.^[66][t]

The rapid expansion of road networks and mass transit systems in the 20th century created a market for mass-produced maps aimed at the traveling public.^[68] Road maps and transit maps became commonplace, including the 1933 London Underground map, which used an innovative schematic design that was more useful for passengers than a geographically accurate layout.^[69] After WWI, civilian cartographers used aerial photography in conjunction with the new science of photogrammetry to generate maps more rapidly than was possible with ground-based surveying.^[70] In the mid-20th century, the study of cartography shifted to a more rigorous and quantitative foundation, emphasizing the fundamentally mathematical nature of the discipline.^[71][u] Cartography was revolutionized in the latter half of the 20th century as computers and satellites enabled the new fields of computer cartography and remote sensing.^[72] Geographic information systems (GIS) allowed vast amounts of geographic data to be dynamically displayed on computer screens, so users could interactively zoom, pan, and choose which data to view.^[73] In the 21st century, maps are commonly displayed on mobile phones, provided by apps such as Google Maps and Apple Maps.^[74]

Layout and hierarchy

An important aspect of map design is the layout, which involves arranging the geographic data and the auxiliary elements (such as the title, legend, map scale, and insets).^[77] Robinson defines layout as "the process of arriving at proper balance. In a well-balanced design, nothing is too light or too dark, too long or too short, or too small or too large, in the wrong place, or too close to the edge".^[78]

The cartographer Cynthia Brewer suggests that a map's design should visually distinguish key elements in a map from less important ones – a consideration called visual hierarchy.^[79] The elements with the highest priority in the visual hierarchy are the map title and features related to the map's primary purpose. Medium priority elements include the background geography. The lowest-priority elements are supplemental notes and information, often found in the margins.^[80] Visually, key elements should appear to be in the foreground, while less important ones are in the background – a figure-ground relationship.^[81]

The background graphics of a map are called the basemap, and its purpose is to provide context for higher priority elements. The basemap can include landforms, topography, transportation networks, or imagery.^[82]

Shape and neatline

Maps can be created in a variety of shapes. A common shape is rectangular, but some polar maps are circular.^[83] The edge of a map's geographic content is delimited by a neatline; the region outside the neatline is the margin.^[84] Some maps cover a quadrangle, which is a region of the Earth's surface bounded by two parallels (circles of constant latitude) and two meridians (lines of constant longitude).^[85] The neatline (extent) of a map may not use the same coordinate system as the map's data; for example, USGS topographic maps use a latitude/longitude quadrangle for the extent, but Universal Transverse Mercator (UTM) for the map's projection and geographic coordinates.^[86] In some maps, the neatline may not be a perfect rectangle or may not have 90-degree corners.^[87]

• Maps with non-rectangular extent
• 
  An equidistant projection centered on Khartoum
• 
  A land hemisphere map with extensions
• 
  A 1657 south-up map of the South Atlantic

Scale

Map scales

This large-scale map has higher resolution and covers a smaller region. This is a scan of a paper map printed with a scale of 1:24,000.^[v]

This small-scale map has lower resolution and covers a larger region. The scale of this digital map varies within the map, but is roughly 1:4,000,000.^[w]

The scale of a map is a numerical value that indicates how measurements on the map relate to the reality they depict.^[89] Map scales are typically stated as a ratio, such as 1:12,000, which means that every centimeter (cm) on the map represents 12,000 cm (or 120 m) on the ground.^[89] Scales can be useful in many contexts. For example, a navigator can measure the distance between two points on a map, and divide by the scale to obtain an approximate value of the distance between the two points in the world.^[89][y]

Maps can be classified as "small scale" (lower resolution, covering large areas) or "large scale" (higher resolution, covering small areas).^[91] There is no official dividing line between large and small scales, although 1:500,000 or 1:1,000,000 are sometimes used as partitions.^[91] In some contexts, a third term – "medium scale" – may be used for maps with scales ranging from about 1:250,000 to 1:1,000,000.^[92]

Because map projections introduce distortion when the Earth's curved surface is represented on a flat map, the scale of a map always varies across the map.^[93] For large-scale maps that cover a small region, these variations are generally small, and the scale can often be treated as constant across the map.^[94] For small-scale maps that cover large areas like continents or the whole Earth, the variations in scale can be large, and the scale should be treated as merely a nominal value.^[94]

The notion of scale is closely related to the concept of resolution, which is the granularity or precision with which locations are measured.^[88][o] Some cartographers define the resolution of a paper map as the distance represented by half a millimeter on the map. For example, a 1:10,000 scale map has a resolution of 5 m; and a 1:1,000,000 scale map has a resolution of 500 m.^[88]

Map scales were originally used in the context of paper maps, where the ratio of map to reality has an unambiguous definition. However, scales can also be applied to digital map databases.^[95] Since a database does not have a definitive paper representation, the scale is instead based on the resolution of the database's feature coordinate values.^[96] For example, a database that contains features stored with a 5 m resolution could be considered to have a scale of 1:10,000.^[88] The same process is used to define the scale of a raster image of the Earth: for example, an image with each pixel representing 2 km would correspond to a map scale of 1:4,000,000.^[88]

Generalization

Generalization is the process of reducing or adjusting the information shown on a map so that it more effectively serves its intended purpose.^[98] The nature of this process depends on the type of map, its scale, and its audience.^[98] Procedures performed during generalization include selection, simplification, exaggeration, aggregation, smoothing, elimination, and symbolization.^[98][z]

The process of generalization is functionally the same for both manually designed maps and interactive digital maps. However, generalization of interactive maps is partially automated by software applications.^[103][aa] The first step in generalization is typically selection, which is simply choosing which types of features to include in the map.^[104] Depending on the purpose of the map, the mapmaker may omit, for example, roads, buildings, bodies of water, or towns with a population under 100,000.^[105]

Simplification is the process of simplifying a particular feature (such as a river, grove of trees, group of buildings, etc.) by eliminating detail.^[106] For example, a grove of eight distinct trees may be replaced by one tree; or a fence defined by twenty straight segments may be reduced to five segments.^[106][ab] The degree of simplification depends on how many features should appear on the final map and how densely they should be placed.^[108][ac]

The process of exaggeration involves enlarging some aspect of an object to better convey the object's real-world essence.^[109] Aggregation is grouping several distinct objects into one. Examples include grouping multiple point objects into one; multiple point objects into an areal object; or multiple areal objects into one.^[110] Smoothing a line or perimeter involves replacing the line with a smoother version that captures the essence of the line while eliminating jagged, fine-scale features.^[111][ad] Symbolization is the process of choosing a graphical depiction to represent each real-world object. Selecting the graphical attributes of the depictions – including shape, color, size, and pattern – is an important part of the symbolization process.^[113][ae]

Symbolization

Symbolization is the process of selecting graphical markings to represent real-world geographic features or data.^[115] The markings can include a wide variety of shapes, dots, icons, graphics, and other visual indicators. Symbolization may indicate magnitude or kind by varying attributes of the graphics, such as color, shape, size, and pattern.^[115] The meaning of the graphics is often explained in a map legend (guide to the map's symbols) on the map, or in a separately published document.^[115]

Symbolization is particularly important in thematic maps, which typically depict the kind or magnitude of a specific datum across a map. Symbolization techniques suitable for thematic maps include proportional symbols,^[116] lines of constant value (for isopleth maps),^[117] dots (for dot distribution maps),^[118] and colored areas (for choropleth maps^[119] and dasymetric maps^[120]). Example maps illustrating these techniques appear in the thematic maps section below.

The process of symbolization should be distinguished from map symbols, which are graphical icons, pictograms, or shapes that are designed to present features or data in a compact manner. Symbols are just one category of graphical elements that symbolization utilizes.^[121] Examples of symbols used in maps include tents (representing campgrounds), airplanes (airports), and the letter "P" (parking).^[122]

Projection

A projection is an algorithm that transforms all or part of the Earth's surface^[ah] into a two-dimensional representation.^[124] There are dozens of projections that mapmakers can choose from when creating a map.^[125] All projections introduce some distortion because it is impossible to represent a spheroidal surface on a flat surface without tearing or stretching it.^[126]

Some projections preserve important characteristics of the spheroidal surface. Equal-area projections preserve the relative sizes of regions.^[127] Conformal projections preserve the angles between intersecting lines, and give the impression that shapes are approximately preserved.^[128] Equidistant projections preserve distances between one or two specific points to all other points.^[129] Some projections – called compromise projections – try to balance multiple goals, without perfectly achieving any one of them;^[130] a notable example is the Robinson projection.^[131] Projections commonly used for maps of the whole Earth include Goode homolosine projection, Mercator, and Robinson.^[132] For maps that cover large parts of the world (but not the full globe), common projections include Lambert azimuthal and Miller cylindrical.^[133]

• Some projections of the Earth
• 
  Interrupted Goode homolosine
• 
  Miller cylindrical
• 
  Robinson
• 
  Van der Grinten

A controversial projection is Web Mercator – a variant of the standard Mercator projection – which was adopted by Google around 2005 for use in its online zoomable global map.^[134] The projection has been criticized by the European Petroleum Survey Group and National Geospatial-Intelligence Agency for its large distortions in the higher latitudes, as well as for inaccuracies in coordinates when zoomed in.^[134][ai]

Coordinate system

Maps of the full Earth often use ellipsoidal coordinate systems which specify locations as degrees of latitude and longitude.

Projected coordinate systems are often used for maps of provinces or small countries.

When a map displays coordinates of places and objects, the mapmaker must select a coordinate system, which is based on a specific geodetic datum.^[136] A geodetic datum consists of two independent parts: a vertical datum for elevation (height) coordinates, and a horizontal datum for horizontal position (e.g., distance north and distance east).^[137]

Vertical datums are imaginary surfaces used as a baseline to measure an object's elevation. Vertical datums are categorized as ellipsoids or geoids.^[138] An ellipsoid, such as WGS84, is an imaginary, smooth spheroid that roughly approximates mean sea level.^[138] Geoids approximate sea level more precisely: they are the shape the surface of the world's oceans would take under the influence of Earth's gravity and rotation alone, without winds or tides. Geoids are not a smooth spheroid: they have undulations due to the variability of the Earth's gravitational field.^[138]

Horizontal datums define a coordinate system for horizontal locations and ignore elevation (height).^[139] A horizontal datum is an ellipsoid that covers the entire Earth and measures locations, in degrees, as latitude and longitude. There are several ellipsoidal horizontal datums available, including World Geodetic System 84, European Datum 1950, and North American Datum 83.^[139]

A coordinate system is either a horizontal datum (an ellipsoid) or a projected coordinate system. Projected coordinate systems specify horizontal locations as XY Cartesian values in units of meters or feet (rather than degrees), and are thus sometimes more convenient to use than ellipsoidal systems.^[140] A notable projected coordinate system is UTM^[135] which is commonly used for military applications because it is a global system in which angles are accurately represented and XY locations are measured in meters, which may be more convenient than degrees.^[141][aj]

For example, the location of the Augusta Raurica archaeological site in Switzerland can be represented in two coordinate systems as:

Many nations define coordinate systems tailored to the country or its provinces.^[144][ak] These local coordinate systems are typically projected coordinate systems.^[145] For example, Britain uses a transverse Mercator projection for its Ordnance Survey National Grid.^[146] A nation may have many such coordinate systems, each tailored for a specific province, state, or region. For example, the US uses 125 coordinate systems that cover the country.^[147]

Colors and patterns

This map uses both color (hue) and pattern (hatching) to distinguish regions.

This thematic map uses a single hue and varies the lightness to distinguish data values.

Colors play an important role in map design: many users prefer colorful maps, and the appropriate use of color can make a map more informative.^[148] Any color may be characterized by a particular combination of three independent attributes: hue, lightness, and saturation.^[149] Of those attributes, hue is generally used to indicate important distinctions within a map.^[150] Lightness can also be used to distinguish features in a map,^[151] particularly for progressively coloring regions in a quantitative map.^[152]

Cartographers have not established an international standard for color conventions.^[153] Examples of color conventions used in some government-produced maps in the US are:^[154][al]

  Blue: water and rivers

  Green: vegetation or forested areas

  Brown: elevation contour lines

  Tan or yellow: desert or arid regions

  Red: urban areas; major roads

  Black: lettering, buildings, railways, boundaries, gridlines, small or medium roads

  Purple: aviation-related graphics (on aeronautical charts)

In maps, patterns are repeating design motifs that fill areas and convey information to the user.^[155] The patterns may consist of lines, dots, pictographs, or hatching.^[156] For example, patterns may be used to distinguish biomes such as swamp, desert, or forest. The International Geographical Union published a set of patterns to be utilized to designate soil types, including patterns for mud, clay, sandstone, and gravel.^[157] Colors and patterns may be used in combination within a single area.^[158]

Typography and labels

Many maps include textual labels that identify features. The design and layout of the text are major factors in the overall graphical quality of the map.^[160] Maps often use multiple fonts and typefaces on a map to convey information to the user. For example, a map may use italic, boldface, or various sizes of lettering to indicate water features vs land features, or to designate the size of a city or town.^[161] Positioning textual labels in a manner that is helpful and attractive is an important part of the design process.^[162] Positioning can be performed manually by a cartographer, or automatically by software algorithms.^[163] Positioning guidelines that are sometimes used include:^[164][am]

• Text should be aligned horizontally, although in large maps covering the whole Earth or large regions (small scale maps) the text may instead be aligned along lines of latitude.
• Text should generally be in a straight line, not curved. Exception: when aligning text along lines of latitude on a small-scale map.
• Spacing between letters should generally be tight.
• When text and graphical objects (such as lines) interfere, the text has priority and the graphic should be interrupted.
• A name should be entirely on land or on water, but not straddle both.
• Labels of point features should be offset in a consistent manner, for example, above and slightly to the side of the feature.

Orientation

The top of this 1695 map of Utrecht, the Netherlands, is slightly north of east.

This 1904 map's top is east.

The orientation of a map is the compass direction toward the top of the map.^[165][an] Modern maps generally have a north-up orientation.^[167][ao] If a map has a non-north orientation (such as magnetic north up), the map will usually include a graphical indicator pointing to true north.^[169] An early map with a known orientation is an Akkadian Empire clay tablet with an east-up map, c. 2300 BCE.^[170] The orientation of ancient Egyptian maps is uncertain, but some may have been oriented south up.^[171] In ancient and medieval Europe, orientation varied, and many maps did not contain an explicit indication of their orientation.^[172] The archetypes of the Tabula Peutingeriana and Ptolemy's map probably were north up.^[172] Mappa mundi were oriented in all four cardinal directions.^[173] Many T and O maps were drawn with east at the top^[174] but some displayed west or south up.^[175]

Accessibility

Cartographers may consider accessibility factors when designing a map, particularly to support users who may have visual impairments or color blindness.^[176] For example, to accommodate red-green color blindness a map may follow these guidelines:^[177]

• Take advantage of varying lightness for red-orange-yellow hues.
• Avoid yellow-green which color-blind users may confuse with orange.
• When using a palette of colors to display values in a thematic map, avoid green and limit colors to red, orange, yellow, and blues.

An example of a thematic color palette that is suitable for red-green color blindness is this divergent color palette developed by Cynthia Brewer:^[178]

For visually impaired map users, tactile maps may be produced that consist of raised surfaces which a visually impaired person can feel with their fingers.^[179] Interactive maps can convey information via auditory or vibration feedback as the user moves a cursor across a digital map.^[180]

Auxiliary elements

Maps often contain a variety of elements or marginalia that supplement the primary geographic imagery.^[182] A map scale is often indicated on a map, either textually or as a graphical scale bar. Many maps, particularly if their orientation is not north up, include an orientation indicator which points north.^[183] Titles are displayed in many maps, although some maps do not need a title and omit it.^[184]

Legends are a critical component of many maps, because they provide the user with essential keys to understanding the map. Legends define graphical symbols and can explain the origin, context, and meaning of the map's thematic data.^[185] Some maps contain smaller maps, called insets. The insets can serve a variety of purposes, such as showing the location of the primary map in global context or showing high-detail maps of points of interest.^[186]

A cartouche is an ornamental symbol – sometimes very elaborate – found on some maps that contains map marginalia such as the title or author's name.^[187] Some globes display an analemma – a figure-eight shaped line – that shows the locations on the Earth where the sun is directly overhead throughout the year.^[188]

Maps in antiquity sometimes displayed creatures such as sea serpents, mermaids, satyrs, sirens, dog-headed people, and centaurs.^[181] Dragons were sometimes included, leading to the creation of the phrase "here be dragons" to designate terra incognita (unmapped or unknown regions).^[189]

Topographic

The topography of Mt. Everest is displayed in this pictorial map with a combination of shaded relief^[190] and oblique perspective.^[191]

This topographic map displays elevation data as contour lines.^[aq]

Topographic maps depict the elevation (height) of the ground.^[190] The height – often expressed as elevation above sea level – can be displayed in a variety of ways, including contour lines or relief shading.^[192] Many topographic maps are general reference maps because – in addition to elevation – they may display a variety of features such as buildings, bodies of water, vegetation, roads, towns, and railways.^[193] Some national mapping agencies produce topographic maps of their countries' lands – including the UK's Ordnance Survey and the US's USGS.^[194] Some nations produce two or more series of topographic maps, each at a unique scale. For example, in the UK, topographic maps are produced at four scales: 1:1,250 (urban areas), 1:2,500 (rural areas), 1:10,000 (mountain and moorland areas), and 1:50,000 (the baseline series).^[195]

Planimetric maps – in contrast to topographic maps – do not include elevation information: they convey only horizontal location information.^[190]

Thematic

Thematic maps focus on depicting a specific type of information and relegate base geography to the background.^[196] Examples include maps depicting weather, population, and geological data.^[197] In contrast to thematic maps, general reference maps display a variety of basic geographic information about a region, typically focusing on towns, highways, railways, and bodies of water.^[197] Many maps have characteristics of both thematic maps and general reference maps, so these two map kinds are not mutually exclusive.^[198]

Symbolization techniques for thematic maps

Proportional symbol^[ar]

Choropleth^[as]

Isopleth^[at]

Dots^[au]

Symbolization techniques commonly used in thematic maps include:^[199]

• Proportional symbols – A map with multiple symbols (such as circles) depicting the datum being represented, with the area of each symbol proportional to the data's value.^[116]

• Lines of constant value (isopleth map) – Lines (usually closed loops) that follow constant values of the datum being represented. Also called "isarithmic map". Elevation contour lines are an example of isopleths.^[117]
• Dots (dot distribution map) – The datum is represented as dots (usually all the same size), where each dot typically represents a fixed quantity of the data.^[118]

• Colored areas (choropleth map) – A thematic map of an area composed of multiple regions (for example, administrative boundaries), each region colored with a single color, and the color variation (hue or lightness) indicates the value of the datum being represented. Choropleth maps often use areal borders that rigidly correspond to political or administrative data-collection boundaries.^[119]

• Colored areas (dasymetric map) – A dasymetric map is similar to a choropleth map, insofar as both represent data as colored regions.^[120] However, the dasymetric areal boundaries are based on multiple data sources, so the resultant areas may be more accurate and insightful than those based on a single data set. Additionally, areal boundaries of dasymetric maps typically do not rigidly adhere to administrative data-collection boundaries.^[120][av]

Qualitative

Some maps may be classified as qualitative or quantitative. A qualitative map (also called a chorochromatic map) depicts nominal data, which can be categorized as two or more kinds, but does not have a continuous numerical basis. Examples include a climate map that divides a region into 15 climate zones or a map that divides a region based on 20 religious affiliations.^[200] Some authorities limit the quantitative/qualitative distinction to thematic maps, but others apply the distinction to any maps that display numerical or statistical data.^[200]

Quantitative

A quantitative map displays the magnitude of a single numerical datum, such as air pressure, population density, or poverty rate. Some quantitative maps – particularly choropleth maps – display data as a set of distinct classes or categories.^[201][ax] For example, the adjacent map of Africa divides forest biomass density into six classes with dividing lines at:

• 50 tonnes
• 100 tonnes
• 150 tonnes
• 200 tonnes
• 250 tonnes

A careful choice of divisions between classes can make a map more useful and informative.^[203] The process of choosing the dividing lines between classes is called "classification".^[201] A variety of classification algorithms are available, including the quantile and equal-interval algorithms.^[204][ay] The cartographer George F. Jenks created the natural breaks algorithm, which analyzes a histogram of the data and selects the low points of the histogram as the class dividing lines.^[205] People may have difficulty distinguishing colors if they are too similar, so at most eight classes should be used when displaying the classes with a simple color gradient.^[206]

Topological

Maps of London Underground

This topological map emphasizes understandability

This conventional map emphasizes accurate geography

A topological map is one that emphasizes graphical simplicity and makes little or no effort to accurately represent geographic distances or locations.^[207][az] The term "topological" means that these maps preserve topology in the mathematical sense: all connections or relationships between objects are preserved even after distances and positions are distorted.^[209] Topological maps are sometimes called "schematic maps" because of their diagrammatic nature: their graphical depictions promote comprehension by sacrificing geographic accuracy.^[210][ba]

An early schematic map was a 4th-century Roman visual itinerarium (travel guide) that aided travelers by depicting roads and towns rather than their geographically accurate positions.^[211] The original was lost, but its contents are preserved in the Tabula Peutingeriana – a copy made c. 14th century.^[212] A notable modern example of a topological map is the official London Underground map.^[213][bb]

Cartogram

A cartogram is a thematic map that depicts a data value by enlarging or shrinking regions so the area of each region is proportional to the region's data value. Cartograms are diagrammatic or schematic in nature and do not attempt to display geographic sizes or distances accurately. Cartograms are a kind of topological map because cartograms typically preserve the positional relationships (that is, the topology) between regions.^[215]

Cartograms can be beneficial when regions with a small geographic area have a medium or large data value: in a conventional map, such regions may be nearly invisible, but in a cartogram they are prominent.^[216] By definition, data density is constant throughout the entire cartogram. For example, a cartogram showing the population of countries would have the same population density (people per unit area on the map) in all countries.^[217] Creating a cartogram that retains the positional relationships between regions can be a complex process requiring sophisticated algorithms.^[218]

Interactive

The GeoNames web app lets users interactively view and manipulate maps.^[219]

This interactive map of postal codes uses geographic data from OpenStreetMap.^[220]

The spread of computers in the latter decades of the 20th century led to a new kind of map: interactive maps, which dynamically display geographic data on an electronic visual display. These maps allow users to view and explore the data by directly interacting with the map. Interactive maps permit users to select which features to display, view details of individual objects, zoom in and out, and adjust the map scale.^[221] These manipulations of content or appearance are in contrast to the limited interactions available with a paper map.^[222] Interactive maps can also display the Earth as a globe, with no map projection applied.^[223] Interactive maps are often used, especially on mobile devices, to provide location-based services, such as providing navigation directions.^[224]

Photomap

A photomap is a georeferenced image that has graphics overlaid to make it usable as a map. The image may consist of several individual images that were combined into a mosaic. The overlaid graphics may include grid lines, descriptive notes, or other marginalia.^[225]

When an image has been orthorectified to remove distortion due to terrain relief, it is called an orthophoto,^[226] and when supplemented with graphics to be suitable as a map, it is an orthophotomap.^[227] After images have been orthorectified, two or more images can be merged into a larger orthophotomosaic. An orthophoto (or orthophotomosaic) can be used as the background (basemap) of a map.^[228]

Astronomical

Astronomers have produced maps of celestial objects for centuries, with telescopic observations enabling increasingly detailed maps of planets, moons, asteroids, and comet nuclei.^[229] Early maps were of objects that appear relatively large through a telescope, such as Mercury, Mars, and the Moon.^[230] Maps of the Moon played an important role in the Space Race during the 1960s and 1970s, including the Apollo program, which landed the first humans on the Moon.^[231] Some astronomical objects – such as the Sun and gas planets like Jupiter – do not have solid surfaces. Nevertheless, they have been mapped to depict their visible features at particular points in time.^[230] Some asteroids and comet nuclei have shapes so irregular that conventional map projections designed for spheroidal objects are not sufficient. Maps for these objects required the invention of novel map projections.^[232] Astronomers map the location of stars and other celestial objects with star charts,^[233] some of which incorporate distance from Earth as a third spatial dimension.^[234]

Classified by medium

Maps may be classified according to the medium in which they are presented. Until the 21st century, most maps were printed as individual sheets of paper.^[235] An atlas is a collection of maps bound as a book.^[236] Globes are three-dimensional representations of the Earth, Moon, or other celestial bodies.^[237] Maps may also be produced as physical three-dimensional raised-relief models. Such models depict topography and can be made of vinyl, plaster, or papier-mâché.^[238] With the development of digital technology, maps increasingly became available in electronic formats. A digital map is stored as computer data and is typically displayed on an electronic visual display such as a computer monitor or smartphone. It may depict the Earth in a two-dimensional representation or as a three-dimensional globe.^[239]

• 
  An atlas is a collection of maps, usually in book form.^[236]
• 
  A globe made by Willem Blaeu in the early 1600s
• 
  Digital maps are often displayed on smartphones.^[239]
• 
  A raised-relief map made of plastic^[238]

Cartographic databases

Cartographers store cartographic data in databases. A database dedicated to storing data for mapmaking is called a cartographic database.^[95] Another type of database that contains cartographic data is a geographic information system: a computer system that stores and analyzes geographic data.^[247][be] GISs can contain a wide variety of data to support many different applications, including cartography, real estate, engineering, architecture, urban planning, environmental protection, transport, and logistics.^[250]

Georeferencing

Cartographic data must be georeferenced before it can be displayed on a map.^[252] Data is georeferenced when information is available to compute the geographic locations of places represented in the data.^[253][bf] Some data may be georeferenced when it is originally collected, such as surveying data, or imagery that was collected by a craft equipped with satellite navigation and an inertial measurement unit.^[255][bg] When a map incorporates data from multiple sources, the data may not be georeferenced with the same coordinate system, units, or scales. In that situation, the mapmaker must convert the data to a common reference system.^[256]

To utilize data that is not yet georeferenced, several techniques are available. If the data contains identifiable landmarks or objects, georeferencing may be possible by matching the landmarks to their corresponding locations in an already georeferenced map or image.^[251] Data may be georeferenced by sending a surveying crew to visit the real-world location to obtain precise geographic locations of the objects represented in the data.^[257] Imagery and aerial photographs may be georeferenced with photogrammetric procedures such as image rectification.^[258]

Imagery and remote sensing

An important source of cartographic data is imagery collected from remote sensing, including satellite imagery and aerial photographs taken from cameras mounted on aircraft or drones.^[259][bd] Remote sensing collects data from various signals: the electromagnetic spectrum (visible light, ultraviolet, infrared, microwave); as well as lidar, sonar, or radar reflections.^[260] Some imagery contains multiple spectral bands. This multispectral or hyperspectral imagery can be exploited by algorithms to extract information about conditions on the Earth's surface that are not possible with a single band.^[261] Applications of remote sensing extend far beyond cartography and include change detection,^[262] forestry,^[263] agriculture,^[264] farming,^[265] vegetation analysis,^[266] geology and Earth sciences,^[267] and hydrology.^[268]

Before imagery can be used for mapmaking, it must be georeferenced using principles of photogrammetry.^[269] One way to georeference an image is to locate several small, identifiable points in the image (such as street intersections, or small landmarks) that have a known geographic location which may be obtained through traditional surveying; or from satellite navigation measurement; or from a map or orthophoto that has been georeferenced.^[270]

Provided that the imagery has been properly georeferenced, it can be used to extract precise geographic coordinate values for any identifiable objects in the image.^[271][bh] For example, a cartographer can extract the locations of terrain and feature data (such as rivers, roads, and buildings) for storage in a database.^[272]

Rectified imagery

Before imagery can be used in a map, it is usually orthorectified with terrain data.^[273]

This is not a "true orthophoto", because the buildings were not modeled in the database. Thus, the buildings appear tilted.^[274]

Many images used in cartography undergo an additional processing step called orthorectification, which requires accurate digital terrain data covering the region.^[273] The orthorectification process geometrically warps imagery to remove terrain-related distortions and foreshortening caused by camera tilt (illustrated in the adjacent diagram). The orthophoto approximates what an imaginary viewer would see if they were directly above, looking straight down.^[273] The positions of features in an orthophoto are geographically correct,^[bi] and an orthophoto can serve as a background basemap within a map, or as a map itself, called an "orthophotomap".^[275]

If imagery contains buildings, orthorectification may produce orthophotos in which the buildings appear to be tilted or leaning.^[274] If that is not acceptable for the map, the mapmaker can generate "true orthophotos" that rectify buildings and other structures so they appear as if the viewer were looking straight down from directly above.^[274] Rectifying structures requires that they be modeled either within the terrain database, or separately from the terrain as 3D wireframe models.^[274][bj]

Searching and indexing

Cartographic data may be roughly grouped into three categories: spatial, temporal, and attributes (which include all other information about features or terrain, including metadata).^[277] Depending on the nature of the map being created, a cartographer may limit data searches to one or more of those data categories. For example, a mapmaker could query a database for railway data covering Sri Lanka in 1990, including the track gauge of each railway segment.^[277]

During the map design process, cartographers must locate relevant data within a database. Databases support that need with indexes, which provide retrieval, searching, and sorting functions. Indexes used to search and sort geographic data (that is, spatial data) require special computer technologies, because spatial data is not comparable to simple numerical or textual data.^[276]

Raster and vector data

Cartographic data that models the real world is often stored in raster format or vector format.^[278] Imagery is commonly stored in a raster format. Linear or areal features (such as roadways, boundaries, or building outlines) are typically stored as vector data.^[279] Terrain data is commonly stored in a raster format, although it may also be stored as a triangular irregular network.^[280] Terrain data, by itself, can be used by cartographers to derive important geographic information such as elevation contour lines, drainage basins, line-of-sight, drainage divides, viewsheds, volume of filled depressions, and watercourses.^[281]

To perform certain kinds of analysis, the data is transformed from one form to another.^[282] Software algorithms exist that automatically detect lines, edges, and boundaries within imagery and generate vector data that roughly delineates roads, buildings, and other linear or areal objects.^[283]

Spatial relationships between nearby objects can be explicitly stored with the objects' vector data in a database. This geospatial topology data can encode whether two features overlap, one is inside another, they share a boundary line, or if they are connected, as well as hierarchical relationships such as which road segments make up a particular roadway.^{[284][bk][bl]}

Attributes and metadata

When storing geographic data in a cartographic database, attributes or metadata may be useful to mapmakers. Attributes include the year the geographic data was collected, identification numbers, geodetic datum, error estimates, the origin or source of the data, and any miscellaneous notes. Attributes can be used, for example, to supply annotations for the map or notes in the map's legend.^[286]

Accuracy

Terminology

Accuracy and precision have distinct meanings in cartography: accuracy is an estimate of error between an object's true location and its location presented in the map. Precision^[bm] is the granularity (or resolution) of location values in the map (irrespective of their proximity to the true location). Some cartographers stipulate that the precision of a map is the real-world distance represented by half a millimeter (on a paper map) or by half a pixel (in raster imagery).^[287]

A related term is "detectable size", which is the width of the smallest discernible feature in a map, generally considered to be twice the precision. Tobler's Rule states that the detectable size (in meters) times 1000 is equal to the map scale.^[287]

Bias and disinformation

All maps are selective representations of geographic reality and therefore involve some degree of inaccuracy, distortion, or omission.^[313] Some of these departures from geographic reality are intentional; others are inherent consequences of simplifying and symbolizing geographic information.^[314] Situations in which mapmakers deliberately mislead the audience include advertising, military disinformation campaigns, political propaganda, and applications for controversial urban development projects.^[315] An example of deliberately inserted misinformation is a copyright trap, which is a fictional object or place inserted unobtrusively into a map by the mapmaker to detect unauthorized copies.^[316] The geographers J.B. Harley and Mark Monmonier argue that all maps should be treated with skepticism because they reflect editorial and content choices made by their creators.^[313]

Some map projections can significantly misrepresent the relative sizes of countries, particularly on world maps.^[317] In the 1970s, the historian Arno Peters asserted that the widespread use of the Mercator projection was "cartographic imperialism", as it shows European countries relatively enlarged compared to developing countries – especially in Africa – nearer to the equator. Peters presented the Gall-Peters projection – an equal-area projection – as an alternative that he regarded as more equitable.^[312][bq]

Another source of potential Eurocentric bias is the north-up orientation used by most maps,^[319] which Guyanese politician Shridath Ramphal argued could contribute to an implicit perception of northern countries as superior.^[320] Australian Stuart McArthur created a south-up world map in 1979 that placed his country in a position of prominence. It was titled "McArthur's Universal Corrective Map of the World".^[321]

Boundary disputes

Maps play a role in boundary disputes between nations; for example, countries use maps during negotiations as tools to support their claims.^[322] Concerns about the location of boundary lines displayed in online maps, such as Google Maps, have led involved countries to instruct data providers to display a particular boundary line.^[323] Google Maps has responded to such demands by storing two versions of the disputed boundary and choosing the version to display based on the requester's location.^[323] Examples of boundary disputes that have led nations to instruct map providers to display a particular boundary line include: Russia and Ukraine,^[324] India and China,^[325] Pakistan and India,^[326] Turkey and the cultural region of Kurdistan,^[327] Cambodia and Thailand,^[323] and Vietnam and China's maritime boundary dispute in the South China Sea.^[323]

Gerrymandering

Maps can be used to skew election results by establishing voting district boundaries in a way that favors a particular outcome. Generally, the political group in power creates electoral maps designed to keep itself in power by diminishing the representation of other groups. This process is called gerrymandering.^[328] Gerrymandering is an example of the broader modifiable areal unit problem, whereby changes to the boundaries of geographic regions can alter statistical outcomes.^[329] The creation of software applications – in conjunction with geographic databases that indicate how individuals are likely to vote – has automated the process of gerrymandering and enabled even minority groups to define boundary lines that provide them with majority representation in legislative bodies.^[330]

Fantasy maps

Some maps depict imaginary regions or worlds. Examples include maps of Treasure Island in the 1883 novel by Robert Louis Stevenson, the Land of Oz in the Wizard of Oz book series (1900 to 1920) by L. Frank Baum, and Middle-earth in The Lord of the Rings (1937 to 1949) by J. R. R. Tolkien.^[331] A 2013 survey of 200 books in the fantasy genre found that 34% contained a map.^[332]

Orienteering

Orienteering is a group of sports in which participants use a map and compass to navigate from point to point in unfamiliar terrain as quickly as possible. In formal foot-orienteering competitions, participants are given a specially prepared orienteering map, usually topographic, which they use to locate control points.^[333]