Elements of Cartography

Gomarasca, Mario A.

doi:10.1007/978-1-4020-9014-1_2

Elements of Cartography

Mario A. Gomarasca²

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First Online: 01 January 2009

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Cartography is of fundamental importance for all geographic data characterized by a spatial attribute, i.e. datum coordinates, as it provides a possible description of the shape and size of the Earth and its natural and artificial details. The role of cartography is to map geographic facts and phenomena (e.g. places) which are identifiable by their position and which can be georeferenced, archived and referred onto maps.

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Cartography is of fundamental importance for all geographic data characterized by a spatial attribute, i.e. datum coordinates, as it provides a possible description of the shape and size of the Earth and its natural and artificial details. The role of cartography is to map geographic facts and phenomena (e.g. places) which are identifiable by their position and which can be georeferenced, archived and referred onto maps.

The basic functions of cartography are

to give both a punctual knowledge of the territory, based on the observation of every single object, and a general one, for a global vision;
to allow and develop deductive and inductive logical processes, related by concomitance, proximity, frequency, etc.;
to act as basic support for classification, planning and land management.

A cartographic map is a flat, approximate, reduced and symbolic representation of the Earth’s surface or of its parts. This is achieved according to systems, or representations, that turn ellipsoidal figures into plane figures and that, through appropriate signs, can reproduce information about the shape and measure of the ground elements, as well as the relative representation of real or abstract phenomena which can be located in space.

A map is a cartographic product realized by integrating different disciplines and techniques. The phases of the cartographic process can be summarized as follows:

survey, selection and annotation of spatial data;
data standardization;
data generalization;
transformation of the points belonging to the terrestrial surface into the corresponding points on the reference surface (geoid: altimetry, ellipsoid: planimetry) through biunivocal correspondence. The terrestrial surface, and of the gravity field, is approximated by choosing a specific coordinate reference system;
representation of the reference surface on the map according to a cartographic reference system, namely the mathematical equations enabling one to represent the terrestrial surface on map plane or screen;
realization of the map, defining its typology, legend and symbols.

Nowadays, the photogrammetric techniques, as well as the most recent remote sensing techniques and laser scanning system data, are replacing the direct survey, thus simplifying and partly modifying the sequence of the phases.

The term cartography is often used with two meanings:

with reference to the discipline;
with reference to the elaborations (maps) resulting from complex cartographic activities.

In this chapter, issues concerning the determination of the size and shape of the Earth, the geodetic reference systems and the cartographic representations are discussed using a descriptive approach. Some elements needed for reading the topographic maps and interpreting the landscapes are also reported.

2.1 Milestones in the History of Cartography

The history of cartography is the intersection of the disciplines that underlie it. An exhaustive revisit is almost impossible, but some of the facts and the figures philosophers, astronomers, mathematicians, geographers, etc. who have left their indelible signs may be mentioned. The purpose of this section is to highlight how the problem of describing and measuring the Earth had always been of great interest among the researchers through different periods and with different approaches that, particularly in the ancient world, resonate still, even with current knowledge.

The Soleto Map is the oldest geographic map ever discovered in Europe. It is a piece of a crate enamelled in black, a little ostrakon of 5.9 cm × 2.9 cm with the incision of the coastal line of the Salentino peninsula, south of Italy, with some Greek toponyms and 11 local toponyms shown with points. The object was discovered by the archaeologist Thierry van Compernolle of the University of Montpellier in Belgium, August 21, 2003 in a large messapic building, confirming the relationship among Iapigi, Messapi and Greeks in the V century BCE (Fig. 2.1a).

The great prehistoric and historical civilizations of the Near and Middle East offer indications of the existence of a sort of rudimentary cartography. Among the most ancient, in Northern Mesopotamia, a graffito has been found, drawn on a clay tablet and representing the Euphrates and a tributary river, the mountains bordering Northern Mesopotamia and the cities, represented by a small circle (Fig. 2.1b and c).

In Valcamonica (Northern Italy), once inhabited by the people of the ancient Camunis, over 170,000 rocks’ figures have been dated back to the period between the Palaeolithic and the Iron Age. Among these graffiti, in a complex chronological definition, are some petroglyphs, which are considered as maps, and which probably describe the articulated disposition of a settlement with houses and workshops, as a highly detailed projection (Fig. 2.2).

The Egyptians even drew cadastral plans for the recognition of property boundaries for cultivated lands as well as a topographic map of a gold deposit in Nubia, preserved in the Egyptian Museum in Turin, and dating back to 1200 BCE.

During the Greek and Roman times, many scholars ventured upon the study of our planet, formulated different hypotheses and proposed solutions for its representation.

Cartography conceived for cultural purposes was first born in ancient Greece. The first map of the world, representing the ecumene, namely the emerged land inhabited by man, is attributed to a philosopher of the ionic school, developed along the Aegean coast of Asia Minor, Anaximander of Miletus. He was a disciple of the philosopher and mathematician Thales (624–546 BCE) and drew the map in the mid-VI century BCE (Fig. 2.3), followed by Hecateus’s work in the V century BCE.

Cartography began its scientific progress in the IV century BCE, still in classical Greece, where Dicearcus of Messina (IV century BCE), a philosopher belonging to the generation after Aristotle, for the first time introduced a mathematical construct element, constituted by an East–West line, that is a parallel, passing through the Pillars of Hercules, Sicily, Athens, Rhodes, Taurus and Mount Imaus, all places that were considered to lie on the same latitude. Thus was the concept of a reference system introduced: the diaphragm having the meaning of parallel and the perpendicular acting as a meridian, while the origin of the axes was in Rhodes.

Eratosthenes of Cyrene (III century BCE) around 250 BCE succeeded in calculating the circumference of the Earth, to a good approximation, starting from the observation of the angular difference between the Sun’s rays over two points of the terrestrial surface. Among the studies and theories proposed in the past, this is undoubtedly the most fascinating method, both for its clarity of reasoning and for its astonishing precision, despite the limited scientific knowledge of that period.

Eratosthenes calculation based on these known facts:

at noon, during the summer solstice, the Sun was exactly on the vertical above the town of Siene in Egypt, near present-day Aswan. Eratosthenes had reached this conclusion by observing that the Sun was reflected onto the bottom of a well in the city. In fact, Siene was actually in correspondence to what is nowadays defined the Tropic of Cancer;
on the same day at the same time, in Alexandria (Egypt), about 5000 stadia (1 stadium: ∼185 m) North of Siene, as calculated by Eratosthenes himself, a vertical pole fixed into level ground, projected a shadow whose size indicated a Sun angle equal to 7°12^′.

The deduction was that if the two lines passing respectively across the centre of the well in Siene (indicated with S in Fig. 2.4) and the prolongation of the fixed pole in Alexandria (A in Fig. 2.4) met at the centre of the Earth, the distance between the two towns was 1/50 of the circumference (360°: 50 = 7°12^′): that is 250,000 stadia (5000 × 50) corresponding to 46,250 km, just 15% more than what is measured nowadays.

While it is possible to endlessly discuss the numbers, the units of measurement, the conversions and the deduced results, there is nothing to object to about the method, which is amazingly ingenious.

Eratosthenes also left a geographic description of the world, divided into regions and showing a wider geographic knowledge along the East–West direction, which improved the construction system started by Dicearcus: it has different reference lines at irregular distances, coinciding with the parallels which pass through familiar places, and lines perpendicular to the previous ones, at uneven distances as well, which get closer to the concept of a geographic grid (Fig. 2.5).

Later, Hipparchus of Nicaea (II century BCE) solved the problem of the coordinates of a point on the Earth by applying astronomical methods. He drew up a list of more than 800 stars assigned to six classes of apparent size and measured the distance between the Earth and the Moon, obtaining a result very close to reality. A supporter of the geocentric theory, he constructed the basis of the Ptolemaic system thanks to his studies in geography and cartography; he introduced the use of geographic coordinates and the method of stereographic representation (Fig. 2.6). His works, almost all now lost, were handed down through the papers of Claudius Ptolemaeus (Greek: Klaúdios Ptolemaĩos; 83–161 CE), known in English as Ptolemy.

The Roman conquests and the development of trade contributed to the expansion of geographic knowledge, but virtually none of the maps drawn on parchment or papyrus during that period have survived until today. Nevertheless, some traces are left in the second half of the 1st century of the work of land surveyors (agrimensores, in Latin), who used to measure the fields and divide into centuries the land subjected to Rome along the main roads, which was the origin to the first wide survey of the territory.

The Romans added nothing to the theoretical basis about the shape and size of the Earth obtained from the Greeks, nor about the distribution of land and water and the ways to represent a spherical surface on a plane. They took credit, in the field of cartography, for their great practical skills, as witnessed by a famous relic dating back to the III or IV century CE, which is known to us thanks to a late medieval copy produced by the geographer Castorius in the XIII century: the Tabula Peutingeriana (Tabula: geographic map in the Roman period, Peutingeriana: from Mr. Konrad Peutinger who found it). It is constituted by a strip, 6.80 m long and 34 cm wide, which represents the outlines of the Roman Empire, from the Iberian Peninsula to the Caspian Sea, including information on roads, towns, distances between them, rivers, mountains, etc.

In the meantime, Marinus of Tyro (I century CE), following the intuitions of the astronomer Hypparcus, used for the first time a grid of reference lines, i.e. meridians and parallels, rectilinear and equidistant. Thus he paved the way to the realization of maps based on a geographic grid, which fixes the different points on the map in relative positions similar to the real ones.

This geometric aspect is particularly evident in Ptolemy’s planisphere, the only one from the ancient world, which is based on mathematical and geometric methods for the Earth’s representation, namely on a long series of longitude and latitude data, reported on a conical projection grid with circular parallels and meridians converging to the Poles (Fig. 2.7 and Plate 2.1).

The subsequent barbarian invasions caused the loss of a large part of the knowledge acquired in ancient times. Only some notes were saved thanks to the preservation by the Arabs and by Christian monks in the period from V to the XI century.

A renewed interest in cartography was registered in Sicily in the XII century thanks to Abu Abd Mhammad, an Arab better known as Edrisi or al-Idrisi. Thanks to him, geography started to rely on direct and precise knowledge, whereas until that time the influence of imaginary concepts and religious beliefs was of the greatest importance. The planisphere that Edrisi drew bears witness to this fact.

The invention of the compass gave a new impulse to cartography, with Genoese and Venetians travelling to Africa, while the Spanish and Portuguese reached as far as Sudan.

Another important figure in the history of cartography was Muhiddin Piri Ibn Haji Mehmet (or Memmed), born in Oelibolu (Gallipoli, Southern Italy) between 1465 and 1470, who died in El Cairo, Egypt, in 1554. He used to be a Turkish pirate, probably of Greek origin. He became Admiral (Re’is in Arabic) of the Crescent fleet and lived in the time of Suleiman II the Magnificent (1520–1566). As Admiral, Piri Reis had free access to the Imperial Library of Constantinople, where many old maps, never afterwards found, were preserved. Finally, he managed to draw a world map. It was the month of the blessed Muharrem, that is the Muslim year 919, corresponding to the period of the Gregorian calendar which goes from March 9th to April 7th 1513 CE, and the map was given as a gift by the admiral to sultan Suleiman I the Cruel (1512–1520) in 1517. This map, considered one of the first world maps showing the Americas, if not the very first, is surely the most precise map drawn up in the XVI century (see Plate 2.2).

He had a passionate interest for his collection of old maps and was considered an experienced man concerning the lands and coasts of the Mediterranean Sea, so in 1523 he was commissioned by Suleiman to draw an atlas which has become a milestone in the history of modern cartography. Some parts of this atlas are still preserved in the Berlin Museum. This book, intended as a navigation atlas, was the Kitabi Bahriye (The Book of the Sea), in which Piri Reis described all the details of coastlines, beaches, currents, bays, straits and shallow waters of the Mediterranean and Aegean Seas.

Reis, constantly searching for new information, also obtained some maps from a mariner who sailed with Christopher Columbus, whose drawings on the parchment, even though yellowed, were very precise.

Be that as he may, the real great innovation in cartography begins in 1569, thanks to Mercator, who first adopted scientific and mathematical procedures to apply a cylindrical, isogonic, increasing latitude projection still known as the conformal cylindrical representation of Mercator.

The very first atlas, intended as a collection of geographic maps, was created in 1570 by Ortelio with the cooperation of most geographers of that period, many Italian among them, who drew the maps according to the knowledge and results of the latest explorations.

More generally, during the Renaissance, Ptolemy’s studies were taken into consideration again, and the grid of parallels and meridians became the reference system that is still used today. Between the XVI and XVII century, directly under the influence of Ptolemy’s innovation, different kinds of projection were introduced, supported by the development of studies in geometry and pictorial art.

Abraham Ortelio in 1570 arranged the Theatrum Orbis Terrarum, the first world atlas.

Gerard Kremer in 1595 introduced the cylindrical projection which still bears his name.

Snellius (XVII century) introduced the trigonometric techniques for the detection of points.

Thereafter, from the XVIII century on, more detailed cartography overcame the restrictions of surveying large properties or military buildings, and land registries started to be compiled.

With the development of new optical instruments, triangulation procedures were introduced, together with the measure of the length of one longitude degree at different latitudes. This was how the realization of modern maps started: in these maps, most of the main points were determined geometrically. An example is the map of France at 1:86 400, drawn by Cassini between 1744 and 1815.

Lambert (XVIII century) and Gauss later generalized the use of modified representations and originated to national cartographies at small and medium scale (1:100,000–1:25,000). The most commonly used method of tacheometry is a complete survey method scheduling the simultaneous planimetric and altimetric survey of the ground; it is based on the use of relatively advanced topographic instruments.

With the birth of aviation, traditional field surveys were supported by the intensive use of aerial surveys.

With the introduction of the analogical stereo-plotter and the improvement of photogrammetric and image-interpretation techniques in the years between 1920 and 1940, the production of maps started to be definitely based on these instruments and methodologies.

The rest, i.e. the introduction of analytical and digital plotters, electronic processors, aerial and satellite remote sensing, digital sensors, information management and processing capacities, is contemporary history.

2.2 Earth Shape: Ellipsoid and Geoid

The size and the shape of the Earth are topics treated by geodesy. Precision measures, time analysis, distances, stars’ position, the force of gravity, etc. allow basic data to be provided for the realization of maps. The principles employed in Earth cartography are also valid and applicable to the cartography of the Solar System (Moon and Planets): Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.

Mankind has always tried to discover the Earth’s shape, using different theories. The Babylonians used to think that the Earth was a flat disk, floating on the sea. Aristotle assumed that it could be a perfect sphere floating in space.

Today we know that the Earth has an almost spherical shape which is very regular (Plate 2.3); in fact the distance between the deepest oceanic depth (Mariana Trench: ∼ 11,000 m) and the highest peak (Mount Everest: 8,847 m) is equivalent to about 1/322 of the distance between a point at the sea level and the centre of the Earth. A globe with 1 m radius would have, in scale, variations of about 1 mm for the two extreme situations in depth and height: as almost imperceptible depression and relief.

Even hypothesizing that the Earth is completely smooth, every point on the terrestrial surface is not equidistant from the core, and gravity’s attraction is different at every point due to

terrestrial rotation around its axis, which generates a centrifugal force (normal to its rotation axis);
some bulges and flattening respectively, at the equator and at the poles;
different composition and density of the upper layers.

Correct knowledge of the Earth’s gravitational field (treated by geodesy and in particular by gravimetry) unequivocally defines the reference surface of the Earth description: the geoid (Fig. 2.8a).

The force lines of the gravitational field (verticals), which are bumpy lines whose direction changes from point to point, together define the field itself and allow us to describe it through equipotential surfaces, or level surfaces (Fig. 2.8b), which are perpendicular to the vertical line at every point. The determination of the vertical at every point of the terrestrial surface is very easy: in fact, it is sufficient to position a plumbline, which unequivocally gives its direction in that point.

Among all the possible equipotential surfaces, the one that has been chosen as reference surface is defined by the mean sea level: the geoid. The geoid is a continuous, smooth surface which is particularly suitable for use as reference. It is found with good approximation based on the surface of the oceans, calculated using points of observations by tide-gauges.

As no reference of the sea and ocean surface exists, measuring the emerged part of the globe requires the use of gravimeters, instruments which can measure the gravity field.

The altimetric position of points lying on the lithosphere is referred to the geoid as an equipotential surface having physical more than geometric consistency.

Hence the geoid is an irregular, theoretical surface, which responds to physical, not mathematical considerations.

The Earth needs to be represented by a shape which allows the positioning of each point through mathematical processes. For this reason, the ellipsoid of rotation, which is the geometric surface that better approximates the geoid, has been defined as the reference surface of the Earth. The idea of spherical geometry was abandoned as the terrestrial surface is characterized by polar flattening, evidence of which has been demonstrated in different historical periods.

As early as 1670, Newton set out a theory to demonstrate that the Earth is not a perfect sphere.

The origin of this geometric anomaly with respect to the spherical model is generally explained in terms of the centrifugal force, C, produced by the rotation of the Earth around its own axis. As it rotates with a constant angular velocity, the zones closer to the equator tend to move with a higher tangential velocity than the zones closer to the poles. This determines the higher centrifugal force at the equator, which is the cause of equatorial bulges. At the poles, where the tangential velocity is lower, there is stronger gravitational attraction towards the centre of the Earth, which is responsible for the typical polar flattening.

Measurements made by the French Royal Academy of Science in 1735–1743 verified that, with same angular width, an arc of meridian at northern latitudes is much longer than the one at the equator (Fig. 2.9).

The Earth, subject to these forces, has a shape which is very similar to an ellipsoid, which is a geometric surface generated by the rotation of an ellipse around its own minor axis (Fig. 2.10). The ellipsoid represents the ideal surface for cartographic applications, as it can be defined in mathematical terms.

The ellipsoid shape is described by the relative length of the major semiaxis (equatorial) a and of the minor semiaxis (polar) b. The flattening ratio f tends to zero as the ellipse becomes more similar to a circle.

The ellipsoid parameters are

major semiaxis (equatorial): a
minor semiaxis (polar): b
first eccentricity: e² = (a²-b²)/a²
flattening: f = (a-b)/a

Note: in the oldest text books, flattening is indicated by α instead of f .

The ellipsoid equation referred to its own axes in geocentric coordinates is formulated as follows:

$$\frac{x^2 + y^2 }{a^2 } + \frac{z^2 }{b^2 } = 1$$

((2.1))

The ellipsoid calculation has been carried out through highly precise geodetic calculations, which in general terms follow Eratosthenes’ method, namely combining astronomical measurements and terrestrial distances measurements, now perfected.

Over the centuries, different ellipsoids have been described, whose geometric characteristics (Table 2.1) were increasingly appropriate to represent an analytical approximation of the geoid.

Table 2.1 Common terrestrial ellipsoidal dimensions used in the past and the WGS84, current reference system, adopted internationally. The Earth’s lithosphere is slightly flattened along the polar axis

Full size table

The task of geodesy has always been the definition of the rotation ellipsoidal parameters according to various methods used in different periods:

geometric operations, characterizing meridian and parallel arc measurements in the period from the XVII to XIX century.
gravity measurements, used in the XX century;
studies exploiting geodetic satellites, which represent the boundary of current methodologies, as GOCE (Gravity field and steady-state Ocean Circulation Explorer): the ESA satellite gravimetric mission.

The Weights and Measures Commission, in 1799, gave the measure of 6,375,739 m for the ellipsoid equatorial axis. In the following years, different measures were suggested (Everest, Bessel, Clarke, Helmert) until the Hayford measure was internationally adopted in 1924 at the suggestion of the International Geodetic and Geophysics Commission.

The geodetic geocentric ellipsoid WGS84, its last realization dating to 2004, was finally defined through modern measurement systems and is still current.

From an historical point of view, but still with serious repercussions on current national cartographies, the problem of defining reference ellipsoids was traditionally dealt with the local scale, separating the planimetric aspect from the altimetric one through the definition of local ellipsoid and geoid. Only the introduction of satellite positioning systems allowed the use of global geocentric systems.

The national cartography of all countries still refers to ellipsoids with a local orientation, so as to better approximate the region represented. It often happens that local reference systems use ellipsoids with common parameters with geocentric ones, but with different orientation; if that is the case, it is called the datum.

Whatever is the ellipsoid adopted, the problem of altimetry is still related to the knowledge of the geoid, particular to the evaluation of the deviation from the vertical. The vertical, V, normal to every point of the geoid surface, generally does not coincide with the normal, N, to the ellipsoid surface; the angle formed by the two directions is defined as deviation from the vertical (ε) (Fig. 2.11a).

Its determination is one of the goals of geodesy: the knowledge of the deviation of a large number of points uniformly distributed over the terrestrial surface allows one to retrieve the geoid shape in relation to that of a specific ellipsoid. Nevertheless, thanks to sophisticated satellite measurement, an almost direct determination of the geoid is possible. Without these data, it would not be possible to link the orthometric (referred to the geoid) and the ellipsoid heights (Fig. 2.12).

2.3 Reference Systems

A reference system is the set of measures and rules for the positioning of the terrestrial surface points in space, according to an established coordinate system.

Once the physical and geometric representations (respectively geoid and ellipsoid) of the terrestrial surface are defined, the problems are the bi-dimensional representation on the map plane and the relations among the different reference systems involved.

The combination geoid–ellipsoid is reflected, in terms of points positioning, respectively in the solution of the altimetric–planimetric problem.

The determination of a convenient reference system requires one to define a global/geocentric reference surface (ellipsoids with geocentric orientation) or a local one (ellipsoids with local orientation).

The choice of the surface, the determination of its dimensional parameters and the definition of convenient geocentric, Cartesian, geographic, etc. coordinate systems do not solve the problem of planar cartographic reference systems which, on the contrary, are based on different types of representations.

The problem of the most suitable modelling of the Earth’s surface, related to the irregularity of the geoid, determines a non-univocal identification of the reference surface. In a national and international context, this leads to a large number of ellipsoids and their positioning the space so as to locally realize the best approximation to the geoid.

2.4 Ellipsoid and DATUM

Before the high demands for global systems valid for the Earth’s surface related to new technologies, like space geodesy and the use of the satellite positioning systems, every nation adopted its own reference system, orienting an ellipsoid with respect to a point defined on their territory, called the emanation point.

An ellipsoid is defined as oriented with reference to a point on the Earth’s surface when it satisfies the following two conditions:

it is tangential to the geoid in that point;
the deviation between the vertical of the geoid and the normal to the ellipsoid assumes constant values at that point.

A planimetric datum is the mathematical model of the Earth, defined by a set of rules and measures, used to calculate the geographic coordinates of the points.

The geodetic reference system, datum, is constituted by fixing the following elements:

ellipsoid;
point of emanation;
azimuth.

In practice, it is constituted by

eight parameters: two parameters of ellipsoid shape, six parameters for position and orientation (directing cosines of a semiaxis);
points compensated network, extended through the area of interest, which fixes it.

In the same datum, many coordinate systems can be used: the transformations from one system to another are always entirely mathematical and do not require the introduction of measures. By contrast the transformation between two datums can be calculated only when there are enough measures linking points in the two systems.

2.5 Coordinate Systems

The coordinate systems which can describe the position of a point in relation to the reference surface are defined on the chosen datum. Knowledge of these systems is fundamental to all procedures of data georeferentiation and for transformation from one reference system to another.

2.6 Ellipsoidic (or Geodetic or Geographic) Coordinates

The geodetic, or geographic, reference system is a particular reference system for the positioning of points on the Earth’s surface, based on angular units.

The position of a point in space is determined through latitude and longitude angular measures (Box 2.1) and through the ellipsoidic height (Fig. 2.13); this way, planimetric and altimetric problems are separated.

The determination of the geocentric geodetic systems, like WGS84, is obtained through parameters like:

angular velocity ω;
gravitational constant GM;
second-degree gravitational normalized coefficient C20.

Box 2.1 Geographic definitions

Full size table

As no particular meridian is identified by a specific characteristic, since all are identical, in 1884 the meridian passing across the Observatory of Greenwich in Great Britain was conventionally adopted as starting point 0°, i.e. the fundamental meridian or first meridian. Longitude increases progressively eastwards and westwards up to 180°, completing an angle of 360° in the two directions. In relation to time series measures, the meridian is slightly shifted, as noted in the following observations regarding the terrestrial axis variations.

According to these rules, it is possible to generate a geographical grid made up of meridians and parallels having the following characteristics:

meridians and parallels intersect with a 90° angle;
number of possible meridians and parallels is infinite.

Meridians are

half of an ellipse from South Pole to North Pole;
at maximum distance from one other at the equator and converging at the Poles.

Parallels are

complete minor circles except for the equator which is a complete maximum circle;
always parallel to each other (Fig. 2.14).

For a curved surface, like rotation ellipsoids, we have the following reference geographic coordinates:

longitude (λ): measured in degrees in the range λ: ±180° with respect to the Greenwich fundamental meridian (λ: 0°) or other local ones (Monte Mario, Iron Island, etc.)
latitude (φ): measured in degrees with respect to the equator. It ranges from φ: +90° at the North Pole and φ: –90° at the South Pole, with φ: 0° at the equator.

2.7 Cartesian Geocentric Coordinates

The spatial reference of a point is given by a triple of Cartesian coordinates (X, Y, Z) referred to a system having its origin in the centre of the ellipsoid (Fig. 2.15b).

An example of Cartesian geocentric coordinates is the WGS84 reference system (World Geodetic System 1984) in which the Cartesian triple (X_WGS84 Y_WGS84 Z_WGS84) has the following characteristics:

origin at the terrestrial centre of mass;
Z_WGS84 axis, oriented towards the position of the medium pole defined in 1984 by the Bureau Internationale de l’Heure;
X_WGS84 axis, defined in 1984 by the intersection of the medium equatorial plane with the plane of the Greenwich meridian;
Y_WGS84 axis, oriented in order to complete a clockwise turn, lies on the equatorial plane.

WGS84 system is used for positioning through GPS (Global Positioning System) technology.

2.8 Planar Cartographic Coordinates

These are the East (E) and North (N) coordinates which determine a reference on the Cartesian plane; they are linked to the geographic coordinates through known analytical transformations whose shape depends on the projection adopted. The planar cartographic coordinate system, for instance in Gauss representation, has

axis (E): coinciding with the transformed equatorial tract for the projection zone;
axis (N): coinciding with the transformed zone central meridian.

Mixed coordinates systems are used both in topography and in geodesy: this happens because planimetric and altimetric problems are treated separately, using the geographic coordinates referred to the ellipsoid for planimetry and those referred to the geoid for altimetry.

2.9 Cartographic Projection

For cartographic representation purposes, it is necessary to project the points recognized on the ellipsoid onto the map plane through appropriate analytical transformations.

As it is not possible to project or develop a spherical surface onto a plane without altering the figure size and shape, every planar representation of the Earth necessarily introduces distortion.

It is possible to keep some characteristics unaltered to the detriment of some others. According to the properties which are kept unchanged, it is possible to define different types of planar projections:

equivalent: maps which keep unaltered the ratio between the areas of the represented surfaces. In these maps, equal areas on the map correspond to equal areas in reality.
conformal or isogonic: maps which keep unaltered the angles between two directions in reality and on the map. In isogonic maps, the angle between two directions in reality is the same as in the map;
equidistant: representations along a particular direction, such as the equator or a meridian, along which the scale factor is kept constant;
aphylaptic: maps which present all the alterations described above, but trying to keep them as small as possible in size.

Only the planisphere is a scale representation which can be considered at the same time equidistant, equivalent and conform. For planimetric maps, this is not possible; for example, they may be equivalent but not isogonic. Therefore, it is usually appropriate to choose a specific representation according to the use for which the map is meant.

Figures 2.16 and 2.17 show some distortions caused by the cartographic representations.

The cartographic representations are classified according to the technique used to create the grid of meridians and parallels. A first distinction separates the projections into pure and modified geometric ones, the former being obtained only through the application of geometric principles, the latter being modified using mathematical functions.

The cartographic projections are obtained by

perspective projection, projecting the ellipsoid points onto a plane;
development projections (cylindrical and conical), projecting onto auxiliary geometric surfaces that can be developed into a plane;
Pure geometric projections, e.g. the polar stereographic one, are currently scarcely used.

In general, maps are nowadays generated through analytical projections: Mercator, Gauss (UTM), Lambert representations, developed mathematically.

2.9.1 Perspective Projection

Some perspective projections may be conceived as follows: imagine that the world as a sphere with iron wire meridians and parallels and suppose that a luminous source generates a shadow of this object on a flat screen tangent to the surface itself. This shadow is an example of perspective projection.

According to the position of the luminous source, the projections can be distinguished as (Fig. 2.18):

centrographic or gnomonic, with point of view (V) or luminous source in the centre of the Earth (C);
stereographic, with point of view lying on the Earth’s surface;
scenographic, with point of view lying outside the Earth’s surface;
ortographic, with point of view or luminous source supposed to be at or near infinity and hence with rays or projection lines in parallels.

In relation to the tangent point of the plane, the projections can be distinguished as

polar, with tangent point in correspondence with the poles;
meridian, with tangent point lying on the equator;
oblique, with any tangent point.

2.9.2 Development Projection

In development projections, the points of the Earth’s surface are transferred onto an auxiliary surface which is then laid onto a plane to produce the map. The most commonly used projection has a cylinder as auxiliary surface (Fig. 2.19).

The Mercator representation is a direct cylindrical projection analytically modified in order to make it conform.

Gauss conformal representation, also known as Mercator transverse projection (or Universal Transverse Mercator – UTM), although with a grid shape similar to the cylindrical inverse, is actually analytical.

2.10 Examples of Cartographic Projections

2.10.1 Mercator Map

A Mercator map is derived from a central direct cylindrical projection, modified in order to make it conformal (Fig. 2.20). Using the ellipsoid as reference surface, the space between the parallels does not increase so evidently as in the central cylindrical projection.

A characteristic of Mercator map is to have meridians and parallels intersect at 90° angle, and a scale factor varies greatly depending on latitude.

Moreover, the use of this projection for areas far from the equator is not generally recommended, as the linear deforming module increases with latitude.

On a Mercator map, a straight line intersects all the meridians at a constant angle, being a line with a constant direction on the Earth: this way the lines with constant course, or loxodromics, look like straight lines, easy to trace, with an obvious advantage, for example, in navigational use.

2.10.2 Gauss Map

Gauss is the most commonly used projection in the world; it is similar to a cylindrical inverse, but derives from an orthomorphic cylindrical equatorial projection, originally suggested by Lambert, and later generalized by Gauss (1777–1855) who referred it to the ellipsoid (Fig. 2.21). During the last century, several scholars introduced some modifications and reports on it, such as Boaga for Italy and Krueger for Europe. The UTM system is based on this projection.

The Gauss representation is conformal. The transformed central meridian and equator are straight lines that become the axes of the planar reference system and are called East and North. The transformed meridians and parallels are families of perpendicular curves, symmetric with respect to East and North axes.

In order to limit the linear distortions, it is necessary to represent an area which is subdivided into longitude bands, called zones. In the UTM system, the Earth has been divided into 60 zones, each 6° wide, numbered from 1 to 60 proceeding from West to East and starting from the Greenwich anti-meridian. The area that can be represented in a zone is a small portion of the Earth’s surface and thus it is necessary to join more zones in case wider areas need to be represented. This representation system is called polycylindrical. Between two adjacent zones, there is always an area of overlap, in which the coordinates of both zones can be expressed.

Every zone is divided into 20 horizontal belts marked by letters and 8° wide (up to φ: ± 80°).

Every zone has its own planar reference system, which is independent as the central meridian changes from one zone to another.

Every zone has a false origin located 500 km East of the central meridian, in order to avoid negative coordinates, as at the equator the zone is about 666 km large, and the North coordinate originates at the equator (Fig. 2.22).

Every zone is divided into squares 100 km as a side, marked by pairs of letters. Any point of the globe is bi-univocally determined by

two numbers: zone;
three letters: one for the belt, two for the square;
eight consecutive numbers: four for the E and four for the N.

2.10.3 Polar Stereographic Projection

This is a pure perspective projection which is conformal. It is used to represent the polar caps, integrating the UTM cartography. In this representation, parallels are traced as circumferences, while meridians are transformed into straight lines. Parallels and meridians intersect at a 90° angle.

2.10.4 Lambert Conical Conformal Projection

The lambert projection is an analytical representation which can be derived from a direct conical projection, where the cone axis corresponds to the terrestrial rotation axis. The cone is tangent to a parallel, called the standard parallel, which is usually taken as the medium parallel of the area to be represented.

Developing the cone onto a plane, the map surface is defined within a circular sector. Meridians are represented on the plane by the cone generating line and thus by straight lines coming out from the homologous point of the cone vertex, while parallels are represented by arcs of circumference which have their centre in the meridians’ convergence point (Fig. 2.23).

2.10.5 Earth Globe Projection: The Planisphere

The possible equivalent representations of the whole Earth’s surface, also called planispheres, are numerous.

The globe or planisphere is an evocative and often artistic way to represent the Earth at a very small scale.

2.11 Reference Scale

When using a planisphere, the reference scale is the ratio between the measures taken among the points of its surface and the measures taken among the same points on the Earth. If the diameter of the planisphere is 1 m, the scale is 1:12,756,370 since this number is the diameter of the Earth in metres, supposing it has a spherical shape.

The scale of a map is the ratio of a single unit of distance on the map to the equivalent distance on the ground. The scale can be expressed in four ways: as a ratio, as a fraction, in words and as a graphical scale. Other secondary ways, like the area scale and the relative scale, are only seldom utilized.

2.11.1 Scale Factor or Scale of Reduction

If the scale of a map is formulated as the ratio between two distances, on the map and on the Earth, this relation is defined as scale factor or representative fraction. The scale factor is dimensionless, thus both terms of the relation must have the same units. The first term represents the distance on the map; the second represents the distance on the Earth. We define reduction scale, or scale, as the ratio between a length measured on the map and the corresponding one measured on the ground:

$${\rm C}\ :\ {\rm T} = {\rm 1}\ :\ {\rm N}$$

where: C: length on the map; T: real length on the ground; N: scale denominator.

For example, in the scale factor 1:25,000, which can be written as a fraction: 1/25,000, 1 cm on the map corresponds to 25,000 cm on the terrestrial surface.

2.11.2 Graphical Scale

A graphical scale is a ruler with ground distances added, included in the margin of most maps. The graphical scale is used to measure distances on the map corresponding to the real distance between two points on the Earth. The distance on the map is marked on the edge of a sheet of paper, which is then placed over the graphical bar scale and the distance read.

This type of scale facilitates the reading of maps reproduced in different dimensions as it follows the enlargement or the reduction.

With the scale factor, this is not possible: the scale has to be recalculated any time there is a reproduction which modifies the dimension of the map.

2.11.3 Area Scale

The area scale, or unit of area, namely the square of the linear scale, is suitable to express the relation existing between an area on the map and the corresponding terrestrial surface. It is used for quick plotting, detail drawing, estimating the number of hectares in given irregular area and accurate measurement of land. It is often placed beside the graphic scale in the thematic maps to allow a quick computation of the surface.

2.11.4 Relative Scale

A relative scale refers to the size of the representation on an image as compared to the size of the object on the ground. In this case, the scale refers to the pixel size.

In orthorectified digital images and numerical cartography, within which the concept of scale is not conceived as in traditional cartography on paper, the scale is usually adopted as a nominal scale: this scale coincides with the scale of a traditional map with the same contents, level of detail and precision.

The term relative can also be related to the definition of scale. In describing the same spatial data, a geographer could refer to it as small scale, whereas an ecologist could refer to it as large scale.

Therefore, the terms small, medium, large scale, or smaller or larger, are often used in common language with reference to the comparison between different scale maps. This quite general language has often created confusion and misunderstanding.

In geomatics, the term small scale refers to a map which covers a relatively large surface of the Earth with the possibility of detecting few details.

The term large scale refers to a map with a high level of detail which covers a relatively small surface of the terrestrial surface.

Although no official limits have been adopted internationally, a commonly agreed classification of topographic maps is shown in Table 2.2.

Table 2.2 Map scale

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2.12 Cartography in the World

All over the world, many institutions, companies and organizations are engaged in activities associated with maps and mapping. In general, they work at different levels, starting from the national (or even sub-national) one and reaching the continental and even global level. International experiences in the field of cartography have always been made difficult by the highly variegated standards, datums and reference systems used for map production; for example, when comparing cartographic products coming from neighbour states. Therefore, international initiatives in establishing supra-national references and standards have become increasingly important over time, especially with the increasing use of global positioning systems through satellite measure.

2.12.1 Cartography Projection in the World

Traditionally, since maps production is a sensitive aspect of power maintenance, administration and government, and also due to the necessity to better depict the territory using local reference systems, cartography has been a national matter, developed and managed through standards and methodologies that were not shared with other nation states. During the last 50 years, a new impulse has been developed for enhancing international cooperation and the supra-national establishment of reference systems, but the vast majority of cartographic production available nowadays shows a large number of both datums and projections, as the example of Table 2.3 shows.

Table 2.3 List of national map projections and datums used in countries worldwide

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2.12.2 International Reference Systems

2.12.2.1 Geocentric System WGS84

As GPS technology expands into the field of topography, a geocentric and global reference system has become needed, in addition to local reference systems already in use: this is the World Geodetic System, whose latest revision is WGS84.

WGS84 is currently the reference system used by the Global Positioning System (GPS), among others. It is geocentric and globally consistent within ±1 m. Current geodetic realizations of the geocentric reference system family International Terrestrial Reference System (ITRS) are geocentric, and internally consistent at the few-cm level, while still being metre-level consistent with WGS84 .

The WGS84 originally used the GRS80 reference ellipsoid but has undergone some minor refinements in later editions since its initial publication. Most of these refinements are important for high-precision orbital calculations for satellites but have little practical effect on typical topographical uses.

The latest major revision of WGS84 is also referred to as ‘Earth Gravity Model 1996’ (EGM96), first published in 1996, with revisions as recent as 2004. This model has the same reference ellipsoid as WGS84 but has a higher-fidelity geoid (roughly 100 km resolution versus 200 km for the original WGS84).

2.12.2.2 Unified European Reference System (ED50)

After the Second World War, as extra-national alliances were being formed, the need to realize a European Cartographic System for the newborn European Community members countries came up: this would be placed alongside to the national systems that all the countries had adopted. This objective was achieved by a general compensation of the European geodetic networks according to the following criteria:

reference ellipsoid: international ellipsoid (HAYFORD);
emanation centre: European medium orientation;
origin of longitude: Greenwich.

As regards the emanation centre, the deviation from the vertical has not been eliminated there, but a residual deviation has been left such as to minimize the deviations at the borders of the area to be represented. This is how the medium European orientation (European Datum 1950 - ED50) became defined.

The new orientation of the reference ellipsoid generates the variation of all the represented points coordinates. After the network general compensation operations, the countries’ trigonometric point coordinates assumed different values than in the national system (e.g. for Italy, Roma40). It is not possible to define analytic relations between the coordinates of a same point in those two systems (ED50 and a national one). Therefore, correction maps and tables both in terms of geodetic coordinates (φ, λ) and plane ones (E, N), called isotransition tables and maps, have been compiled to allow one to pass from one system to another with satisfactory approximation. The adopted representation is the UTM, according to what said above, to which the kilometric grid refers. UTM ED50 sheets have geographic coordinates according to the meridians and parallels transformed, but obviously there is no correspondence between the national sheets and the sheets of UTM ED50.

For example, the UTM ED50 kilometric grid is overlapped on the Italian national Gauss–Boaga reference system, so in the new IGM UTM ED50 production the Gauss–Boaga grid is preserved at the border of every map.

2.12.2.3 North American Datum (NAD83)

The North American Datum is the official datum used for the primary geodetic network in North America. In the fields of cartography and land use, there are currently two North American Datums in use: the North American Datum of 1927 (NAD27) and the North American Datum of 1983 (NAD83). Both are geodetic reference systems, but each is based on different measurements.

NAD27 is a datum based on the Clarke Ellipsoid of 1866. This Ellipsoid was created by a manual survey of the entire continent. The geodetic centre of NAD27 is a base station at Meades Ranch in Kansas.

As both satellite and remote sensing technology improved and were made available for civilian applications, it became obvious that the NAD27 approximations were not sufficiently accurate.

The North American Datum of 1983 was created to meet requirements for better accuracy and precision. It is based on the GRS80 ellipsoid; an ellipsoid derived from satellite geodesy.

ellipsoid: NAD83
a (major semiaxis): 6,378,137 m
e² (eccentricity): 0.006694300229

A point having a given latitude and longitude in NAD27 may be displaced on the order of many tens of metres from another point having the identical latitude and longitude in NAD83. So it is important to specify the datum along with the coordinates. The North American Datum of 1927 is defined by the latitude and longitude of an initial point (Meades Ranch in Kansas), the direction of a line between this point and a specified second point, and two dimensions that define the spheroid. The North American Datum of 1983 is based on a newly defined spheroid (GRS80); it is an Earth-centred datum having no initial point or initial direction. NAD83 is the datum currently used for North American (U.S. and Canada) official cartography, commonly displayed using Lambert conformal conic projection.

2.12.2.4 Geocentric Reference System for the Americas (SIRGAS)

The Geocentric Reference System for the Americas (Sistema de Referencia Geocéntrico para las Americas, SIRGAS), created in 1993 with the support of the International Association of Geodesy (IAG), is the regional densification of the global International Terrestrial Reference Frame (ITRF). Its definition is identical to the International Terrestrial Reference System (ITRS). The reference coordinates are associated to a specific (reference) epoch, and their variation with time is taken into account by discrete station velocities or by a continuous velocity model, which comprises tectonic plate movements and crustal deformations. Realizations or densifications of SIRGAS associated to different reference epochs give rise to the same reference system and, after reducing their coordinates to the same epoch, are compatible at the millimetre level.

The SIRGAS geodetic datum is defined by the origin, orientation and scale of the SIRGAS system, and the geographical coordinates are derived by applying the parameters of the GRS80 ellipsoid.

The extension of the SIRGAS frame is carried out by national densifications of the continental network, which serve as local reference frames.

The first realization of SIRGAS (SIRGAS95) corresponds to ITRF94, epoch 1995.4. It is given by a high-precision GPS network of 58 points distributed over South America. In 2000, this network was re-measured and extended to the Caribbean, Central and North American countries. To account for this extension, the meaning of the acronym changed from the original Sistema de Referencia Geocéntrico para América del Sur to the current Sistema de Referencia Geocéntrico para las Américas. The new realization (SIRGAS2000) includes 184 GPS stations and corresponds to ITRF2000, epoch 2000.4. The coordinate accuracy of these two realizations is about ±3 … ±6 mm.

2.13 Transformation Among Reference Systems

Territorial information from different sources is often characterized by different reference systems or different types of coordinates. For this reason, there are specific software application packages that perform with good precision any kind of transformation from national systems to WGS84 data.

The complete treatment of this topic would require much more detail than this book can provide, so the reader is referred to specific publications.

When facing the problem of coordinate conversion from one reference system to another, it is important to consider that the ellipsoids are locally oriented and the commonly adopted altimetric measures, i.e. the orthometric height H referred to the geoid, is separated from the ellipsoid itself.

2.14 Map Classification

Maps can be classified according to different criteria and in function of the discriminative elements taken into consideration.

2.14.1 Basic and Thematic Cartography

The term General Map, used by Anglo-Saxon authors, is generally acknowledged to refer to a map. Thematic maps are a different class than general maps and are aimed at more specific or circumstantial purposes.

The different phases of the realization of a map are based on a sequence of logical processes applied to the knowledge of tangible or abstract phenomena.

According to common currents of opinion, maps can be classified according to

content
scale
chronological facts.

As far the content is concerned, different types of maps can be distinguished as follows:

general maps, or reference maps, or topographic maps: the ground elements are represented providing all the possible information, as far as the scale permits, without considering special phenomena that regard human activities or particular physical phenomena (i.e. determining climate conditions or factors). The purpose is to represent the territory while preserving a metrical proportion of the elements’ size when possible or, alternatively, using a symbol;
thematic maps: referring to a simple topographic base; the purpose is to represent the territory by surfaces or themes with uniform characteristics; the base of the thematic maps thus comes from information obtainable through general maps.

2.14.1.1 Topographic Maps

Maps representing morphological elements of the ground, hydrography included, using conventional symbols, are the foundation of the topographic maps category, which is extended to include the position of urban areas, roads, railway lines, political and administrative boundaries and other human-made infrastructure.

Topographic cartography is metrical; historically it has been produced using topographic and airborne photogrammetric surveys. With satellite acquisitions using high geometric resolution sensors is now possible to produce metrical maps from satellite data, until now mainly used to produce thematic maps only.

2.14.1.2 Thematic Maps

With regard to thematic cartography, difficulties related to the definition and classification are confirmed by the late suggestion of a unifying term: the expression Thematic Cartography appears in 1953, at least three centuries after the publication of the first cartographic documents nowadays defined as thematic. Anyway, this name cannot completely replace the heterogeneous presence of names like special, applied, inventory, analytical or synthetic cartography.

The thematic map is an instrument of landscape data representation, both geometric and statistical or demographic, where the different aspects of the territory are represented through qualitative and quantitative symbols laid on a topographic or geographic map. The production of a thematic map includes processes of information extraction from different original sources, such as already existent maps, in order to obtain a new product. For each thematic map, an appropriate legend is compiled, thus enabling the user to read one or more phenomena concerning the territory.

Two elements emerge from the wide range of definitions of thematic maps:

the representation of one or more thematic classes, which introduce a characterization, is a specificity aimed at separation with respect to the basic cartography;
the permanence of a basic reference which is strictly contiguous with the previous one is needed.

The thematic map, involving a different, more articulated knowledge and analysis level than general cartography, highlights the distribution of single geographic objects by knowing the internal spatial variations of a built space.

The realization of thematic maps is addressed not only to researchers in geographic, physical or anthropical fields, but many social sciences also use them to represent and analyse data with reference to their spatial position. With respect to information representation using tables, the thematic map has greater capacity in terms of synthesis, visual effect and hypothesis of correlation among phenomena.

While the topographic map takes care of the metrical characteristics, the thematic map identifies the surface typology with precision. Thematic maps can be maps of altimetry, slope, exposure, land use, land cover, vegetation, lithology, erosion, urban development, land use modification, bathymetry (Fig. 2.24), etc.

Within thematic cartography, classes can be distinguished according to many parameters: characteristics of phenomena represented, representation means and techniques, theme categories.

Analytical maps provide information about the extent and distribution of one or more similar phenomena related to the characteristics of geographic space. These maps can represent punctual phenomena (e.g. well distribution), linear ones (e.g. the communication network) or areal ones (e.g. land use/land cover).

Synthetic maps provide correlations among more themes or define homogeneous areas according to specific unified analysis elements. These maps are being increasing by use in many applied fields related to land planning, operating with the overlay of different thematic planes in Geographical Information Systems.

Other expressions of thematic cartography come from depicting the instantaneous situation of a phenomenon, static maps, or from the cycle of its changes, dynamic maps.

According to the themes represented, maps can be distinguished in two categories:

anthropic, representing themes directly referring to the human presence and activities, such as demographic density, population socio-economic characteristics, land use types;
physical, to analyse natural phenomena, such as climate, geology, geomorphology, vegetation, fauna.

The symbology adopted for thematic cartography not only partially coincides with the general cartographic one but also has its own characteristics. As the thematic map is still closely related to its foundations, generally made up of physical (orography, hydrography, etc.) and/or anthropic (boundaries, road conditions, urban areas) elements, it is possible to exactly place the themes treated in the map and, at the same time, to note the correlations between the represented themes, distinctions and physical elements.

Moreover the thematic map can be

direct, if finding the needed information is linked with the interpretation of primary sources that provide data collected by direct investigations, such as observations, prospecting, surveys, inquiries, photogrammetry and remote sensing;
derived, if the information comes indirectly from secondary sources, i.e. by the use of already processed data and derivable from cartographic, statistical or bibliographical documents; for example the erosion map derived from the synthesis of information contained in the thematic maps of geomorphology, slope, exposure, etc.

As the orthophoto maps and orthoimages were introduced as the base on which the themes are overlayed, derived from aerial or satellite acquisitions giving an immediate view of the ground situation at the moment of acquisition and reporting, some references and numbers are needed to identify the classes.

2.14.2 Classification According to Scale

As the elements which can be directly represented are linked to their representation scale, obviously different scales require the adoption of different graphic standards (Table 2.4). In fact, reducing the scale factor increases the need to use conventional signs to represent ground elements of interest, which would not be representable elsewhere. If the maps have a kilometric grid and/or a geographic grid, with appropriate references, they are named regular.

Table 2.4 Classification of thematic maps and reference scales

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Maps are classified, with reference to their scale, as

geographic: from very small-scale planispheres 1:1,000,000;
corographic: from 1: 1,000,000 to 1: 100,000 excluded;
topographic: from 1:100,000 included to 1:5000;
technical: higher than 1:10,000 scale.

2.14.3 Maps from Satellite

An image’s geometric resolution limit is given by the image matrix cells size; enlargements over 2 pixels/mm generate the perception of a single cell as a discrete element (Box 2.2). For some applications where the spectral information is more important, it is possible to extend this resolution, producing an out-of-focus, pixellated image. When the images are reproduced and visualized by operating enlargements or reductions, it is more common to relate them to the ground by a graphic scale, which is better than the scale factor.

In any case, for convenience and comparison with traditional cartography the traditional scale factor is widely used. For studies dealing with the use of digital images, the representation of territorial information scales can be divided into three groups: global, regional or local.

A typical product that can be obtained through remotely sensed satellite images, undergoing a geometric correction and integrated with the insertion of some topographic elements and toponyms, is the space-map. This map is realized in very short time and is thus suitable for use in cases when updated information is more important than a detailed metric precision, i.e. for civil protection interventions.

2.14.3.1 Global Scale

This term refers to scales smaller than 1:250,000, used in studies at global level. In relation to the scale of intervention and to resolution characteristics, NOAA-AVHRR satellites are the most used. SPOT-Vegetation, Envisat-MERIS, Resurs-01, IRS-P3-WiFS, etc. are interesting for their potentialities. Possible applications are the study of the landscape’s historical evolution, contribution to forecasting agricultural crops, monitoring phytosanitary condition of large cultivated and wooded areas, production of small-scale thematic cartography, Vegetation Indices (VI), landscape units and land use analyses, thermal maps, agro-meteorological studies, etc.

Box 2.2 Relationship between the most frequently used satellite imagery, their applications and the most appropriate scales of cartographic restitution

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2.14.3.2 Regional Scale

This includes scales between 1:250,000 and 1:100,000, useful for regional or basin level studies. The second- and third-generation satellite sensors for remote sensing that belong to this group are Landsat TM, SPOT-HRV/XS, IRS-1C/LISS, Landsat ETM+, MODIS, etc. Updated and synoptic land use/land cover thematic cartography obtained by image classification is a valuable tool for medium-scale analysis.

CORINE and AFRICOVER projects have been realized at this scale.

2.14.3.3 Local Scale

The use of satellite remote sensing always refers to smaller scales than those generally used for technical cartography (1:5000–1:10,000), which is related to the representation pixel size which, in normal contrast conditions, does not affect the continuous vision of the image when its side is smaller than 0.5 mm. With this limit, the 10 m HRV/Panchromatic SPOT allows a theoretical representation scale of 1:20,000. Possible applications are land use/land cover classification, topographic and thematic cartography updating, etc.

Airborne multispectral and most of all hyperspectral acquisitions allow thematic representation at detailed scales smaller than 1:5000, with the possibility of going beyond the graphic resolution limit due to the high spectral information content.

New perspectives arise with the availability of space images acquired by high-definition sensors which, having geometric resolution lower than 1 m and able to perform stereoscopic acquisition, bring the use of remote sensing in large-scale maps production closes.

Maps have been classified in time in different ways, some of which are reported in Box 2.3.

Box 2.3 Map classification systems used in the past

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2.15 Technology and Cartography: Numerical and Digital Cartography

Nowadays, cartography has to deal with the vast spread of information technology, which is becoming manifest in everything, not only in scientific fields. By retaining its philosophical characteristics of consistency, truth and readability, cartographic subjects are passing through an evolutionary phase intended to assure their wider use. This changes its form and, through the form, the way it is used. Cartography skills nowadays presuppose a control of the data, less and less hardcopy, becoming more numerical, while applications within Geographical Information Systems (GIS) become the privileged users of basic spatial data. Cartography is available to users in three forms: traditional, automatic and numerical/digital, a sequence that also describes its evolution.

2.15.1 Traditional Cartography

Traditional cartography is a ground representation framed into a coordinate system, organized in drawn tables, completed by a frame and appropriate parameters.

The information represented is of two kinds:

planimetric: natural and artificial details of the ground are reproduced by projecting them onto the drawing plane;
altimetric: contour lines and elevation of point define the ground altimetry. The information is conceptually separated from the planimetric data and it can be represented through appropriate descriptive symbols.
The characteristics that turn a drawing into a map are also:
scale (1:N), where N is the scale factor indicating the number of times the distance between two points is reduced on the map;
map key, which gives the user the map interpretation key through the semantic evidence of the adopted symbols that refer to different types of lines, patterns, conventional signs, etc.

As stated above, a map is the product of the collaboration of disciplines like geodesy, topography, photogrammetry. It has to respect the three basic criteria of

consistency, contradiction between reported types of information has to be excluded;
reliability, the reported information must correspond to the reality;
readability, the interpretation has to be unique.

These criteria are the foundation of any kind of cartographic production and are independent of the technical evolution and the details specifically required in each instance.

They are defined by compiling appropriate lists reporting technical rules to follow during the map’s production in order to provide the customer with an a priori guarantee of the final product’s quality.

2.15.2 Automatic Cartography

Automatic cartography is the link between traditional cartography and the numerical version. It arises from production needs and is included in the traditional cartography production process in terms of numerical data management aimed at the reproduction of geodata on a map; it represents the traditional cartography content in numerical, vector or raster form and allows its easy reproduction.

It does not have a numerically codified structure of the geometric elements represented. It turns the hardcopy information into digital data during photogrammetric projection or later by vector or raster digitization of existing hardcopy cartography.

2.15.3 Numerical Cartography

Numerical cartography preserves all the qualitative and metric characteristics of traditional cartography, giving a representation defined as follows:

data storage and structuring are performed in numerical form on magnetic media of the represented objects’ coordinates and their codification with respect to the typology;
data visualization on video allowing management and hardcopy reproduction (plotter);
unlike traditional cartography, the visualization can be realized at any scale. It is then fundamental to be able to distinguish between:
- representation scale, which scale, can be any depending only on the software management adopted;
- nominal scale, uniquely defined by the metric accuracies respected during the production phase and established in the list of technical rules.

The nominal scale is the largest scale at which a numerical cartography map can be reproduced while preserving its metric accuracy. The visualizations at scales larger than the nominal one allow better reading of the data, but do not determine an increase of data accuracy.

Numerical cartography is a mirror image of traditional cartography in philosophical terms. While the latter is a drawing that contains, in implicit form, coordinates defining an object, the numerical form is made up of an organized archive of coordinates containing their visualization in implicit form.

The way numerical data are organized allows access to the electronic archives, which can be done through programming logics typical of computers. Hence information can be objectively extracted and is not only based on deductive skills of the human user in charge of the analysis.

Since it is intrinsically numerical, numerical cartography is univocal in metrical terms as it eliminates all the subjective elements in measurement operations done on hardcopy drawings and the problems related to this deformation and degradation. The object codification system also allows a qualitative univocity.

Numerical cartography automatically performs classification, selection, statistics based on the objects’ codification, geometry and topographic position. This makes the datum preferable for the realization and use in Geographical Information System (GIS).

With regard to information content, numerical cartography can be divided into

planimetric: only the objects’ planimetric coordinates (E, N) are stored;
plano-altimetric: the planimetric information about the objects’ positioning (E, N coordinates pairs) and the altimetric information about the ground, which preserves the form of contour lines and points of equal elevation (height), are stored separately;
3D: all the objects are described by their three spatial coordinates (E, N, orthometric height). In particular buildings volumetric units are described by their altitude at the eaves and at the base, assuring a useful three-dimensionality in different applications, not least the propagation of electromagnetic signals, which is interesting for telecommunications field.

2.15.3.1 Numerical Data Format

Numerical representation establishes the definition of a reference conventional nomenclature:

object, any natural or artificial element not separable any further (lake, building, etc.);
geometrical element, or geometric primitive, the minimum representation element (point, broken line, polygon) with which a codification is associated;
entity: complex object made up of one or more geometric elements.

As in the case of a traditional representation, the graphic element which represents the biggest difference is constituted by the curve line; in numerical cartography, this does not actually exist and is replaced by a broken line whose proximity among vertices has to be so dense as to ensure a difference between the real trend, continuous curve, and the represented one, broken line, less than the graphical error to the map scale. This concept lies at the base of the different techniques used in the restitution phase for the numerical representation of curve lines.

2.15.3.2 Information Content of the Numerical Data

In terms of planimetric content, numerical cartography has some innovative aspects in comparison with traditional cartography, mainly in relation to the representation philosophy based on a coordinate archive. This kind of archiving excludes the possibility of deduction processes typical of the direct observation of a drawing. In traditional cartography, a road can be intuitively recognized by exclusion, as it represents an area not belonging to the surrounding buildings, and not by its internal codification. In the numerical case, aiming the smart computerized access to the data, implicit information has to be made explicit by an appropriate codification. Hence, unlike the traditional case in which the objects represented have a background that can be classified deductively, in the numerical case there is no background to allow objects emerge from a visual inspection of the map. The whole area has to be filled in order to leave no space for deduction. Thus road sections and nodes have to be represented through codified polygons or points.

The territory is divided into homogeneous surfaces which are

isolated: all the surfaces that are delimited by closed broken lines (polygons) defined as separation lines (also shallow heights, like pavements) between artificial structures from a public space walking level;
services: areas intended to have homogeneous use occupied by permanent infrastructures, like railway stations, airports, water treatment plants, power plants;
green areas: areas intended to have homogeneous use occupied by permanent land cover types like parks, camping areas, etc;
open spaces: agricultural areas, bare soil areas, quarries, landfills, etc.;
water bodies: lakes, rivers, harbours, basins, etc.;
road sections: road sections defined longitudinally by the objects delimiting them and transversally by virtual lines traced at distances that depend on the use of the data;
nodes: areas resulting from the intersection of many sections (squares, etc.).

Considering the altimetric aspect, when present, four categories are described:

elevation of points;
contour lines;
points of equal elevation describing the planimetry of an entity;
height at the eaves of volumetric units.

The last two categories only concern numerical cartography. In the first case, the altimetric description is given by a set of four coordinates, code, East, North, Altitude, of each vertex of a geometric element involved in defining the represented entity. They are usually at the base heights and have to be coherent with respect to the ground average altimetric trend indicated by the points of equal elevation and the contour lines.

In case of heights at the eaves of volumetric units, the auxiliary altimetric information is expressed as a correspondence of points internal to the volume described, to which the altitude at the eaves is associated.

2.15.3.3 Code System

Objects, geometric elements and codification of entities are necessary to assure data tracing and query automatisms which allow us to easily use geographic data.

One commonly used system (Fig. 2.25) is the tree structure, defined by strings of eight numerical characters subdivided into four pairs to provide description levels, for each of the 99 (01–99) different possible categories.

Character pairs AA represent categories from 01 to 99 for each level so each entity can be identified univocally.

Some examples of categories are Railway communications (01), Road conditions (02), Buildings and infrastructures (03), Hydrography (04), Vegetation (05), Orography (06), Administrative boundaries (07), directly surveyed points (08).

Cartography updating and multi-level query result facilitated this data organization.

2.15.3.4 Data Organization

In terms of data storage, the basic idea is to realize archive structures so as to allow quick access and efficient query management. This need is typical of the numerical cartography with respect to the traditional one and is at the basis of GIS.

The management of archives of codified coordinates that represent objects and entities is realized by relational structures, typical of electronic archives, which link information contents by pointers and field identifiers functional to this operation.

Archive files are structured by record, object describer or entity, to which they refer. As the entities are represented by the coordinates (code, East, North and Altitude) of the vertices of the broken line delimiting them, each entity defines a record with a different length from the others. This problem affects access efficiency and thus query speed. The basic idea is hence to split the information through the realization of nested files containing constant length records, related among them by appropriate pointers. In particular the information will be split by defining a file that describes the entities and a coordinate’s file linked to one another by pointers.

2.15.3.5 General Quality Criteria and Map Production Problems

This kind of numerical cartography requires, in the production phase, some controls for the solution of geometric incongruities which in the traditional case were automatically solved by the operator’s direct intervention. So, for instance, the non-intersection among lines or the non-closing of a broken line that defines a polygon in the traditional case would be meaningless. In the numerical case, instead, if a broken line delimiting an area cannot close, this area is not recognized when an automatic query is launched.

Some editing procedures have been developed, which can solve the following types of situations:

fusion of points representing the same vertex and many times assigned slightly different coordinates;
non-intersection among lines;
non-alignments;
non-parallelism;
non-squaring of right angles;
non-continuity of lines conceptually continuous;
non-congruence of altimetric data associated to contiguous entities.

Moreover, there are further geometric conditions and operational specifications to take into account when dealing with numerical cartography.

2.15.3.6 Production Methods

Three typologies of numerical cartographic data production are identified:

direct field survey with topographic instruments;
direct photogrammetric projection;
digitization of existing cartography.

Though this division suggests a corresponding data quality classification, based on the various components that concur to define a numerical cartography quality, control networks precision, celerimetric survey quality, flight altitude, aerial triangulation, editing quality, points collimation, etc., it is more appropriate to consider the categories listed above as a classification based on data generation:

1st generation, for direct survey;
2nd generation, for photogrammetric survey;
3rd generation, for the digitization of the previous two;
4th generation, for the direct numerical production during restitution phase.

2.15.3.6.1 Direct Survey

The direct survey not only is carried out by a tool set made up by an electronic or integrated theodolite (total station) for measuring the azimuth and zenith angles and the distances but could also be performed using an appropriate GPS instrumentation. It schedules the planning and realization of a general network and of the survey activity. Data are recorded in numerical format by the instrument and then transferred to a computer as fixed length files organized in codified records. Anyway, the codification and the file format have not yet been standardized.

2.15.3.6.2 Photogrammetric Survey

The direct photogrammetric survey is commonly realized in the same way as the classic photogrammetric projection. In this case (analogical, analytical or digital), plotters must have appropriate mass memories in which to store the large amount of coordinates and codes of the projected points and must complement automatic devices for measurements (encoders).

The difference with classic restitution is that the operator has to assign the appropriate code to all the projected entities. Dedicated visualization devices, or superimposition devices, allow, in the analytical and digital case, to overlap the already projected cartography in vector format onto video, so that the operator can have immediate feedback on his work.

Projection software, moreover, allows setting of the tolerance, the entity end and closure, the planimetric and altimetric closing, aimed to automatically solve some incongruence situations among those noted above.

There are four types of projected entities:

punctual;
linear or polylines;
areal or polygon;
text.

Plotters allow the automatic or semi-automatic generation of DEM (Digital Elevation Models) by collecting points that belong to regular grids with distribution and density characteristics defined by the operator. The result is an archive of X-, Y-, Z-coordinates corresponding to nodes of a regular grid.

2.15.3.6.3 Digitization of Existing Cartography

Third-generation numerical cartography production is certainly the most economical to realize. It includes a numerization process that transforms data on hardcopy maps into numerical data through digitizer devices.

This type of production, though, introduces some drawbacks:

degradation of data precision with respect to the original characteristics of the hardcopy document:

graphical error (0.2 mm) due to line heterogeneity and thickness;
support deformation (up to 1–2% values and can be anisotropic);
any parameters transfer error;

data precision degradation with respect to the original one, transformed by numerization instruments:

precision of the used digitizer;
precision in the points collimation/restitution, related to the quality of the pointing device;

considering its derived nature, it could refer to an obsolete hardcopy data source with insufficient updating;
the produced numerical data is planimetric. It is always possible to integrate it later with elevation of points and contour lines, adding graphic layers.

2.15.3.6.4 Instruments for the Digitization

Digitization, or numerization, is the operation that turns the data on hardcopy into numerical data by means of digitizers:

manual vector digitizers;
automatic scanning raster digitizers;
manual vector digitizers (Fig. 2.26).

They are constituted of three main elements:

plain surface (table) where the map lies;
pointing and acquisition device (cursor);
interface connecting to a computer.

The table is constituted by a plastic support over which a grid of linear conductors, run through by electric power, is overlaid; the cursor indicates a solenoid whose centre is represented by the pointing cross that defines the position of the solenoid in respect to the absolute reference that is the table. An appropriate interface transfers the position information to the computer that records it. A keyboard designed to assign the codes completes the pointing device. These instruments’ points positioning precision varies from 0.5 to 0.1 mm and mainly depends on the resolution (diameter and distance of the conductors in the grid).

Before performing this kind of acquisition, the operator has to orient the map, namely defining the planar roto-translation parameters with a four-parameter scale variation (most common transformation) to make the table coordinates (X, Y) coincide with the cartographic coordinates (E, N). This operation requires the identification of at least two control points on the map, their acquisition and the assignation of the corresponding cartographic coordinates. The number of points to be used in this phase (possibly belonging to the frame) is defined in the lists of rules as well as the highest residual differences acceptable after the orientation (generally < 0.3 graphical mm).

2.15.3.6.5 Raster Scanners

A raster digitizer, known as a scanner, is an automatic digitization system for which data, though numerical, are expressed as a matrix, like in a digital image (Fig. 2.27), and not as an archive of coded coordinates or vector mode.

In this representation, each element of the matrix generated during the scanning process represents the radiometric tone, or grey tone, correspondent to the graphic element that it represents. Thus black cells will refer to mapped entities, white cells to the background areas. The image matrix is generated by the following steps: illumination of the hardcopy support with a light source, acquisition (photo-sensitive sensor) of the luminous radiation reflected by the support itself and recorded signal analogical/digital conversion by a digital sampler. If the support is a colour one, the scanning is performed independently for the single representation bands RGB (red, green, blue) and consequently three independent matrices will be generated.

The scanning process is related to the resolution of the instrument, which defines the cell size in the image matrix, and according to the geometrical distortions generated.

The resolution is measured in dpi (dots per inch); the instruments on the market perform resolutions variable between 300 and 4000 dpi corresponding to cells’ physical size ranging between 80 and 7 μm. The lower limit is fixed in dependence of electronic constraints on the signal-to-noise ratio.

The most common devices aimed at signal detection are the CCD (Charge-Coupled Device), electronic components (chips) made up by photo-sensitive elements organized in linear vectors or matrices and able to transfer the radiometric information through variations induced in the electric units. The signal recorded by a CCD is an analogical one. At the end of the digitization, a sampling device (analogical/digital converter) has to proceed to the transformation. This can be performed according to different modes:

binary digitization: the recorded signal is represented by one bit only, this way determining the assignation of a value between 0 and 1 to each cell of the image matrix.
grey tone digitization: the signal is represented by a higher number of bits (4, 8, 12) such as to ensure an image made up by a number of degrading grey tones depending on the number of bits employed (4 bits: 2⁴ values, 8 bits:2⁸ values, etc.):
colour digitization: the generation of colour images can be obtained through 8-bit single scanning followed by assignation of a codified RGB palette, or by a scanning process characterized by separated RGB bands (24 bits) to be reconstructed in additive synthesis.

As the radiometric resolution, i.e. the representation bit number, increases, the amount of data to be stored increases too.

The process of image orientation also has to be carried out in the case of the scanning process, but this time after the acquisition, in order to align lines and columns respectively to the East–West and North–South directions. The transformation can still be a planar roto-translation with four-parameter scale variation, still with at least two necessary control points. Unlike the vector case, this operation is realized on a raster datum that involves all the cells, with reference to the entities mapped on the background, and requires a radiometric resampling operation that can alter the represented objects’ geometry.

In order to improve the processing and to transform represented entities into vectors, further processing procedures can be carried out.

The instruments on the market, according to their use and performance, can be classified as follows:

DTP scanners (DeskTop Publishing): addressed to non-cartographic applicative domains, they are the cheapest and most common product. They are planar and reach 1200 dpi geometric resolution. Usually they show such geometrical distortions and mechanical positioning instability to exclude an appropriate cartographic use.
photogrammetric scanners: they were ideated within the photogrammetric domain and have very high geometric resolutions and mechanical positioning accuracy ranging between 2 and 5 μm. The present size limits their use in relation to the hardcopy datum to be digitized, as they can work with an A4 sheet size at maximum. They are planar instruments, too.
cartographic scanners: they are generally rotating drum type, a fact which limits accuracy. They allow acquisition of size formats up to A0.

2.15.3.7 Data Transfer

The sharp conceptual and operative separation between the datum production and its use within a GIS requires facing the problem of transferring the numerical utilization, which is not yet univocally solved.

The production phase, as a consequence of production needs related to the instrumentation and to the operative modes, generates the datum in different file working formats that are often not managed by the information systems: these ones in fact, due to their internal structures and to the applicative domains to which they refer, tend to use different management file formats and surely different from those used in production.

This fact suggests defining a unified transfer file format so as to easily put the two productive and applicative/management segments in communication. For example, the main transfer files today adopted in Italy are the DIGEST (Digital Geographic Information Exchange Standard) and the NTF (National Transfer Format).

2.16 Map Reading

Geographic maps, and in particular large-scale topographic maps that are even more detailed, provide a faithful description of the characteristics of the represented territory. Their description is more detailed the bigger the elements drawn by conventional symbols.

In order to make clear the elements of the geographic maps’ description, it is important to recognize the meaning of everything the map reports and to be able to interpret what the map represents from a visual point of view.

According to its definition, a geographic map is a plane, approximated, reduced and symbolic representation of a more or less extended portion of a terrestrial surface. The symbols used, arbitrarily chosen by the cartographers in the past, have now been established by proper international conventional rules.

In modern maps, the different entities are represented as seen from above, according to a zenith view, not in partial or total perspective, as used to be the case in ancient maps. Maps, and in particular the topographic ones, show varied and considerable information; they represent existing physical or anthropic–geographic elements and imaginary elements too – like administrative, regional boundaries – different geographical grids, as well as information and data about the systematic, the editorial characteristics, etc., similarly to how information is reported on a printed book.

The elements reported on maps can be grouped as follows:

systematic and editorial ones;
geodetic–topographic, metrics and similar ones;
natural landscape;
anthropic landscape.

Cartographic symbols mainly reflect the last two elements. Its purpose is to describe the real world on maps, using conventional signs that are comprehensible to anyone and as quickly as possible. Some conventional signs have a direct relation with the represented object aspect (imitative symbols), both for their shape or for the organization of the elements that constitute them, while other ones, on the contrary, are independent of it.

Generally these symbols are always associated ones, as the landscape is mainly constituted by a complex of elements. The topographic representation of landscapes made by a single element, such as sea areas, big lakes, deserts, glaciers, can be considered exceptional. In flat alluvial zones, the represented elements are usually vegetation, hydrography, human activity elements, while in mountainous areas, together with the previous ones, there are others about orography, soil and rock aspects, exposures, etc. In the first case, there is a simple landscape, while in the second one the landscape is infinitely more complex as altimetric and planimetric aspects sum together; the map representing this latter situation requires more experience and good knowledge of representation techniques.

Legends were introduced in the XVI century, when two kinds of signs were used at the same time, together with writings and numbers, to represent, describe and denominate objects on a map:

symbols: signs only in part independent of what they represent;
signs: conventional signs completely independent of what they represent.

Usually the symbols are made by black graphical signs and, in polychrome maps, by colours with colour tones varying with symbol categories.

Simple graphical signs of landscape elements are points and lines which, properly arranged and combined, recall the real aspect of what is on the territory, making things easier for those who analyse the map.

For a long time, maps have been not only graphical products but real artistic compositions. With the modern representation techniques, graphical aspects have been partially preserved but artistic ones have been lost.

2.16.1 Elements of the Natural Landscape

Symbols used to represent elements and shapes of natural landscapes are much more numerous than geodetic and topographic ones and can be grouped into the following categories:

orography;
continental hydrography;
marine hydrography;
natural vegetation.

The last three groups of elements can be considered as one group including entities characterizing the planimetry of a region.

Orography is a non-flat region relief and can be represented using several techniques and systems variable in function of map type and scale. Lots of these systems are obsolete but have been widely used in the past, like

altimetric zonation;
dash, stroke or line;
herring-bone system;
hill shading;
hatching;
contour line system.

Since methods and instruments reconstructing and visualizing 3D models of the territory also in a dynamic way and with different angles of view (see Chapter 9) have been developed, the systems described above are valid for reading the already existing cartography and for the production of cartography that still relies on them.

The shapes that contribute to represent orography can be grouped in different ways, for example, in relation to the type of phenomena they represent (glaciers, carsism and volcanic phenomena, etc.) or to the specific objects (rocks, debris, peaks, etc.).

2.16.2 Elements of the Anthropic Landscape

Natural landscape elements and shapes are represented with particular symbols, which reflect human activities and most of its products. They have transformed the original aspect of the landscape and contributed to produce a new, anthropic one. The bigger the map scale, the bigger the number of elements in the anthropic landscape that can be represented. Some are independent and others correlate to those described above. They can be grouped as follows:

human settlements and various buildings;
communication lines;
irrigation systems;
agricultural land use, natural land cover excluded;
quarrels, mines and similar;
political and administrative boundaries, etc.

2.16.3 Generic Nomenclature

Besides the elements relative to the soil’s physical aspect and to human activity, all the maps types report various kinds of different importance scripts, related to what is represented; the map without these scripts is called mute.

Until 1840, the toponyms used to be transcribed without any particular rule, then it was agreed to use special graphic signs for different groups of toponyms. This way the scripts got a symbolic meaning, as it is possible to understand the toponyms’ importance or their differential relations in relation to the way they are realized (regular, italic, capital letters, bold, font size, etc.).

Toponyms of topographic maps, especially large-scale ones, often have intrinsic meanings, including for example a morphologic meaning. Thus, the toponym analysis is often useful in relation to the numerous cases in which a simple common name has become a toponym to which more than one place is associated. A complete toponym contains itself a reference to a particular aspect of the surface.

2.17 Summary

The purpose of cartography is to represent real geographic objects on maps, providing both a punctual and general knowledge of the territory, establishing spatial relationships among the reproduced objects and producing tools used in planning and management of territory. The origins of this science go back to very ancient times, passing through the Egyptians and Greeks, the Renaissance in the Mediterranean Basin, to the present day. One of its main issues since antiquity has been to give a 2D representation of the 3D Earth’s surface; a crucial step in this process is the definition of a reference surface (which is the subject of Geodesy) that better approximates the Earth’s surface in each portion. Once the geoid and the ellipsoid were defined as two different reference surfaces, the second one, responding to geometrical laws, was used to define several reference systems, both local and global. In relation to a reference system, several coordinate systems can be defined through mathematical models (DATUMs). The aim of a coordinate system is to describe the position of any point in respect of the chosen reference system.

Besides locally valid reference systems, some reference systems are recognized worldwide, like the WGS84 (World Geodetic System 1984), or at European level, the ED50 (European Datum 1950). The correspondence between local and global reference systems is not direct, and the coordinate conversion from one system to another is required. For this purpose, specific software performing with acceptable precision transformations from national, ED50 and WGS84 data have been conceived.

The production of maps is realized by projecting the reference surface of interest onto the map plane; this step produces some deformations. Maps are classified according to the type of deformation introduced by analytical transformation, or according to the characteristics of the projection or of the auxiliary surface onto which it is projected. Further parameters used to classify maps are the content of the map (general maps/thematic maps) and the scale (geographic, corographic, topographic, technical). The scale factor is a basic element of the map which gives an idea of the entity of the reduction of the map and affects the amount of detail that can be directly represented on the map itself.

As informatics is spreading in many sectors of science, cartography too has been influenced by computer technology. If traditional cartography is realized on paper boards, digital cartography is based on numerical format data that are visualized on a screen and allows the data to be dynamically used in Geographical Information Systems.

To be used, both traditional and digital maps need to be interpreted. In fact a geographic map is defined as ‘a plane, approximated, reduced and symbolic representation of a more or less extended portion of terrestrial surface’; according to its scale, any map reproduces many elements of the represented surface, which are expressed as symbols codified by a legend. Both natural and man-made elements are symbolically depicted, and toponyms are reported.

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National Research Council of Italy, Institute for the Electromagnetic Sensing of the Environment, Via Bassini, 15, 20133, Milano, Italy
Mario A. Gomarasca

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Mario A. Gomarasca
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Gomarasca, M.A. (2009). Elements of Cartography. In: Basics of Geomatics. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9014-1_2

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DOI: https://doi.org/10.1007/978-1-4020-9014-1_2
Published: 09 July 2009
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9013-4
Online ISBN: 978-1-4020-9014-1
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2.1 Milestones in the History of Cartography

2.2 Earth Shape: Ellipsoid and Geoid

2.3 Reference Systems

2.4 Ellipsoid and DATUM

2.5 Coordinate Systems

2.6 Ellipsoidic (or Geodetic or Geographic) Coordinates

2.7 Cartesian Geocentric Coordinates

2.8 Planar Cartographic Coordinates

2.9 Cartographic Projection

2.9.1 Perspective Projection

2.9.2 Development Projection

2.10 Examples of Cartographic Projections

2.10.1 Mercator Map

2.10.2 Gauss Map

2.10.3 Polar Stereographic Projection

2.10.4 Lambert Conical Conformal Projection

2.10.5 Earth Globe Projection: The Planisphere

2.11 Reference Scale

2.11.1 Scale Factor or Scale of Reduction

2.11.2 Graphical Scale

2.11.3 Area Scale

2.11.4 Relative Scale

2.12 Cartography in the World

2.12.1 Cartography Projection in the World

2.12.2 International Reference Systems

2.12.2.1 Geocentric System WGS84

2.12.2.2 Unified European Reference System (ED50)

2.12.2.3 North American Datum (NAD83)

2.12.2.4 Geocentric Reference System for the Americas (SIRGAS)

2.13 Transformation Among Reference Systems

2.14 Map Classification

2.14.1 Basic and Thematic Cartography

2.14.1.1 Topographic Maps

2.14.1.2 Thematic Maps

2.14.2 Classification According to Scale

2.14.3 Maps from Satellite

2.14.3.1 Global Scale

2.14.3.2 Regional Scale

2.14.3.3 Local Scale

2.15 Technology and Cartography: Numerical and Digital Cartography

2.15.1 Traditional Cartography

2.15.2 Automatic Cartography

2.15.3 Numerical Cartography

2.15.3.1 Numerical Data Format

2.15.3.2 Information Content of the Numerical Data

2.15.3.3 Code System

2.15.3.4 Data Organization

2.15.3.5 General Quality Criteria and Map Production Problems

2.15.3.6 Production Methods

2.15.3.6.1 Direct Survey

2.15.3.6.2 Photogrammetric Survey

2.15.3.6.3 Digitization of Existing Cartography

2.15.3.6.4 Instruments for the Digitization

2.15.3.6.5 Raster Scanners

2.15.3.7 Data Transfer

2.16 Map Reading

2.16.1 Elements of the Natural Landscape

2.16.2 Elements of the Anthropic Landscape

2.16.3 Generic Nomenclature

2.17 Summary

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