Cartography and Map Production

Determining Equiarea Projections for Geographic Information Systems

Pedro Castaneda, Universidad Distrital

Geographic Information Systems technology has been widely developed over the last years to such extent that it has current applications in all the professional fields. One of its main objectives is the homogenizing and standardization of information with the sole purpose of improving its management in order to obtain an accurate response of the phenomena present in the handling of Natural Resources. Different studies on the management of Natural Resources, using GIS, hope to identify areas that are utilized, affected, improved, transformed as well as those dealing with any modifications of the same. For this reason GIS is based upon existing cartography, which has been developed with a system of conformable projection. It stands to reason that the use of this projection does not enable an estimation of exact areas and distances. Taking this into consideration an investigation has been undertaken pretending to solve the problem. The current proposal hopes to show the results found; these gave us a methodology to select and EQUIAREAL projection and the way to transform the estimated information conformable with that of the equiarea. During the latest seminars and symposiums the needs of transforming the cartographic information utilized by the GIS into an equiareal system has been discussed, considering the cartography of a country or region is produced using a conformable projection.

2- GENERAL OBJECTIVES To prevent the study of the EQUIAREAL projection selection for GIS applications and the equation of the projection transformation conformable to the equiarea.

3- SPECIFIC OBJECTIVES - Presentation of the methodology of projection selection. - Projection selection. - Definition of the equation of transformation of current projection data into the selected one.

4- JUSTIFICATION Geographic Information Systems handle in their graphics modules points, nodes, lines, arcs and polygons. All its applications generally perform estimates of distances and areas based on the polygons created in the different coverages, but the coordinates of the vertexes that are used in these estimates are values transformed by a conformable projection which generates errors in area. To sort out this distortion it is required that the data be transformed by an EQUIAREAL projection.

5. THEORETICAL FRAMEWORK The terrestrial surface representation or part of it in a half plane creates a series of distortions that the cartography must solve. The most frequent distortions are those of angle and shape, in area, distance and direction, for which cartography has developed systems of representation that enable the elimination of one or various of such distortion. These area the CARTOGRAPHIC PROJECTIONS, where we find EQUIAREAL CONFORMABLE, EQUIDISTANT and AZIMUTHAL projections. It is impossible to generate a system that will eliminate all the types of deformations, but several of these can be adjusted. However, we cannot come up with a map that is both CONFORMABLE and EQUIAREAL. If it is conformable then the area is deformed and vice versa. To determine or select the projection for a map you must first execute a theoretical selection and then a mathematical one. This methodology was designed by TISSOT.

6- METHODOLOGY
6.1- A group of projections was selected from a theoretical point of view. From an array of existing, flat, cylindrical and conical projections those that were more adjusted to geographic location, geometric shape and properties to be preserved conditions were selected.
6.2- Select the definite EQUIAREAL projection following Tissot's theory. From the group of projection selected before we proceed to apply Tissot's theory. Which means defining the equations of flat coordinates x, y, gaussian elements and the semiaxis of Tissot's Indicatory Ellipse from which we can estimate the vectors or deformation in an angle, area, distance, and direction, that will finally enable the selection of the definite projection according to the objective of the study.
6.3- Determine the process of transformation of the coordinated estimated for the projection conformable to the equiareal projection. Once the EQUIAREAL projection has been selected we proceed to define the methodology that will allow us to transform the projection data CONFORMABLE to that of the EQUIAREA. The procedure can be executed using quadricules that will derive into an equation of transformation or by way of vectors of deformation defined by the semiaxis of Tissot's Indicative Ellipse.

7.- APPLICATION While checking the results a deodesic polygonal was selected and transformed by way of Gauss' Conformable Projection and The Equiareal projection was selected. Once the x, y values are found some of their points are plotted in each projection to see if their quadricules are parallel or form and angle. The conversion factors is applied according to the result. If they are not parallel the conformable data is first converted into equiareals to estimate their area; but if they are parallel the area is estimated with conformable data and the resulting area is affected by the corresponding factor of distortion.

Census Cartography

Emilse Rincon, Av Eldorado - Ofc 110

The National Administrative Department of Statistics - DANE- began developing since 1991 the project of cartographic update and automation and its main objective is to have an updated and automated census cartography that will make it possible to:

Establish a census cartographic base to be used nationally-wide in the urban areas as well as in the rural ones in order to give out georeferenced statistical data and to support the operative designs of census and research carried out by DANE, guaranteeing its geographic coverage.
Enable the making of thematic maps, analysis and modeling of statistical data, by way of integrating the corresponding spatial and alphanumerical information.
To supply specialist and researchers with tools that will ease the processes of evaluation of statistical information.

The process of complementing on the field cartography involved the dynamic work of an important group of national engineers and investments in field equipment, such as: compasses, metric measuring tapes and GPS. The work performed on the field enabled incorporating new developments of cartographic base and the addition of important sites of reference (schools, banks, health centers, among others): prior to the fieldwork, routes that enabled the coverage of the entire municipality were designed for the rural areas, so as to georeference the roads and main sites of interest like schools, churches, etc. provided that they were not present in the basic chart. It is important to point out that the sites of interest and roads are of utmost interest for DANE, because the census cartography must permit the major location reference on the field to those that will utilize it. The initial capturing (digitizing) of the information was performed in Spans-Tydig, and later of a graphic data base in ARC/STORM was developed for the storage, for which case it was necessary to transform all the digitized cartographic information into ArcInfo format, where editions are being executed to the said base to guarantee the accurate topological structuring of the geographic elements for its latter storage. A pioneer test in being carried out over the department of Atlantico in order to understand the storage methodology, test that includes approximately 25 100/1000 scale sheets and 35 5/1000 scale sheets of the urban area. With this information in hand we hope to come up with the methodology that will be used for the other departments. Arc/Storm, as the administrator of the data base, will permit future maintenance, cartographic update and modifications in the census sectorization due to city growth, in a rapid manner and in such a way that it will guarantee statistic comparison and the control of the coverage among the census and the different surveys undertaken.

DESCRIPTION OF THE CARTOGRAPHIC INFORMATION RURAL CARTOGRAPHY
The cartography of IGAC (Instituto de Agustin Codazzi) corresponding to different years and on a 1:25,000 scale was used as a base for most of the county, and for those zones where this scale did not exist, scales 1:100,000, 1:200,000 and 1:50,000 were taken from the IGAC cartography as well.

Roads Network- Includes all the types of roads, highways, ways, railroad tracks, with texts indicating the direction of where some roads lead to.
Hydrographic Network- Contains rivers, creeks, sewers, draining points, lagoons and ditches, with the corresponding names of rivers and creeks.
Hypsometry- Contains level curves, which were captured at 200 meters.
Toponimia and symbology- This level contain all the names of sites and symbols (construction, schools, mines, water tanks, etc.) found in the cartographic base that was used.

URBAN CARTOGRAPHY
To digitize the urban cartography the most updated cartography was used, information which would correspond to maps or plots produced by the Planning offices of the municipalities, departments, IGAC and/or DANE. Digital restitution was hired for the main 20 cities of the country (due to its density and extension), for which case the hired firms had to make the respective aerophotogrammetric flights and the corresponding digital restitution in 1:5000 scale. The digitizing of the urban areas include the following levels of information:

Graphic output: Includes the delimitation of blocks, names of boroughs, road nomenclature sites such as churches, schools, hospitals, hotels, etc., and natural formations.
Census sectorization: corresponds to the sector and section that make up the census areas defined by DANE for the execution of surveys.
Virtual Network (coverage): It is a polygon network where each block is enclosed and where each of the polygons a label (polygon identifier) is then assigned containing the basic information of the DANE code for the block, label that will later on enable the integration of the alphanumerical information to the graphic information.

Use of the Cartographic Production System (CPS) by the Swedish National Road Administration

Asa Carlsson, T-Kartor

The Swedish Road Administration is using the Cartographic Production System (CPS) to quickly produce maps at different scales. CPS operates as a cartographic database management system, using the concept of a Master Data Base (containing source data) and Product Databases, which define the display characteristics of map features stored in the Master Database. The Swedish Master DataBases (Karda) primarily contains road data and city location data. There are several different Product Databases in use. One is a map to help drivers of heavy vehicles to find a route with bridges that can support the weight of the vehicle or are high enough to let the vehicle pass underneath. Other map products may use different routing factors, such as dangerous goods limitations or rush hour traffic rules. The MDB is also used within an ArcView project that is distributed via CD-ROM to all departments within the Road Administration. The project displays new roads, tourist activities, etc. The graphic profile is created by the Map Layout Module of CPS. Other examples of map products are site location maps, background maps for television broadcasts of road conditions, and large sign products for tourism applications. The use of Product Databases maintains standardization among map types.

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