CARIS Geomatics Reference Guide

Transcription

1 CARIS Geomatics Reference Guide

2 CARIS (Global Headquarters) 115 Waggoners Lane Fredericton, NB Canada E3B 2L4 Phone: 1 (506) (English/French/Spanish) Fax: 1 (506) info@caris.com Assistance: support@caris.com Web site: CARIS USA 415 N. Alfred Street Alexandria, VA United States Phone: 1 (703) Fax: 1 (703) info@caris.us CARIS EMEA Bremvallei LV 's-hertogenbosch The Netherlands Phone: +31 (0) Fax: +31 (0) sales@caris.nl Assistance: support@caris.nl CARIS Asia Pacific Level 3 Shell House, 172 North Terrace Adelaide SA 5000 Australia Phone: +61.(0) info@caris.com December 2015

3 Trademarks owned by CARIS This is a listing of USPTO-registered trademarks and trademarks owned by Universal Systems Ltd. doing business as CARIS ("CARIS") and might also be trademarks or registered trademarks in other countries. Please note that laws concerning use and marking of trademarks or product names vary by country. Consult a local attorney for additional guidance. CARIS permits the use of its trademarks and registered trademarks only where they are used in reference to CARIS and its products, the markings used are appropriate to the country or countries of publication, and CARIS is explicitly acknowledged as the owner of the mark. CARIS reserves the right to withdraw this permission at its sole discretion for any use it feels is inappropriate or adverse to its interests. CARIS otherwise prohibits the use of any of its registered symbols, insignia, or other identifying marks without express written approval. Violations are subject to liability for damages, injunctive relief, attorney's fees and other penalties. Not all trademarks used by CARIS are listed in this document. Failure of a mark to appear on this page does not mean that CARIS does not use the mark nor does it mean that the product is not actively marketed or is not significant within its relevant market. The absence of a product or service name or logo from this list or the absence of a TM or TM Reg. USPTO notation against a product or phrase listed below does not constitute a waiver by CARIS of its trademark or other intellectual property rights concerning that name or logo. The following are trademarks or USPTO-registered trademarks of CARIS: Article 76 Module Bathy DataBASE Bathy DataBASE Server BASE Editor BASE Manager BDB CARIS CARIS and EIVA Survey Suite CARIS GIS CARIS Notebook CARIS Onboard ChartServer CPD Core Production Database Easy View EAM Engineering Analysis Module HIPS HPD HPD Server Hydrographic Production Database Limits and Boundaries Module LIN LOTS LOTS Browser LOTS Limits and Boundaries LOTS Article 76 One Feature, One Time Paper Chart Composer Paper Chart Editor Ping-to-Chart Product Editor Publications Module S-57 Composer SIPS Source Editor Spatial Fusion Spatial Fusion Enterprise Those trademarks followed by or footnoted as TM Reg. USPTO later in this document are registered trademarks of CARIS in the United States; those followed by or footnoted as TM Reg. CIPO are registered trademarks of CARIS in Canada; those followed by or footnoted as either TM Reg. USPTO and CIPO or TM Reg. USPTO, CIPO are registered trademarks of CARIS in both the United States and Canada; those followed by or footnoted as TM are trademarks or common law marks of CARIS in Canada and the United States, and in other countries. The trademarks and names of other companies and products mentioned herein are the property of their respective owners. Copyright owned by CARIS All written and image content in this document not protected by the copyrights of others is Copyright 2011, CARIS. All rights reserved. All reproduction and redistribution is strictly prohibited without the express prior written consent of CARIS. Copyright 2015 CARIS. All rights reserved.

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5 Table of Contents 1 General 2 Map 3 CARIS Mapping Information Earth s Physical Form Great and Small Circles Meridians and Parallels Scale Projection Ellipsoid Coordinate System Resolution Projections Projection Types Mercator Transverse Mercator Oblique Mercator Miller Cylindrical Robinson Sinusoidal Equal Area Orthographic Stereographic Gnomonic Azimuthal Equidistant Lambert Azimuthal Equal Area Albers Equal Area Conic Lambert Conformal Conic Equidistant Conic (Simple Conic) Polyconic Summary Glossary References Support Files About Support Files The Master File The Symbol File The Font Table The Colour Map The Colour Table Geodetic Parameter Files The Map Definition File The Datum File

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7 1 General Mapping Information This chapter deals with elements of cartography that might be useful when preparing a geospatial management project. In this chapter... EARTH S PHYSICAL FORM... 8 SCALE PROJECTION...11 ELLIPSOID COORDINATE SYSTEM RESOLUTION... 17

8 General Mapping Information Earth s Physical Form When viewed from a distance, the earth looks like a sphere, but it is actually an oblate spheroid a sphere compressed along the polar axis and bulging slightly along the equator. A cross-section through the poles gives an ellipse rather than a circle. The equator, positioned midway between the poles, is the largest possible circumference of the spheroid. According to the International Ellipsoid of Reference, the polar diameter is miles and the equatorial diameter is miles. Earth's oblateness, as expressed by flattening at the poles, is therefore miles or 26.70/7927= , a fraction slightly greater than 1/297. Great and Small Circles The surface intersection of any plane that cuts a sphere exactly in half is the largest circle that can be drawn on the surface of a sphere. These are known as great circles. Any circles produced by planes that do not cut through the centre of earth are smaller than great circles and are called small circles. Great circles have important properties with respect to such global subjects as navigation (shortest distance between any two points on the earth s surface), global positioning, and the subdivision of earth (parallels and meridians). Meridians and Parallels The axis of rotation provides a base for Axis of rotation the geographic grid, a series of intersecting lines drawn on the globe for the purpose of fixing the location of surface features. It consists of a series of north-south lines connecting the poles (meridians of longitude) and a set of east-west lines running parallel to the equator (parallels of latitude) A single meridian of longitude contains 180 degrees of arc that coincide with the north and south poles. Two opposite meridians of longitude cut through the centre of earth and represent a single great circle. All meridians extend in a true north-south direction. They are spaced farthest apart at the equator and converge to common 8 CARIS Geomatics Reference Guide

9 General Mapping Information points at the poles. For any point drawn on the globe there exists a corresponding meridian of longitude. The longitude of any location on earth may be defined as the arc measured in degrees along a parallel between that location and the prime meridian. The prime meridian is almost universally accepted as the one that passes through the Royal Observatory at Greenwich near London, England. It is also referred to as the Meridian of Greenwich and has an assigned value of 0 degrees. Meridians of longitude range from degrees west and degrees east from the prime meridian. Parallels are always parallel to one another and maintain equal distances apart. They are true east-west lines that intersect meridians at right angles. All parallels of latitude are small circles except the equator. Any point on the earth lies on a parallel except the north and south pole, which occupy a point. The latitude of any location on earth may be defined as the arc measured in degrees along a meridian between that location and the equator. Latitude values may therefore range from 0 degrees at the equator to 90 degrees north or south at the poles. CARIS Geomatics Reference Guide 9

10 General Mapping Information Scale Scale is the ratio between the size of a feature and its representation on a map. Scale is displayed in the format: Scale factors for the UTM grid. 1:scale_value [e.g. 1:10000] where scale_value is the relative size of a real feature compared to a map feature 1 unit in length. Scale_ value is sometimes called scale denominator since it represents the denominator of the scale ratio (the numerator is 1). A large scale map has a large scale ratio, meaning scale_value is small. A small scale map has a small scale ratio, meaning scale_value is large. Large scale maps cover small areas in detail. Small scale maps cover large areas in less detail. A large scale map might have a scale of 1:500 while a small scale map might have 1: The scale is important in GIS because it: aids in selecting the resolution at which data is stored determines what detail can be presented on a digital map The stated scale of the map is only true for the area where the line of tangency, or line of intersection, used in the projection touches or intersects the earth's surface represented by the map. Everywhere else the map scale will be slightly different from the stated true scale. The lines of the UTM grid are uniform in spacing so that the printed squares on a map are exactly the same in dimension. However, no map printed on a flat sheet can preserve a truly constant scale in all parts of the map. Consequently, the fact must be accepted that the 1000-metre grid square does not everywhere represent a ground square of exactly 1000 x 1000 metres. On the grid lines, the scale factor is 1.0 but on the outer edge of the grid zone, the scale factor is These scale errors may appear trivial, but a GIS is designed as an extremely accurate mapping system and it will accommodate this kind of information. Correct data entry for the header is important because it permits greater maximum locational accuracy when integrating files and executing GIS analysis on spatial data. 10 CARIS Geomatics Reference Guide

11 General Mapping Information Projection A map projection is a way of representing an area of the globe on a flat surface. It involves the transfer of meridians and parallels from the curved spherical surface of the globe, or part of the globe, to a flat surface. The fundamental problem is to make this transfer within acceptable limits of accuracy. Certain geometric surfaces such as the cone and the cylinder can be cut lengthwise and unrolled to make a flat sheet. But because the earth has a compound-curvature geometric form, the surface cannot lie flat without serious distortion. Consequently, it is impossible to make a perfect map projection. The problem of distortion may be considered negligible for very small maps (those six kilometres across or less), but increases as the map area becomes larger. Because of distortion, many maps, in particular those covering large areas, display changes in scale and as a result show different area coverages in different parts of the map projection. Map projections may be classified according to the form of the geometric surface on which the projection is made. For more information, see MAP PROJECTIONS ON PAGE 19. CARIS Geomatics Reference Guide 11

12 General Mapping Information Ellipsoid The fact that the earth is not a true sphere must be taken into account if accurate measurements are to be made from maps. For mathematical calculations, an ellipsoid is used as a best estimate of the earth s surface. This allows conversion between geographic latitude and longitude, and the X (eastings) and Y (northings) coordinates of the projection. Projections are calculated on the most appropriate ellipsoid for a local area. The same projection on different ellipsoids are not equivalent. You must note the ellipsoid of your map. If your data is represented on different projection and ellipsoids, you can apply a corrective shift if the extent of the area is small, for example, the area covered by a 1: map sheet. To do this, you need the geographic latitude and longitude for the same points on the different ellipsoids. The difference between the points is calculated and that difference applied as a shift to the points in the reference ellipsoid. Consult your local or national mapping agency if you do not have this information. The oblateness of earth causes the degrees of latitude to change slightly from the equator to the poles. Making accurate maps demands the exact positioning of earth's features and this in turn requires the exact plotting of the meridians and parallels that form the framework upon which details are positioned. Exact lengths of degrees of latitude and longitude can only be stated after the true dimensions of the earth s spheroid are agreed on. For purposes of mathematical calculations an ellipsoid represents the best estimate of the earth's surface. A number of ellipsoids are in use around the world. Computations for each spheroid are based on the lengths of the semi-major axis of the ellipsoid (representing the radius of the equatorial circle) and the semi-minor axis (representing exactly one half of the polar axis) according to the formula f=(a-b)/a where f represents oblateness or flattening at the pole. This table lists the dimensions of the semi-major and semiminor axes of four common ellipsoids. 1 Ellipsoid Semi-major Axis a Semi-minor Axis b Flattening Approximate fraction Bessel ,356, /299 Clarke ,378, ,356, /295 Everest ,377, ,356, /300 International 6,378, ,356, / Ellipsoid data obtained from the CARIS datum.dat file. 12 CARIS Geomatics Reference Guide

13 General Mapping Information North American topographic maps reference the North American Datum 1927 (NA27) or the North American Datum 1983 (NA83) ellipsoid, both of which are based on the Clarke 1866 (CL66) ellipsoid. European ellipsoids ER50 and ER79 and Australian ellipsoids AS66, AS84 and AUST are all based on the International ellipsoid (INTL). Although the differences in the figures in the above table may seem trivial, they give some idea of the degree of precision that forms the basis for the production of accurate topographic maps. CARIS 2 software supports a number of ellipsoids including these: Airy ATS, 1977 (AT77) Australian Geodetic 1984(AS84 Australian Geodetic 1966 (AS66) Australian National Ellipsoid (AUST) Bessel, 1841 (BESL) Borneo Rectified Skew Orthomorphic Grid Ellipsoid using Kertau 1948 (KRBO) Clarke, 1866 (CL66) Colosofsei 1940 (CL40) Everest (EVER) Everest Ellipsoid revised Kartau datum (EVDK) Evet Ellipsoid revised Timbalai (1948 datum (EVTI) European 1950 (ER50) European 1979 (ER79) Geodetic datum 1949 (GD49) Geodetic Reference System 1980 (GR80) International (INTL) NAD, 1927 (NA27) NAD, 1983 (NA83) World Geodetic System 1972 (WG72) World Geodetic System 1984 (WG84) 3 Ellipsoidal information is contained in a text file called datum.dat. 2. This term is a trademark of CARIS (Universal Systems Ltd.), Reg. USPTO and CIPO. 3. CARIS software can compute any ellipsoid that it does not presently support if the values for the semi-major and semi-minor axes are added to datum.dat. CARIS Geomatics Reference Guide 13

14 General Mapping Information Coordinate System Spherical and plane coordinates A coordinate system is any system that references a point location on the earth s surface with respect to a pre-determined set of intersecting east-west and north-south lines. For instance, parallels and meridians are used throughout the world as the geographic (lat/long) coordinate system or geographic grid. Any point location, or area, on earth, can be accurately referenced by means of its geographic coordinates. Although the system of latitudes and longitudes based on the prime meridian of Greenwich is widely used, not all countries adhere to this convention. Some European countries such as Germany and France use a prime meridian of their own choosing for at least some of their maps. Geographic coordinates are considered spherical coordinates because they represent circles (or ellipses) that reference points on a spherical (spheroidal) surface. Meridians are not equidistantly spaced lines over the entire globe nor can they form the basis of a square net on any of the useful map projections. To overcome the limitations of a spherical coordinate system, plane coordinates have been invented. Plane coordinates provide a system of two sets of straight lines that on a flat map-sheet intersect each other at right angles. A plane coordinate system consists of true squares on the map that are superimposed on the geographic grid. The Universal Transverse Mercator grid system (UTM) has its origins in the military grid coordinate system but is now also widely used superimposed on Transverse Mercator and Lambert Conformal maps developed for civilian use in Canada and the United States, as well as many other countries. The UTM grid system consists of 60 grid zones each 6 degrees longitude in width. An additional half-degree on each side provides for overlap into the adjacent zone. The origin of each grid zone lies at the intersection of its central meridian (which is a straight north-south line occupying the central position of the grid zone), and the equator (which is a straight east-west line). To have all grid line values (called Eastings and Northings) increase to the right and up respectively, the central meridian for each grid zone in the northern hemisphere has been given an arbitrary value of metres east, and the equator an arbitrary value of 0 metres north increasing in values towards its bounding northern latitude. In the southern hemisphere the equator has been given the arbitrary value of metres north decreasing towards its bounding south latitude. The UTM grid uses the metre as its basic unit of length and the grid is a network of squares, each 1000 metres wide. Numbers on the grid line increase towards the right (Eastings) and up 14 CARIS Geomatics Reference Guide

15 General Mapping Information (Northings). The procedure is to first state the Eastings value then the Northings value. 4,989,000N 88 N ,985,000N Choosing the coordinate system 619,000E 626,000E E UTM Eastings and Northings of part of the 1: NTS map St Stephen New Brunswick, (Canada) and Maine, (United States of America). Elevation differences can be represented by a vertical coordinate system. A vertical coordinate system has only one axis. One point on the axis is designated as the origin or vertical datum and is assigned a coordinate value of 0. Other points have a vertical coordinate equal to their elevation difference from the origin. Mean sea level is commonly used as a vertical datum. In giving the coordinates of a point on a map, or the windowed out corner coordinates of part of a map, the first step is to determine the 1000 metre grid square within which the point lies. The grid coordinates of its lower left-hand corner designate each grid-square. For a particular point location within the grid square the coordinates may be read to a tenth of the grid, which is one hundred metres. Another digit may be read to locate a point within ten metres accuracy. CARIS software uses four horizontal coordinate systems: Coordinate System Description The coordinates are expressed as Northings and Eastings of a projection in metres on the ground (hence Northings and Eastings in MetRes). Distances and bearings can be carried across adjacent map sheets with this coordinate system, meaning that a continuous database can be established. Its application includes the atlas grid and is used primarily in land-based applications. CARIS Geomatics Reference Guide 15

16 General Mapping Information Coordinate System NRMR LLDG Description Coordinates expressed in metres on the map have no reference to a specific location on the ground (hence Non Registered, MetRes). This type of coordinate system is used when a map needs to be created for demonstration purposes only where the information necessary for relating the map to the real world (control points) is not necessary. Coordinates are expressed in latitude and longitude in decimal degrees on a reference ellipsoid (hence Latitude and Longitude in Decimal degrees). Data may be digitized in Latitude and Longitude by typing the coordinates or by batching a number of measurements and applying them at one time. Another method of obtaining data is to digitize in another coordinate system and then convert to LLDG. Coordinates are expressed in metres at the chart scale (hence CHart in MetRes). All distances and bearings are relative to that chart. Thus a stored position near the top right-hand corner of the physical map would be similar to the actual map dimensions. This stored position can nevertheless be transformed to Northings and Eastings or geographic latitude and longitude as required. This coordinate system is used primarily for hydrographic charting. 16 CARIS Geomatics Reference Guide

17 General Mapping Information Resolution The resolution of the data is the smallest possible distance that can be measured between two points. Two points which are separated by a distance less than the resolution are considered to be coincident. For example, if the resolution of your True position Rounded position data is one metre at ground scale, two points less than a metre apart cannot be distinguished. The location of points will be rounded to the nearest metre. The level of accuracy of data varies according to the way data is True position Rounded position collected. The coordinate accuracy of data taken directly from a stereoplotter is generally higher than that taken from a paper map, assuming that the scales are similar; a list of surveyed coordinates is likely to be the most accurate of all. The requirements for accuracy vary with circumstances and almost always require compromise. In certain applications, the requirements for accuracy must be tempered by the nature of the physical conditions. For example, natural features such as soil types, forest species, or climatic regions do not have sharply defined limits. The transition from one type to another tends to be gradual. Boundaries are only approximate at best. Collecting boundary data at sub metre accuracy is not warranted. However, boundaries imposed by humans can be presented at a higher level of accuracy. In some instances, such as legal property boundaries, this high level of accuracy is required. Requirements for accuracy may also be tempered by the requirements of another agency that uses the data you collect. Future use of the data also tempers accuracy requirements. If more accurate data will be available in the future, collect the present data to that accuracy. This allows for future capture of more accurate data without reconstructing existing files. If the cartographic appearance is important, a fine resolution may be required to retain the smooth appearance of a line. A coarse resolution will result in jagged lines on a plot. Too fine a resolution, however, can result in jagged lines, showing the shakiness of the digitizing operator s hand. The recommended rule of thumb for choosing a resolution is to capture all data at the highest level of accuracy available to you. CARIS Geomatics Reference Guide 17

18 General Mapping Information 18 CARIS Geomatics Reference Guide

19 2 Map Projections Use of material from United States Geological Survey (USGS) is for descriptive purposes only and does not imply endorsement by USGS of CARIS products or services. A map projection is a way of representing an area of the globe on a flat surface. It involves the transfer of meridians and parallels from the spherical surface of the globe to a flat surface. Because the earth has a compound-curvature geometric form, the surface cannot lie flat without serious distortion, therefore it is impossible to make a perfect map projection. Certain geometric surfaces such as the cone and the cylinder can be cut lengthwise and unrolled to make a flat sheet, and these can be used to create projections of varying accuracy. All, however, are distorted in some way. The degree and kinds of distortion vary with the projection, the scale, and the area being mapped. Some projections are suited for large mainly north-south areas, others for mainly east-west areas, and others for areas oblique to the equator. Other projections are severely distorted in small scale maps but accurate in large scale maps. To choose the best map projection for the task, first determine which attributes must be accurately displayed. This chapter should give you a basic knowledge of the properties of commonly used projections (United States Geological Survey, n.d.). In this chapter... PROJECTION TYPES...20 MERCATOR...23 TRANSVERSE MERCATOR...24 OBLIQUE MERCATOR...25 MILLER CYLINDRICAL...26 ROBINSON...27 SINUSOIDAL EQUAL AREA...28 ORTHOGRAPHIC...29 STEREOGRAPHIC...30 GNOMONIC...31 AZIMUTHAL EQUIDISTANT LAMBERT AZIMUTHAL EQUAL AREA ALBERS EQUAL AREA CONIC LAMBERT CONFORMAL CONIC EQUIDISTANT CONIC (SIMPLE CONIC) POLYCONIC SUMMARY GLOSSARY REFERENCES... 41

20 Map Projections Projection Types Map projections may be classified according to the form of the geometric surface on which the projection is made. Azimuthal Azimuthal (also called zenithal) projections have their meridians and parallels projected onto a flat screen tangent to the Earth surface, or onto an enclosing box, with the central point as tangent point. The radial scale is r'(d) and the transverse scale is r(d)/(r sin(d/r)) where R is the radius of the Earth. Cylindrical Conic Cylindrical projections wrap a cylinder around the globe then unroll the cylinder to make a flat map. They consist of horizontal and vertical lines and, unlike azimuthal and conical projections, the whole world can be shown on a single map, Instead of a single standard parallel, some cylindrical projections cut the globe on two parallels 45 N and 45 S, with the projection lines emanating from a source on the equator diametrically opposite the projection surface. Between the two parallels, the scale is slightly reduced. To the north and south, the scale is increased till it reaches excessive values at the poles. The polar regions are also badly distorted in the east-west direction to maintain the parallel relationships of the meridians. Conic projections transfer the geographic grid from a globe to a cone resting on the globe, then cut and unroll the cone to create a flat map When the apex lies directly above a pole and the cone touches the globe along a single parallel, the projection is referred to as the perspective conic projection. The parallel that touches the cone is called the standard parallel. On this parallel the scale is exactly as stated for the map or chart and is the same as on the globe from which the projection was made. Everywhere else the scale will be larger on the map and increasing north and south from the standard parallel. Some conic projections use two standard parallels representing two lines of intersection where the plane of projection cuts the globe. The resulting map has two parallels along which the scale is exactly the same as on the globe. The cone is called the secant cone. In a secant cone projection, scale increments north and south of the two parallels are reduced in proportion to the scale decreases between the parallels. The position of the two standard parallels should be selected to minimize scale changes in the mid latitudes of a continent or country. The Lambert Conformal Conic projection, used in the US for aeronautical charts, is a perspective conic projection with two standard parallels and all other parallels adjusted so that the map has true conformal properties but also has the property that any line drawn on it is almost a great circle. 20 CARIS Geomatics Reference Guide

21 Map Projections Polyconic projection maps are based on a number of cones, each centred on two standard parallels positioned at progressively higher latitudes. For example, USGS uses the polyconic net as a base for its topographic maps as well as various other maps in the United States. One disadvantage of polyconic maps is that its meridians are curved inwards towards the top. Because of this curvature, adjoining maps, when trimmed along the bounding meridians, do not have an exact fit. CARIS projections Maps using the following projections can be used directly by CARIS programs: Projection Azimuthal Cassini Gauss_Krueger Gnomonic Hotine Oblique Mercator B Lambert Conformal Conic Lambert Conformal Conic Mercator Polar Stereographic Polyconic Rectified Skew Orthomorphic Stereographic Transverse Mercator Universal Transverse Mercator Code AZ CA GK GN HB L3 LC ME PS PO RS ST TM UM Maps using the following projections must be transformed before they can be used by CARIS programs. Projection Alaska Conformal Albers Equal Area Equidistant Conic A Equidistant Conic B Equirectangular Hammer Interrupt Mollweide Interrupted Goode Lambert Azimuthal Code AC AE EA EB ER HA IW IG LA CARIS Geomatics Reference Guide 21

22 Map Projections Projection Miller Cylindrical Mollweide Orthographic Robinson Sinusoidal Equal Area State Plane Van der Grinten Wagner IV Wagner VII Code MC MW OG RO SU SP VG W4 W7 Canadian 1: NTS maps are usually based on the Transverse Mercator Projection in conjunction with the Universal Transverse Mercator Grid (UTM). The United States Department of the Interior (Geological Survey) 1: (Quadrangle) maps are usually Polyconic. United States 1: Aeronautical charts as well as world 1: aeronautical charts are Lambert Conformal. 22 CARIS Geomatics Reference Guide

23 Map Projections Mercator General Directions Distances Scale Areas Used for navigation or for maps of equatorial regions. Any straight line on the map is a rhumb line (a line of constant direction). The equator and other parallels are straight lines whose spacing increases toward the poles and which meet meridians at right angles. Meridians are equally spaced straight lines. The poles are not displayed. A Mercator map is conformal, but it is not perspective, equal area, or equidistant. Directions along a rhumb line are true between any two points on the map, however, a rhumb line is usually not the shortest distance between points. True only along the equator. Reasonably correct within 15 degrees of the equator. Special scales can be used to measure distances along other parallels. Two particular parallels can be made correct in scale instead of the equator. Sometimes used in conjunction with a Gnomonic map where any straight line is on a great circle and shows the shortest path between two points. Distorted. Distortion increases with distance from the equator and is extreme in polar regions. Shapes Type Shapes of large areas are distorted. Distortion increases with distance from the equator and is extreme in polar regions. Angles and shapes in any small area are essentially true, Cylindrical. Mathematically projected onto a cylinder tangent to the equator. The cylinder may be secant History Presented by Gerardus Mercator in Central meridian (selected by mapmaker) Great distortion in high latitudes. Examples of rhumb lines (direction true between any two points) Equator touches cylinder if cylinder is tangent. Reasonably true shapes and distances within 15 degrees of Equator. Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 23

24 Map Projections Transverse Mercator General Directions Can be joined at their edges only if they are in the same zone with one central meridian. Also used for mapping large areas that are mainly north-south in extent. Graticule spacing increases away from the central meridian. The equator is straight, but other parallels are complex curves concave toward the nearest pole. The central meridian and each meridian 90 degrees from it are straight. Other meridians are complex curves concave toward the central meridian. The map is conformal. Reasonably accurate within 15 degrees of the central meridian. Distances Areas Shapes Type True only along the central meridian selected by the mapmaker or along two lines parallel to it. Reasonably accurate within 15 degrees of the central meridian. Distortion increases rapidly outside the 15 band. Reasonably accurate within 15 degrees of the central meridian. Distortion increases rapidly outside the 15 band. Reasonably accurate within 15 degrees of the central meridian. Shapes and angles within any small area are essentially true. Distortion increases rapidly outside the 15 band. Cylindrical. Mathematically projected onto a cylinder tangent to a meridian. The cylinder may also be secant History Presented by Johann Heinrich Lambert in Central meridian selected by mapmaker touches cylinder if the cylinder is tangent. Equator Can show whole Earth, but the directions, distances and areas are reasonably accurate only within 15 of the central meridian. No straight rhumb lines. Note Directly supported. (United States Geological Survey, n.d.) 24 CARIS Geomatics Reference Guide

25 Map Projections Oblique Mercator General Directions Distances Areas Shapes Type History Used for regions along a great circle other than the equator or a meridian, with their general extent oblique to the equator. This can show the shortest distance between any two preselected points on the great circle as a straight line. Rhumb lines are curved. Conformal but not perspective, equal area, or equidistant. Graticule spacing increases away from the great circle but conformality is retained. Both poles can be shown. The equator and other parallels are complex curves concave toward the nearest pole. Two meridians 180 apart are straight lines but all others are complex curves concave toward the great circle. Reasonably accurate within 15 of the great circle. Distortion increases with distance and is excessive toward the edges of a world map, except near the path of the great circle True only along the great circle (line of tangency) or along two lines parallel to it. Reasonably accurate only within 15 of the great circle. Distortion increases with distance and is excessive toward the edges of a world map, except near the path of the great circle. Reasonably accurate only within 15 of the great circle. Distortion increases with distance and is excessive toward the edges of a world map, except near the path of the great circle Reasonably accurate only within 15 of the great circle. Distortion increases with distance and is excessive toward the edges of a world map, except near the path of the great circle. Cylindrical. Mathematically projected onto a cylinder tangent or secant along any great circle except the equator or a meridian. Developed between 1900 and 1950 by Rosenmund, Laborde, Hotine et al. Line of tangency the great circle that touches cylinder if cylinder is tangent. In this projection, shortest distances between points along line of tangency are straight lines. No straight rhumb lines. Equator Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 25

26 Map Projections Miller Cylindrical General Directions Distances Scale Used to represent the entire Earth in a rectangular frame. Popular for world maps. Looks like Mercator but is not useful for navigation. Displays poles as straight lines. Not equal area, equidistant, conformal, or perspective. True only along the equator. True only along the equator. In high latitudes, distortion is extreme. Avoids some of the scale exaggerations of Mercator, but distorts both shapes and areas. Areas Shapes Type Distorted. In high latitudes, distortion is extreme. Distorted. In high latitudes, distortion is extreme. Cylindrical Mathematically projected onto a cylinder tangent at the Equator History Presented by O.M. Miller in Central meridian (selected by mapmaker) Change in spacing of parallels is less than that on Mercator projection. Equator always touches cylinder Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) 26 CARIS Geomatics Reference Guide

27 Map Projections Robinson General Directions Distances Used in Goode s Atlas, National Geographic s world maps since 1988, and in a growing number of other publications. May replace Mercator in classrooms. Uses tabular coordinates instead of mathematical formulas to make the Earth look right. This achieves a better balance of size and shape of high-latitude lands than Mercator, Van der Grinten, or Mollweide. Russia, Canada, and Greenland appear truer in size but Greenland looks compressed. Not conformal, equal area, equidistant, or perspective. True along all parallels and the central meridian. Constant along the equator and other parallels, Scale True along 38 N and S. Constant along any given parallel The same along N and S parallels that are an equal distance from the equator. Distortion Type All points contain some distortion, with the greatest near the poles and lowest along the equator and within 45 of centre. Pseudocylindrical or orthophanic ( right appearing ) History Presented by Arthur H. Robinson in Central meridian (selected by mapmaker) 90 Concave meridians are equally spaced Equator Straight Equator, parallels, central meridian. Central meridian is 0.53 as long as Equator Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 27

28 Map Projections Sinusoidal Equal Area General Distances Areas Shapes Used in atlases to show distribution patterns, by USGS to show prospective hydrocarbon provinces and sedimentary basins of the world, and for maps of Africa, South America, and other large areas that are mainly north-south in extent. An easily plotted, equal-area projection for world maps. A map may have a single central meridian or several central meridians (interrupted form). Graticule spacing retains the equivalence of area. Not conformal, perspective, or equidistant. True along all parallels and the central meridian(s). Proportional to those same areas on the Earth. Increasingly distorted away from the central meridian(s) and near the poles. Type Pseudocylindrical. Mathematically based on a cylinder tangent to the equator History Used by Cossin and Hondius beginning in Also known as the Sanson-Flamsteed projection. Central meridian (selected by mapmaker) The maker of this interrupted Sinusoidal map used three central meridians. Equator Uninterrupted Sinusoidal Areas are equal. Scale true only on central meridians and on all parallels. Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) 28 CARIS Geomatics Reference Guide

29 Map Projections Orthographic General Directions Distances Scale Areas Shapes Type History Used for perspective views of the Earth, moon, and planets. The Earth appears as it would on a photograph from deep space. Perspective but not conformal or equal area. True only from the centre point of projection. In the polar aspect, true along the Equator and all other parallels. Decreases along all lines radiating from the centre point of projection. Any straight line going through the centre point is a great circle. Distorted by perspective. Distortion increases away from the centre point. Distorted by perspective. Distortion increases away from the centre point. Azimuthal. Geometrically projected onto a plane. The point of projection is at infinity The Egyptians and Greeks knew of the Orthographic projection 2,000 years ago. Oblique - Mapmaker selects any point of tangency except along the Equator or at Pole Plane of projection Equator Polar - Mapmaker selects North or South Pole Equatorial - Mapmaker selects central meridian Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 29

30 Map Projections Stereographic General Directions Scale Areas Shapes Type History Can be used to map large continent-sized areas of similar extent in all directions, such as the Arctic and Antarctic. Used in geophysics to solve spherical geometry problems. Polar aspects are used for topographic maps and navigation charts for latitudes above 80. Conformal and perspective but not equal area or equidistant. True only from the centre point of projection. Increases away from the centre point. Any straight line through the centre point is a great circle. Distortion increases away from the centre point Distortion of large shapes increases away from the centre point Azimuthal. Geometrically projected on a plane. The point of projection is at the surface of the globe opposite the point of tangency. Dates from the second century BC and is ascribed to the Greek astronomer Hipparchus. Oblique - Mapmaker selects any point of tangency except along the Equator or at Pole Plane of Projection Equator Polar - Mapmaker selects North or South Pole Equatorial - Mapmaker selects central meridian Point of Projection Note Directly supported. (United States Geological Survey, n.d.) 30 CARIS Geomatics Reference Guide

31 Map Projections Gnomonic General Directions Scale Areas Shapes Type History Used in conjunction with Mercator by some navigators to find the shortest path between two points, Used in seismic work because seismic waves tend to travel along great circles. Perspective (from the Earth s centre onto a tangent plane) but not conformal, equal area, or equidistant. True only from the centre point of projection. Any straight line drawn on the Gnomonic map is on a great circle. Increases rapidly away from the centre point. Distortion increases away from the centre point. Distortion increases away from the centre point. Azimuthal. Geometrically projected onto a plane. The point of projection is the centre of a globe Considered to be the oldest true projection map and is ascribed to Thales, the father of abstract geometry, who lived in the sixth century B.C. Oblique - Mapmaker selects any point of tangency except along the Equator or at Pole Plane of Projection Equator Polar - Mapmaker selects North or South Pole Equatorial - Mapmaker selects central meridian Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 31

32 Map Projections Azimuthal Equidistant General Directions Distances Areas Shapes Type Useful for airline distances from a centre point of projection and for seismic and radio work. Oblique aspect used for atlas maps of continents and world maps for radio and aviation use. Polar aspect used for world maps, maps of polar hemispheres, and the UN emblem. True only from the centre point of projection. True only from the centre point of projection. Correct between points along straight lines through the centre. Any straight line drawn through the centre point is a great circle. All other distances are incorrect. Distortion increases away from the centre point. Distortion increases away from the centre point. Azimuthal. Mathematically projected onto a plane tangent to any point on the globe. The polar aspect is tangent only at a pole. Oblique - Mapmaker selects any point of tangency except along the Equator or at Pole Plane of projection Equator Polar - Mapmaker selects North or South Pole Equatorial - Mapmaker selects central meridian Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) 32 CARIS Geomatics Reference Guide

33 Map Projections Lambert Azimuthal Equal Area General Directions Scale Suited for regions that extend equally in all directions from centre points, such as Asia and the Pacific Ocean. Equal area but not conformal, perspective, or equidistant. True only from the centre point. Decreases gradually away from the centre point. Areas Shapes Type In true proportion to the same areas on the Earth. Quadrangles bounded by two meridians and two parallels at the same latitude are uniform in area. Distortion increases away from the centre point. Any straight line drawn through a centre point is on a great circle. Azimuthal. Mathematically projected onto a plane tangent to any point on the globe. The polar aspect is tangent only at a pole History Presented by Johann Heinrich Lambert in Oblique - Mapmaker selects any point of tangency except along the Equator or at Pole Plane of Projection Equator Polar - Mapmaker selects North or South Pole Equatorial - Mapmaker selects central meridian Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 33

34 Map Projections Albers Equal Area Conic General Directions Distances Scale Areas Suited for large areas that are mainly east-west in extent and that require equal-area representation. Used for thematic maps. Maps of adjacent areas can be joined at their edges if they have the same standard parallels and scale. Not conformal, perspective, or equidistant. Reasonably accurate in limited regions. True on both standard parallels. True only along standard parallels. The maximum scale error is calculated at 1.25% on a map of the conterminous states with standard parallels of 29.5 degrees North and 45.5 degrees North. Proportional to the same areas on Earth. Type Conic. Mathematically projected onto a cone conceptually secant at two standard parallels History Presented by H. C. Albers in Two standard parallels (selected by mapmaker) Equal areas. Deformation of shapes increases away from standard parallels. Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) 34 CARIS Geomatics Reference Guide

35 Map Projections Lambert Conformal Conic General Directions Distances Areas Used to show a country or region that is principally east-west in extent. One of the most widely used map projections in the United States. It looks like Albers Equal Area Conic, but graticule spacings differ. The Lambert Conformal Conic projection retains conformality. Conformal but not perspective, equal area, or equidistant. Reasonably accurate. True along standard parallels. Reasonably accurate elsewhere in limited regions. Distortion is minimal at the standard parallels but increases with distance. Shapes Distortion is minimal at the standard parallels but increases with distance. Shapes on large-scale maps of small areas are essentially true. Type Conic. Mathematically projected onto a cone conceptually secant at two standard parallels. History Presented by Johann Heinrich Lambert in Two standard parallels (selected by mapmaker) Large-scale map sheets can be joined at edges if they have the same standard parallels and scales. Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 35

36 Map Projections Equidistant Conic (Simple Conic) General Directions Distances Areas Shapes Used in atlases to show areas in the middle latitudes. Good for regions within a few degrees of latitude and on one side of the equator. One example, the Kavraisky No. 4, is an Equidistant Conic projection in which standard parallels are chosen to minimize overall error. Not conformal, perspective, or equal area. A blending of Lambert Conformal Conic and Albers Equal Area Conic. Reasonably accurate but distortion increases away from standard parallels. True only along meridians and along one or two standard parallels. Reasonably accurate but distortion increases away from standard parallels. Reasonably accurate but distortion increases away from standard parallels. Type Conic. Mathematically projected onto a cone tangent at one parallel or conceptually secant at two parallels History Prototype was developed by Ptolemy in the year 150 and improved by De l Isle around Two standard parallels (selected by mapmaker) Distances along meridians and standard parallels are correct. Shapes and areas are distorted. Note Not directly supported. Maps must be transformed before being used. (United States Geological Survey, n.d.) 36 CARIS Geomatics Reference Guide

37 Map Projections Polyconic General Directions Distances Areas Shapes Type History Used almost exclusively for large-scale mapping in the United States until the 1950s. Now nearly obsolete and no longer used by USGS for new plotting in its Topographic Map series. Best suited to areas with a north-south orientation. A compromise of many properties. Not conformal, perspective, or equal area. True only along the central meridian. True only along each parallel and along the central meridian. True only along the central meridian. Distortion increases away from the central meridian. True only along the central meridian. Distortion increases away from the central meridian. Conic. Mathematically based on an infinite number of cones tangent to an infinite number of parallels Thought to have originated around 1820 by Hasslet. The slant heights of the tangent cones become the radii of the parallels of latitude Note Directly supported. (United States Geological Survey, n.d.) CARIS Geomatics Reference Guide 37