Relationship between map projections and distortions

Map projection - Wikipedia

relationship between map projections and distortions

There are four basic characteristics of a map that are distorted to some My article is not to discuss the benefits of map projections but to look at . Meet Living Map – the company that is bridging the information gap between. The map projection has distorted the graticule. To preserve individual angles describing the spatial relationships, a Conformal projection must show the perpendicular Equidistant maps preserve the distances between certain points. A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. . In large-scale maps, Cartesian coordinates normally have a simple relation.

I feel it is more about the technology, although I do see there appears to be less importance placed on some of these at some levels of education. Technology has become more than a tool to help us but more and more a tool to do the work for us. I know I do and my spelling has suffered at the hands of technology. Maybe the data was captured at 1: What was the original purpose of the data you are using for your maps?

Have you read the metadata associated with your data, or did it even come with metadata. Too often I see data being used in a way that it was not intended.

About map projections

This maybe due to scale, symbology, attributes or just poor representation. Just because your GIS software can symbolise your data in a certain way, is this really enhancing or degrading the original data. Many maps were a work of art and the essential map elements were there to make it useful to the end users.

It is impossible to flatten any spherical surface e. Similarly, when trying to project a spherical surface of the Earth onto a map plane, the curved surface will get deformed, causing distortions in shape anglearea, direction or distance of features. All projections cause distortions in varying degrees; there is no one perfect projection preserving all of the above properties, rather each projection is a compromise best suited for a particular purpose.

Different projections are developed for different purposes. Some projections minimize distortion or preserve some properties at the expense of increasing distortion of others.

This scale can be measured as the ratio of distance on the globe to the corresponding distance on the Earth. Throughout the globe this scale is constant. For example, a 1: The principal scale or nominal scale of a flat map the stated map scale refers to this scale of its generating globe. However the projection of the curved surface on the plane and the resulting distortions from the deformation of the surface will result in variation of scale throughout a flat map.

In other words the actual map scale is different for different locations on the map plane and it is impossible to have a constant scale throughout the map. This variation of scale can be visualized by Tissot's indicatrix explained in detail below.

Measure of scale distortion on map plane can also be quantified by the use of scale factor. This can be alternatively stated as ratio of distance on the map to the corresponding distance on the reference globe. A scale factor of 1 indicates actual scale is equal to nominal scale, or no scale distortion at that point on the map.

Scale factors of less than or greater than one are indicative of scale distortion. The actual scale at a point on map can be obtained by multiplying the nominal map scale by the scale factor. As an example, the actual scale at a given point on map with scale factor of 0. Scale factor of 2 indicates that the actual map scale is twice the nominal scale; if the nominal scale is 1: A scale factor of 0.

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As mentioned above, there is no distortion along standard lines as evident in following figures. On a tangent surface to the reference globe, there is no scale distortion at the point or along the line of tangency and therefore scale factor is 1. Distortion increases with distance from the point or line of tangency.

Map Projections and Coordinate Systems

Between the secant lines where the surface is inside the globe, features appear smaller than in reality and scale factor is less than 1. At places on map where the surface is outside the globe, features appear larger than in reality and scale factor is greater than 1. A map derived from a secant projection surface has less overall distortion than a map from a tangent surface.

The distortion pattern of a projection can be visualized by distortion ellipses, which are known as Tissot's indicatrices.

Why Every World Map You've Ever Read is Wrong

Each indicatrix ellipse represents the distortion at the point it is centered on. The two axes of the ellipse indicate the directions along which the scale is maximal and minimal at that point on the map. Since scale distortion varies across the map, distortion ellipses are drawn on the projected map in an array of regular intervals to show the spatial distortion pattern across the map.

relationship between map projections and distortions

The ellipses are usually centered at the intersection of meridians and parallels. Their shape represents the distortion of an imaginary circle on the spherical surface after being projected on the map plane. The size, shape and orientation of the ellipses are changed as the result of projection.

Circular shapes of the same size indicate preservation of properties with no distortion occurring. Sting Equal area map projections also known as equivalent or authalic projection represent areas correctly on the map.

The areas of features on the map are proportional to their areas on the reference surface of Earth. Maintaining relative areas of features causes distortion in their shapes, which is more pronounced in small-scale maps. Sting In conformal map projections also known as orthomorphic or autogonal projection local angles are preserved; that is angles about every point on the projected map are the same as the angles around the point on the curved reference surface.

Similarly constant local scale is maintained in every direction around a point. Therefore shapes are represented accurately and without distortion for small areas.

relationship between map projections and distortions

However shapes of large areas do get distorted. Meridians and parallels intersect at right angles. As a result of preserving angles and shapes, area or size of features are distorted in these maps. No map can be both conformal and equal area.

Here the area distortion is more pronounced as we move towards the poles. A classic example of area exaggeration is the comparison of land masses on the map, where for example Greenland appears bigger than South America and comparable in size to Africa, while in reality it is about one-eight the size of S.

America and one-fourteenth the size of Africa. A feature that has made Mercator projection especially suited for nautical maps and navigation is the representation of rhumb line or loxodrome line that crosses meridians at the same angle as a straight line on the map. A straight line drawn on the Mercator map represents an accurate compass bearing.

Preservation of angles makes conformal map projections suitable for navigation charts, weather maps, topographic mapping, and large scale surveying. Examples of common conformal projections include Lambert Conformal ConicMercator, Transverse Mercatorand Stereographic projection.

Sting In equidistant map projections, accurate distances constant scale are maintained only between one or two points to every other point on the map. Also in most projections there are one or more standard lines along which scale remains constant true scale.

Distances measured along these lines are proportional to the same distance measurement on the curved reference surface. Similarly if a projection is centered on a point, distances to every other point from the center point remain accurate. Equidistant projections are neither conformal nor equal-area, but rather a compromise between them. However while there are changes in the ellipses, their north-south axis has remained equal in length.

This indicates that any line joining north and south poles meridian is true to scale and therefore distances are accurate along these lines.

Equidistant projections are used in air and sea navigation charts, as well as radio and seismic mapping. They are also used in atlases and thematic mapping. Examples of equidistant projections are azimuthal equidistantequidistant conic, and equirectangular projections.

Map projections and distortion

These projections can also be equal area, conformal or equidistant. The gnomonic map projection in the image is centered on the North Pole with meridians radiating out as straight lines.

In gnomonic maps great circles are displayed as straight lines. Directions are true from the center point North Pole. True-direction projections are used in applications where maintaining directional relationships are important, such as aeronautical and sea navigation charts. Sting Some projections do not preserve any of the properties of the reference surface of the Earth; however they try to balance out distortions in area, shape, distant, and direction thus the name compromiseso that no property is grossly distorted throughout the map and the overall view is improved.

They are used in thematic mapping.