Map projections and distortion
An illustration of the Earth rendered 2D using the mercator projection. In fact, map projections are really only useful where they do not distort the Earth. There's almost no difference near the north pole, but the south is super stretched out. A comprehensive introduction to map projections, and types of projections based on Examples of cylindrical projections include Mercator, Transverse Mercator, . This scale can be measured as the ratio of distance on the globe to the. The relationship between the globe and the types of map projections and to observe the distortions . shape tangent to the sphere define a region of constant .
- The Mercator and Other Projections
- Map projection
The three types of developable surfaces are cylinder, cone and plane, and their corresponding projections are called cylindrical, conical and planar. Projections can be further categorized based on their point s of contact tangent or secant with the reference surface of the Earth and their orientation aspect. Keep in mind that while some projections use a geometric process, in reality most projections use mathematical equations to transform the coordinates from a globe to a flat surface.
The resulting map plane in most instances can be rolled around the globe in the form of cylinder, cone or placed to the side of the globe in the case of the plane. The developable surface serves as a good illustrative analogy of the process of flattening out a spherical object onto a plane.
Cylindrical projection In cylindrical projections, the reference spherical surface is projected onto a cylinder wrapped around the globe.
The cylinder is then cut lengthwise and unwrapped to form a flat map. The diameter of the cylinder is equal to the diameter of the globe. The tangent line is the equator for the equatorial or normal aspect; while in the transverse aspect, the cylinder is tangent along a chosen meridian i.
At the place where the cylinder cuts through the globe two secant lines are formed. Such lines of true scale are called standard lines. These are lines of equidistance. Distortion increases by moving away from standard lines.
The graticule layout is affected by the choice of the aspect.
Map projection - Wikipedia
The meridians are vertical and equally spaced; the parallels of latitude are horizontal straight lines parallel to the equator with their spacing increasing toward the poles.
Therefore the distortion increases towards the poles. Meridians and parallels are perpendicular to each other. The meridian that lies along the projection center is called the central meridian. Conical conic projection In conical or conic projections, the reference spherical surface is projected onto a cone placed over the globe.
The cone is cut lengthwise and unwrapped to form a flat map. For the polar or normal aspect, the cone is tangent along a parallel of latitude or is secant at two parallels.
These parallels are called standard parallels. Distortion increases by moving away from standard parallels. Features appear smaller between secant parallels and appear larger outside these parallels. Secant projections lead to less overall map distortion. Conical aspect — equatorial normaltransverse, oblique The polar aspect is the normal aspect of the conic projection.
The cone can be situated over the North or South Pole. The polar conic projections are most suitable for maps of mid-latitude temperate zones regions with an east-west orientation such as the United States. Oblique aspect has an orientation between transverse and polar aspects.
Transverse and oblique aspects are seldom used. Planar projection — Azimuthal or Zenithal In planar also known as azimuthal or zenithal projections, the reference spherical surface is projected onto a plane.
In the secant case the plane intersects the globe along a small circle forming a standard parallel which has true scale. The normal polar aspect yields parallels as concentric circles, and meridians projecting as straight lines from the center of the map.
The distortion is minimal around the point of tangency in the tangent case, and close to the standard parallel in the secant case.
Map projection - types and distortion
Planar aspect — polar normaltransverse equatorialoblique The polar aspect is the normal aspect of the planar projection. The plane is tangent to North or South Pole at a single point or is secant along a parallel of latitude standard parallel. The polar aspect yields parallels of latitude as concentric circles around the center of the map, and meridians projecting as straight lines from this center. Azimuthal projections are used often for mapping Polar Regions, the polar aspect of these projections are also referred to as polar azimuthal projections.
In transverse aspect of planar projections, the plane is oriented perpendicular to the equatorial plane. And for the oblique aspect, the plane surface has an orientation between polar and transverse aspects. These projections are named azimuthal due to the fact that they preserve direction property from the center point of the projection.
Great circles passing through the center point are drawn as straight lines.
What four things do map projections distort?
Examples of azimuthal projections include: Azimuthal Perspective Projections Some classic azimuthal projections are perspective projections and can be produced geometrically. They can be visualized as projection of points on the sphere to the plane by shining rays of light from a light source or point of perspective. Three projections, namely gnomonic, stereographic and orthographic can be defined based on the location of the perspective point or the light source.
Great circles are the shortest distance between two points on the surface of the sphere known as great circle route. Gnomonic projections map all great circles as straight lines, and such property makes these projections suitable for use in navigation charts.
Distance and shape distortion increase sharply by moving away from the center of the projection. Points close to center point show great distortion on the map. Stereographic projection is a conformal projection, that is over small areas angles and therefore shapes are preserved. It is often used for mapping Polar Regions with the source located at the opposite pole. The light rays travel as parallel lines. The resulting map from this projection looks like a globe similar to seeing Earth from deep space.
There is great distortion towards the borders of the map. Map projection types based on distortion characteristics As stated above spherical bodies such as globes can represent size, shape, distance and directions of the Earth features with reasonable accuracy. 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.
Map Projections - types and distortion patterns
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.
Basically, we put the Earth in a cylinder and then blow it up like a balloon. Finally, we unroll this cylinder to make a 2D map. If you roll up a map correctly, it forms a hollow cylinder. This might seem like a strange way to make a map. But, it actually makes sense. As we expand the Earth to fit our cylinder, it is inevitably distorted. Yet where is it least distorted? Near and around the center. Fortunately, the majority of people live closer to the equator than the poles. Conic Projections Our next map projection is the conic projection.
Conic projections are made by projecting the Earth onto a cone. Basically, we repeat the cylinder method. But, instead of a cylinder, we use a cone. Boy, it must be really loud in Antarctica! Notably, this map projection is actually more accurate than the cylindrical projection.
It distorts the Earth less overall. However, its distortions are more problematic. This is an issue because more people live south of the Equator than at the poles. Remember, cylindrical projections mostly distort the poles. But to do this, they have to cut out some of the ocean. Is it a map or a colorful orange peel? An advantage of this map is that it allows us to see how big the continents really are.
Africa is huge, and Australia much smaller. A disadvantage is that it is not useful for traveling. We still have to navigate over the blank areas! What is the Mercator Projection? The Mercator Projection is the most widely used map projection today.
It is a type of cylindrical projection.