An equal area projection is a map projection that shows regions that are the same size on the Earth the same size on the map but may distort the shape, angle, and/or scale. Pro- Shows sizes accurately. Con- Distorts shapes. However I do understand the wish not to waste space, so maybe a map that is almost It almost seems as if Strebe liked the modified Snyder projection a lot, so he tried to create a similar projection In a nutshell, (If you want to know what I mean when I say »decent shape«, read the Wagner-Denoyer article, or be satisfied with the summary that on Wikipedia. The Sinusoidal projection and the Werner projection are equal area projections of the world. the United States National Grid. Look at the following images: check Figure 5.7 (page 215). Various configurations approach a rectangular shape which sometimes can be advisable. on. According to my measurements, the map itself uses about 89% of its circumscribing rectangle. The Hobo–Dyer map projection is a cylindrical equal-area projection, with standard parallels (where there is no north-south nor east-west distortion) at 37.5° north and south of the equator. Of course, you do need the software Geocart to use them which probably is kind of look perfectly normal, just like a world map has to look – maybe even the two Strebe-Snyder projections as well. the Wagner VII. If we for example have a map dataset of the United Kingdom and we want to compute distances between locations which could be cities, we should make sure that our projection suits the region, e.g. This map was created as an improvement on the Robinson projection. Shapes, directions, angles, and distances are generally distorted. Note that all except the latter are pointed-pole projections – we’ll be coming back to this matter later. Btw, you also can use the selection form or the list of projections to select the ones you’d like to compare. The Robinson projection was created to show the globe as a flat image readily. Strebe-Snyder Pointed Pole at 35°S. The kinked meridians are a certain flaw, but in an But now, let’s look at the single steps of Strebe’s technique, taking the Mollweide projection as example. Now, look at Strebe’s series again: Five of them are pointed-pole projections, but – in the configurations shown above – projections don’t meet your preferences!« Credits. In contrast, a real pole-line projection, gabi1955. was created by the interruption along the equator. for decorative use. It didn’t occur to me before, but the aspect ratio of Strebe 1995 is close If you don’t know what an affine transformation is, read Strebe’s paper or look it up lines meeting at right angles. This projection compresses shapes in higher latitudes, but shapes are good in the central section. for a rectangular map. Smyth equal-surface (a.k.a. Sinusoidal Equal Area Used frequently in atlases to show distribution patterns. In this step, Every projection has its own set of advantages and disadvantages. It didn’t occur to me before, but the aspect ratio of Strebe 1995 is close 5 of these exist, namely S, T, N, H and O. The scale along all parallels in the sinusoidal part, between 40°44'12'' north and south, and along the central meridians of the projection is accurate. Used in Goode's Atlas, adopted for National Geographic's world maps in 1988, appears in growing number of other … By the way, there is a projection which is somewhat similar (apart from the kinks), both regarding the outer Advantages: The original ODT map is printed on two sides, … distribution of distribution in the Strebe-Kavraiskiy V lead in my opinion to more »natural« shapes of the continents. Homolosine projection. Mollweide Projection . This time in the returned image, the two layers overlay in the Sinusoidal projection, the default from the service. But let’s be honest, most people are not interested in the matter or don’t even know that something And now, for the last time (I promise!) However many people who cheered the AuthaGraph world map praised the Winkel Triple.). that in my opinion there is little in favour of the cylindrical projection. We have reached the final result, which is equivalent just like The simple Geographic lat/lon projection is only used for the coarsest resolution grid, produced at 0.05 km (~ 5.5 km), which is referred to as the Climate Modeling Grid (CMG). This type of equal-area projection is a combination of the Homolographic and the Sinusoidal. Bonne φ1 = 16°N very much. in which each parallel – originally straight in the sinusoidal – is bent into the arc of a circle without stretching it. The latter is an equal-area projection which "trades the accuracy of angle and shape for a accuracy of proportions in area" which means that in the distribution of countries in relation to each other is fairly realistic. Normally, the Sinusoidal projection is applied between the 40 degrees south and 40 degrees north latitudes, grafted to the Homolographic in the areas out of the above mentioned range. Obviously, he succeeded. of the three projections consist only of meridians converging at the poles. North America 39 terms. The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. The aspect ratio approaches 1:2, the kinks are relaxed Hence, are the coordinates given as eastings and northings from the origin of the projection which at this point should allow us to start measuring? in regards of the outer shape and the distribution of distortions. … and the Strebe-Snyder Pointed Pole, 20°S. There are advantages and disadvantages to this approach. All meridians are curved lines. a »latitude of curvature« is used as parameter, which is the Bonne φ1 but without the meaning Web maps consist of tiles which are square. Low-error equal-area transformation of Hammer-Wagner [Wagner VII] with twofold symmetry (when the projection is centered to the Greenwich meridian) Scale is true along parallels with latitudes $ \phi = \pm 40.7 $ B. V.V. In 1992, Daniel »daan« Strebe developed a series of equal-area projections by the distribution of distortions (see below). seemingly have a pole-line. like map projections exist. if you are using a cylindrical map projection it won't be easy for you to calculate the distance between the places as you do in ordinary maps.but cylindrical projection can cover large area so the size of the map will be compact. Well, the reason is quite straightforward. While the previous example used about 89% of the total area, Of course I’m aware that in many cases, you might prefer a cylindrical projection because of other But meanwhile I’ve changed my mind. If you don’t know what an affine transformation is, read Strebe’s paper or look it up and overall, it’s not dissimilar to Wagner VII (a projection that I like a lot). This article describes an alternative intermediate projection. Some may preserve elements of direction, distance or area better or worse than others which is why a careful selection of a suitable projection is so crucial. which is not very surprising since Wagner designed it to be an equal-area replacement for the The projection is interrupted along the equator by applying the Bonne transform independently a deal breaker for most people…. appropriate configuration they don’t stand out very much – or even might be advantageous, if you need Alternative formats reduce the distortion along outer meridians by interrupting the continuity of the projection over the oceans and by centering the continents around their own central meridians, or vice versa. – A peculiar property of all six projections are the kinks of the meridians at the equator, Unlike cylindrical equal area projections, they both reflect the fact that lines of latitude are shorter nearer the poles than those near the equator. (For the latter two, this property is more pronounced than for the Strebe-Mollweide.) to both northern and southern hemispheres, which significantly reduces distortion. But I thought that this For the sake of completeness we have also added the Haversine Formula, also know as the The Great Circle Distance which can be used to measure distances between points from coordinates given in degrees (latitude and longitude). The polar aspect is used by the U.S. Geological Survey in the National higher distortion again, the advantage is that this way, all major landmasses including Antarctica I also wanted that the outer meridians don’t bend too much so that e.g. manipulating six existing projections. The difference is quite obvious. Equal-Area Projection. or at least does not depart too much from equivalence, and The Sinusodial projection is an equal-area map, much like the Mollweide though much more distorted. to Winkel Tripel, here you are. Some well known GCS are The World Geodetic System 84 (WGS84 Datum), The North American Datum 83 (NAD83 Datum) or The Ordnance Survey of Great Britain 36 (OSGB36 Datum). Strebe himself described them as undesirable, but I really don’t mind them. Two of them have been shown on map-projections.net for a while now, the other four have now been added. Let's focus on Cornwall which lies in the SW square. The fundamental concept of how grids including their eastings and northings work is the same, so let's pick one tangible example. might be a good place to show such a configuration…. Strebe-Mollweide with Bonne φ1 = 24°S approaches a rectangular shape, which sometimes Each grid cell (square) features an identifier which consists of 2 grid letters, the first being the identifier of the 500 x 500 km square it belongs to. And finally, another specimen of the more unusual type of projections: ", Gisgeography.com on Equal Area Projection Maps, A Treasure of Knowledge about Map Projections, The Guardian Writing About Different Projections, © 2020 GIS • OPS | ROUTING, OPTIMISATION, QGIS & SPATIAL DATABASES, https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system, By continuing, you accept the privacy policy, Specifying a Location on a Plane requires a Map Projection. The Sinusoidal projection is used to map the Equatorial regions of each interrupted lobe . With this basic tutorial followed by some practical examples we would like to just touch this broad topic and help you understand why and when they matter when you are trying to measure distances or compute areas of interest for analysis. The Mollweide projection was first created by Karl Mollweide in 1805 and then familiarized again by Jacques Babinet in 1857. If you’re working with a data set of persons per square mile, for example, your map needs to make sure each square mile looks the same size. While equal area projections preserve area, it distorts shape, angles and cannot be conformal. (Just like the Wagner VII’s circumscribing rectangle is close to Bartholomew’s Winkel Tripel version, Craster equal-area), which has a similar aspect ratio. An easily plotted equal-area projection for world maps. Basically every projection has advantages and disadvantages. A set of 21,872 discrete distortion vindicatrices were positioned on the ellipsoid surface, centred on the cells of a Snyder icosahedral equal-area grid. This study compares the performance of five popular equal-area projections supported by Free and Open Source Software for Geo-spatial (FOSS4G)—Sinusoidal, Mollweide, Hammer, Eckert IV and Homolosine. Strebe-Hammer, Bonne φ1 = 29°S. 7) Sinusoidal Equal Area The Sinusoidal Equal Area map projection is considered a pseudo-cylindrical projection. Both have their own advantages and disadvantages. The scale along all parallels in the sinusoidal part, between 40°44'12'' north and south, and along the central meridians of the projection is accurate. Also known as Sanson–Flamsteed—as a world map, this projection maintains equal area despite conformal distortion. Twice before, I’ve experimented with creating a projection that’s either truly equal-area Strebe-Mollweide, Strebe-Kavraiskiy V and Strebe-Snyder Pointed-Pole will be added to my personal list Sounds too abstract? AP Human Geography Urban Models. In the field of to Winkel Tripel’s, too. Let’s compared it to an equal-area projection that’s really rectangular – the cylindrical Smyth equal-surface (a.k.a. be printed, is rectangular, too, and you don’t want to waste space. In this following example we will be computing straight line distances between Penzance and London in PostGIS with different projections to emphasize the importance of choosing wisely. But in this context, he’s a real eye-catcher! So now you might say: »Ha! Used by the USGS to show prospective hydrocarbon provinces and sedimentary basins of the world. Goode homolosine is an equal-area (equivalent) projection. So if the intended use doesn’t specifically require a rectangular map, I’d happily sacrifice There are intermediate projections with similar properties, of which the best known is the Bonne projection. It’s centered to 11° South und 11° East. Please leave the following four input field blank in any case! Only Strebe-Sinusoidal has a really striking appearance. 433.65 kilometers (which is of course way off for the UK but would be very suitable for measuring distances in Melbourne or Sydney!). So What we should be looking at are larger scale PCS as uniform (national) grids which will yield realistic & trustworthy distance results. are favorable in regards of the goals mentioned above, especially the latter two. The radius of the arcs is determined by choosing an arbitrary standard parallel φ1. So if you’re looking for an equivalent alternative Jean Cossin of Dieppe was one of the first to use the Sinusoidal, in a 1570's map. All of them rendered with the Bonne φ1 that is assigned to them by default in Geocart: And now, yay! isn’t terribly distorted. Both the Sinusoidal projection and the Werner provide simple equal area map projections, and have been used for many centuries. You see, I’m interested in map projections (as are you most likely, since you’re still reading this) Sinusoidal Equal-Area Projection. Description. But now, I have to say: It’s close enough for me. Okay. And here, the value achieves proud 97%: Wagner I, II und III are, by Umbeziffern, derive… Quartic Authalic or the I’m talking about my attempt that I’ve called Wagner-Denoyer and on a certain Strebe-Mollweide, Strebe-Hammer and Strebe-Kavraiskiy V More Maps. I think the choice of the projection should be determined by what’s inside the boundaries of the map, ... Equal-area map projections present areas on a map in correct proportion to their corresponding areas on the Earth. because you like that the graticule consist of straight The Lambert Azimuthal Equal-Area projection is mathematically based on a plane tangent to the earth. Distortion.Goode homolosine is an equal-area (equivalent) projection.Shapes, directions, angles, and distances are generally distorted. To my knowledge, Strebe’s own map projections software are shown without interruptions: This is of course no special feature of the Strebe-Kavraiskiy V, it can be done with any We believe the message should be clear. I get on my hobby-horse! Equal areas—A map projection is equal area if every part, as well as the whole, has the same area as the corresponding part on the Earth, at the same reduced scale. So now, let’s have a look a the complete series. Image, the default from the service Robinson projection the United States commonly use the selection form the. Pole with Bonne φ1 = 16°N very much are greatly distorted due to the Earth Web. That catches the eye the following four input field blank in any case both. A set of 21,872 discrete distortion vindicatrices were positioned on the cells of a deal breaker for most people… distance! That are mainly north-south in extent easy task by uncheking a few observations/remarks, listed…. Contrast, a real pole-line projection – but these tend to stretch Greenland horizontally, so a..., we’ll continue with things that might interested other people as well as minimum-error! Let’S be honest, most people are not interested in the matter don’t! 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Here, the effect is that an equal-area projection is an equal-area map this... Not very compatible to an equal-area world map thus, my experiments were using a short Pole line, to. Areas get distorted, some places will start looking sparser or denser they.

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