A fine globe will place all features within 0.5 mm of the correct location. U.S. Geological Survey Professional Paper 1453. Two Thousand Years Map Projections: A Working Manual. Area. No projection can preserve all these properties, and as a result, all flat maps are distorted to some degree. States Government Printing Office. Section E1 - Period A – Room 230. Press. McGraw-Hill. School Year 17-18 Semester 2. Area 2. Porter C.I. In other Equidistant projections, the equator and all meridians are true. the generating equations r = Rp, 0 = A, for the azimuthal equidistant projection can be gen- CONCLUSIONS eralized to create a large class of “new” pro- A recent book includes the following state- jections, namely T = Rpq, B = A, where the ex- ment: zyxwv ponent q is an arbitrary positive element from the set of real numbers. The boundary meridians bulge outward excessively producing considerable shape distortion near the map outline. In contrast to previous setups, it does not project well-known phase-shifted sinusoidal fringes and Gray code patterns, but aperiodic sinusoidal … The Sinusodial projection is an equal-area map, much like the Mollweide though much more distorted. Shapes, directions, The other meridians are sinusoidal curves, bulging away from the central meridian and equally spaced. Bulging meridians produce Map Projections: A Working Manual. Shape and angles are correct along the central meridian and equator. In accomplishing this, the unavoidable east-west stretching of the map, which increases as distance away from the equatorincreases, is accompanied by a corresponding north-south stretching, so that at every point location, the east-west scale is the same as the north-south scale, making the project… Its name is derived from sine. Bulging meridians produce considerable distortion toward the edge of the projection. This article describes an alternative intermediate projection. U.S. The property of the Mercator projection map that made it useful to navigators is that it preserves angles. Specified in [square brackets]: Actual size of the projection (minus the black or white background). Sinusoidal graph (blue) with constants A = 2, B = 3, C = 4, D = 5 and sin x (red). General Cartography (1938), p. 88. Washington, DC: United States Government Printing Office. Distortion values are symmetric across the equator and the central The sinusoidal projection is a pseudocylindrical equal-area projection displaying all parallels and the central meridian at true scale. Scale is true only on the central meridian and the parallels. There are intermediate projections with similar properties, of which the best known is the Bonne projection. The other meridians are sinusoidal curves, bulging away from the central meridian and equally spaced. Shape 3. The equator and the central meridian are projected as straight lines, where the projected equator is two times as long as the central meridian. Properties of Sinusoidal Projection. As another example, nates, but in the properties of the projections. The Sinusoidal projection is an equal-area world map projection that has straight, horizontal parallels spaced equally at their true distances. We will continue to investigate this problem. SATEC @ W.A. At one time this grid was called the "Sanson-Flamsteed" projection in honor of Nicholas Sanson, the French cartographer, and Flamsteed, the … The projection has also been used for maps of continents near the equator, like South America and Africa, centered on their own central meridians. The central meridian is a straight line and all other meridians are equally spaced sinusoidal curves. The projection distorts shape, area, scale, and distance in an attempt to balance the errors of projection properties. Mercator's 1569 edition was a large planisphere measuring 202 by 124 cm, printed in eighteen separate sheets. The subsections below describe the sinusoidal projection properties. angles, and distances are generally distorted. Usage Sinusoidal is a pseudocylindric projection. For example, in the Sinusoidal projection, the equator and all parallels are their true lengths. In the sinusoidal projection, areas on the data grids are proportional to the same areas on the Earth, and distances are correct along all parallels and the central meridian. Snyder, J. P. (1993). a point are obtained by The sinusoidal projection is also used for ar- x R( o) cos chiving AVHRR datasets for the world, be- y R (1) cause the sinusoidal projection is a component part of the interrupted Goode Homolosine where R equals the radius of the sphere, projection used for referencing those data equals longitude east of Greenwich, o equals (Steinwand, Hutchinson, and Snyder 1995). Finally, the data are neither conformal, perspective, nor equidistant (USGS 2000). The Mercator projection doesn’t preserve area correctly, especially as you get closer to the poles. There are intermediate projections with similar properties, of which the best known is the Bonne projection. Scale is true along Fortunately, you can choose from many different map projections. [1], The best uses for this projection are mapping Africa or South America, since the distortion is least in these areas.[2]. The equator and the central meridian are projected as straight lines, where the projected equator is two times as long as the central meridian. Also known as Sanson–Flamsteed—As a world map, this projection maintains equal area despite conformal distortion. Geological Survey Professional Paper 1395. Formula for a Sinusoidal Function A sinusoidal function can be written in terms of the sine (U. Washington): Where A, B, C, D are fixed constants and A & B are positive. The Sinusoidal Projection is a coordinate transform often used to map geographical coordinates on to a flat surface in order to generate a map. Of course, Bonne's projection could also be mated, along a standard meridian, with the Polyconic, and the Sinusoidal could be joined, along the Equator, with the Mercator or the Miller Cylindrical; as long as the two projections are everywhere conformal and have uniform scale where joined, they do not have to have the same properties elsewhere. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later. Raisz, Erwin. Distortion values are symmetric across the equator and the central meridian. The poles are presented as points and they appear as protruding edges. The graticule is symmetric across the equator and the central meridian. Sinusoidal functions are very common in science and mathematics, as many natural patterns oscillate (such as physical waves, electromagnetic radiation, etc.) Other meridians are sinusoidal curves. Still others (for example, Two-point Equidistant) show true scale between one or two points and every other point on the map. Each projection preserves or compromises or approximates basic metric properties in different ways. Areas are represented accurately. The … Bearing 5. 04-0092_ncrs being used to project the data. The lateral meridians quite excessively bulge outward, producing considerable shape distortion at and near the map outline. Direction 4. All meridians are curved lines. moderate near the projection center. This page was last modified on 25 October 2014, at 15:25. The Sinusoidal projection and the Werner projection are equal area projections of the world. Snyder, J. P. (1987). Some of these properties are: 1. Map Projections. To achieve this accuracy with a Sinusoidal projection--at least at the boundaries of all land masses--requires each gore to extend no more than about 6 degrees from its central meridian: that would be 30 gores in each hemisphere, 60 total. The projection is similar to the sinusoidal projection except a meridian follows a section of a parabolic curve. Geological Survey Professional Paper 1395. 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. The central meridian is straight, and the others are curves that derive from a true division of each parallel. Sinusoidal is an equal-area (equivalent) projection. U.S. Geological Survey Professional Paper 1453. Jean Cossin of Dieppe was one of the first to use the Sinusoidal, in a 1570's map. Projection. Distance 6. of Map Projections. This has … Section H3 - Period D – Room 230 Properties Shape. Below are the sections from the resample.log. The poles are greatly distorted due to the odd shape of the map. Distance The item Africa: Sinusoidal Projection represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries. This property is preserved, at least for half of the Equator, if we consider the transverse aspect of the Sinusoidal projection as well: The shape of South America suggests that an oblique Sinusoidal projection might be useful in producing an equal-area map of South America with low angular distortion. The graph of has an amplitude (maximum distance from x-axis) of 1 and a period (length of function before it repeats) of . The sinusoidal projection is appropriate for thematic world maps although its use is not recommended. Flattening the Earth. Snyder, J. P. and Voxland, P. M. (1989). Robinson; Sinusoidal Equal Area; Sinusoidal equal-area maps have straight parallels at right angles to a central meridian. No distortion along the central meridian and the equator. Scale Map projections can be constructed to preserve one or some of these properties, though not all of them simultaneously. This is his famous world map of 1569. Many properties can be measured on the earth's surface independently of its geography. every parallel and the central meridian. Sinusoidal projection definition is - an equal-area map projection capable of showing the entire surface of the earth with all parallels as straight lines evenly spaced, the central meridian as one half the length of the equator, and all other meridians as curved lines. Sinusoidal is an equal-area (equivalent) projection. Smaller regions using the interrupted form exhibit less distortion than the uninterrupted sinusoidal projection of the world. Local angles are correct along the central meridian and the equator but distorted elsewhere. There are four main properties: Area — Some projections distort areas (e.g., Mercator projection) Notice how Greenland is about as big as South America on a Mercator projection. The purpose of the map, then, determines which projection should form the base for the map. Image of: Sinusoidal. Each is distinguished by its suitability for representing a particular portion and amount of the earth's surface and by its ability to preserve distance, area, shape, or direction. We propose to use an array projector for 3-D shape measurements, which enables much higher projection frame rates of up to the 100-kHz range. Shapes are increasingly distorted away from the central meridian and near the poles. We are unsure which value is Page 1. The parallels are straight lines that intersect centre meridian at right angles. 7) Sinusoidal Equal Area The Sinusoidal Equal Area map projection is considered a pseudo-cylindrical projection. This item is available to borrow from all library branches. It was presented by John Evelyn Edmund Craster in 1929. Flattening the Earth. The mapping platform for your organization, Free template maps and apps for your industry. U.S. The central meridian is straight, and the others are curves that derive from a true division of each parallel. 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. The Mercator projection was invented by Gerardus Mercator, a Flemish mapmaker. Two Thousand Years As in all cylindrical projections, parallels and meridians are straight and perpendicular to each other. MCV4U1-E1/H3 – Calculus and Vectors - Grade 12 University Preparation. His name is a latinized version of Gerhard Kramer. considerable distortion toward the edge of the projection. The Nomenclature and Classification of Map Projections, University of Colorado at Boulder - Map Projection Overview with Illustrations, http://wiki.gis.com/wiki/index.php?title=Sinusoidal_projection&oldid=748841. An Album of Map It is typically stated that this projection is area- Projections. of Map Projections. The Sinusoidal projection is an equal-area world map projection that has straight, horizontal parallels spaced equally at their true distances. An Album of Map sumption that surface properties change little during this period of time, POLDER-3 can provide an adequate sampling of di-rectional space for a given pixel to reconstruct BRDF of surface ... level-3 gridded product in the Sinusoidal projection at 463.3-m spatial resolution. B. DISTORTION PROPERTIES angles, areas, directions, shapes and distances become distorted when transformed from a curved surface to a plane all these properties cannot be kept undistorted in a single projection usually the distortion in one property will be kept to … Distortions are Distortions are moderate near the projection center. The Sinusoidal projection and the Werner projection are equal area projections of the world. Chicago and London: University of Chicago – whuber Dec 10 '12 at 17:19 In reality, South America is eight times larger than Greenland. The projection was developed in the 16th century. However in the SINUSOIDAL PROJECTION PARAMETERS: the incorrect 6370997.000000 is reported. Projections. Direction. A Sinusoidal function or sine wave is a function of an oscillation. Sinusoidal is a pseudocylindric projection. Washington, DC: United This projection compresses shapes in higher latitudes, but shapes are good in the central section. • Media related to Sinusoidal projection at Wikimedia Commons Since many p… meridian. The sinusoidal projection is also known as the Sanson-Flamsteed and Mercator-Sanson projection after the cartographers who used it. The parallels are equally spaced straight lines perpendicular to the central meridian. Scale is true along every parallel and the central meridian. In the Sinusoidal Equal Area projection all parallels and the central meridian are standard lines. A sinusoidal interrupted Mollweide projection discards the central meridian in favor of alternating half-meridians which terminate at right angles to the equator. A modern Mercator projection map. 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