Local linear scale factors in map projections in the direction of coordinate axes

Lapaine, Miljenko; Frančula, Nedjeljko; Tutek, Željka

doi:10.1080/10095020.2021.1968321

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…x = Rcos φsin λ, y = −Rcos φcos λ, (22) where φ and λ are latitude and longitude, respectively. For example, for the northern hemisphere, φ ∈ 0, π 2 , and λ ∈ [−π, π] (Figure 1).…”

Section: Orthographic Projection-normal Aspectmentioning

confidence: 99%

“…So, it is a projection equidistantly mapped along the parallels. Furthermore, the angle β between the images of meridians and parallels is π/2, and the maximum and minimum values of the local linear scale factor are determined by [22]:…”

Section: Orthographic Projection-normal Aspectmentioning

confidence: 99%

“…Thus, the normal aspect orthographic projection is an equidistant projection in the direction of parallels, which is one of the main directions. According to [22], the main directions ψ can be determined from the expression (28)…”

Section: Orthographic Projection-normal Aspectmentioning

confidence: 99%

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Parallels in Cartography: Standard, Equidistantly Mapped and True Length Parallels

Lapaine

2024

Geographies

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In the literature on map projections, we regularly encounter the name standard parallel or standard parallels. However, it is obvious that a unique definition of a standard parallel is not universally accepted. To fully clarify the meaning of standard parallels, the author proposes the notion of equidistantly mapped parallels, which has not been common in the literature so far. Equidistantly mapped parallels can be in the direction of the parallel or in the direction of the meridian. Here, it is shown that every standard parallel is also an equidistantly mapped parallel, but that the reverse need not be true. If the parallel is mapped equidistantly in the direction of the parallel, then its length in the projection plane is equal to the length of that parallel on the sphere. The opposite does not have to be true, i.e., if the length of the image of the parallel in the projection plane is equal to the length of the parallel on the sphere, this does not mean that the parallel was mapped equidistantly. In addition to standard and equidistant parallels, the concept of parallels of true length also appears in the theory of map projections. They should also be distinguished from standard and equidistant parallels.

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Section: Orthographic Projection-normal Aspectmentioning

confidence: 99%

Section: Orthographic Projection-normal Aspectmentioning

confidence: 99%

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Parallels in Cartography: Standard, Equidistantly Mapped and True Length Parallels

Lapaine

2024

Geographies

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“…In any software that serves to select a map projection, as well as in any GIS, distortion display options should be built in. Formulae for determining the local linear scale factor in a direction of a coordinate axis are especially important in working with raster data [8,[20][21][22].…”

Section: Instead Of Conclusionmentioning

confidence: 99%

“…Furthermore, the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas are derived. The paper is a generalization to the ellipsoid of a previous paper developed for a sphere [8]. Tissot's indicatrices illustrate linear, angular, and areal distortions of maps, defined as follows:…”

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confidence: 99%

Local Linear Scale Factors in Map Projections of an Ellipsoid

Lapaine

2021

Geographies

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The main problem in cartography is that it is not possible to map/project/transform a spherical or ellipsoidal surface into a plane without distortions. The distortions of areas, angles, and/or distances are immanent to all maps. It is known that scale changes from point to point, and at certain points, the scale usually depends on the direction. The local linear scale factor c is one of the most important indicators of distortion distribution in the theory of map projections. It is not possible to find out the values of the local linear scale factor c in directions of coordinate axes x and y immediately from the definition of c. To solve this problem, in this paper, we derive new formulae for the calculation of c for a rotational ellipsoid. In addition, we derive the formula for computing c in any direction defined by dx and dy. We also considered the position and magnitude of the extreme values of c and derived new formulae for a rotational ellipsoid.

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Design and Application Research of Virtual Surveying and Mapping Mechanical Drawing Teaching Assistant System: Based on WebGL Technology

Dai

2024

J. Inst. Eng. India Ser. C

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Local linear scale factors in map projections in the direction of coordinate axes

Cited by 5 publications

References 6 publications

Parallels in Cartography: Standard, Equidistantly Mapped and True Length Parallels

Parallels in Cartography: Standard, Equidistantly Mapped and True Length Parallels

Local Linear Scale Factors in Map Projections of an Ellipsoid

Design and Application Research of Virtual Surveying and Mapping Mechanical Drawing Teaching Assistant System: Based on WebGL Technology

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