There is no such thing as Lenticular.
https://www.mapthematics.com/ProjectionsList.php
This shows "Lenticular". How does this word make sense? And why aren't all "Miscellaneous" projections in "Lenticular"?
Lenticular
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Atarimaster
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Re: Lenticular
The short answer:
daan explained the term »lenticular« in his Projection Essentials tutorial.
The long answer, mainly regarding the statement that »there is no such thing as Lenticular«:
The categorization of map projections is, to a certain extend, arbitrary. It isn’t cast in stone.
For example, cylindrical projections are a special case of conic projections, with the apex moved to infinity. Yet, as you pointed out yourself, they are also a special case of pseudocylindric projections. But nobody ever refers to e.g. the plate carrée as conical (for good reason).
When Eckert introduced his six famous projections in 1906, he didn’t use the term pseudocylindrical or its german equivalent unecht-zylindrisch but called them Polarongkoide. In his last book, published posthumously in 1939, he also used unecht-zylindrisch; while Winkel in 1921 explicitly dismissed the term polarongkoid for Eckert V to call it unechte Berührungszylinderprojektion
(pseudo tangent cylindrical projection). Winkel I and II are usually listed as pseudocylindrical – Winkel himself called them unechte Schnittzylinderprojektionen (pseudo secant cylindrical projections), so basically, he sub-divided the pseudocylindrical group into those which have a single standard parallel and those which have two.
Winkel Tripel and Wagner’s projections VII to IX are sometimes called polyconic, sometimes pseudozimuthal. Winkel said cylindric-azimuthal projection, and Wagner just noted derived from the equatorial azimuthal projection. In Geocart, they are called lenticular – so what?
Everybody is free to suggest new terms and categorizations. If they are sensible and practical, they might adopted by other authors and over time, it might seem as if there never had been any different categories. If not, they sink into oblivion, like Eckert’s Polarongkoide.
To myself, I call projections like the American Polyconic, Dietrich-Kitada or the Lagrange (in some configurations) cell division projections. If I’d publish that term somewhere, then hey, maybe it’s widely used in 40 or 50 years (although I seriously doubt that), and only my respect for Mr. Canters stops me from saying what I call his low-error polyconic projection with straight equator and symmetry about the central meridian (I like that projection, but my private term sounds quite insulting).
And did you know that many german cartographers refuse to use the word Projektion and use Kartennetzentwurf instead, because they argue that Projektion should only be used for those that can be projected physically?
And by the way, I think it’d be a bad idea to throw all projections that aren’t cylindric, pseudocylindric, azimuthal or conic into one big class, whatever that class might be called.
daan decided to split them up into »Lenticular« and »Miscellaneous« (for reasons that are given in the tutorial mentioned above). Maybe that’s a good classification, maybe not. At the end of the day, it doesn’t matter, since currently, there simply is no universally accepted term for projections that don’t fall into the four groups I just mentioned.
Kind regards,
Tobias
daan explained the term »lenticular« in his Projection Essentials tutorial.
The long answer, mainly regarding the statement that »there is no such thing as Lenticular«:
The categorization of map projections is, to a certain extend, arbitrary. It isn’t cast in stone.
For example, cylindrical projections are a special case of conic projections, with the apex moved to infinity. Yet, as you pointed out yourself, they are also a special case of pseudocylindric projections. But nobody ever refers to e.g. the plate carrée as conical (for good reason).
When Eckert introduced his six famous projections in 1906, he didn’t use the term pseudocylindrical or its german equivalent unecht-zylindrisch but called them Polarongkoide. In his last book, published posthumously in 1939, he also used unecht-zylindrisch; while Winkel in 1921 explicitly dismissed the term polarongkoid for Eckert V to call it unechte Berührungszylinderprojektion
(pseudo tangent cylindrical projection). Winkel I and II are usually listed as pseudocylindrical – Winkel himself called them unechte Schnittzylinderprojektionen (pseudo secant cylindrical projections), so basically, he sub-divided the pseudocylindrical group into those which have a single standard parallel and those which have two.
Winkel Tripel and Wagner’s projections VII to IX are sometimes called polyconic, sometimes pseudozimuthal. Winkel said cylindric-azimuthal projection, and Wagner just noted derived from the equatorial azimuthal projection. In Geocart, they are called lenticular – so what?
Everybody is free to suggest new terms and categorizations. If they are sensible and practical, they might adopted by other authors and over time, it might seem as if there never had been any different categories. If not, they sink into oblivion, like Eckert’s Polarongkoide.
To myself, I call projections like the American Polyconic, Dietrich-Kitada or the Lagrange (in some configurations) cell division projections. If I’d publish that term somewhere, then hey, maybe it’s widely used in 40 or 50 years (although I seriously doubt that), and only my respect for Mr. Canters stops me from saying what I call his low-error polyconic projection with straight equator and symmetry about the central meridian (I like that projection, but my private term sounds quite insulting).
And did you know that many german cartographers refuse to use the word Projektion and use Kartennetzentwurf instead, because they argue that Projektion should only be used for those that can be projected physically?
And by the way, I think it’d be a bad idea to throw all projections that aren’t cylindric, pseudocylindric, azimuthal or conic into one big class, whatever that class might be called.
daan decided to split them up into »Lenticular« and »Miscellaneous« (for reasons that are given in the tutorial mentioned above). Maybe that’s a good classification, maybe not. At the end of the day, it doesn’t matter, since currently, there simply is no universally accepted term for projections that don’t fall into the four groups I just mentioned.
Kind regards,
Tobias
Re: Lenticular
Also I noticed that there is no pseudoconic category, and pseudoconical projections are in conic category.
Re: Lenticular
Excellent explanation, Tobias!
Cylindric and pseudocylindric are the only two categories that Geocart rigorously observes. Those two categories are precisely, unanimously defined, and they each contain enormous numbers of projections described by the literature.
Pseudoconic is not so precisely defined. Geocart puts anything that is conic, polyconic, “pseudoconic”, cardioid, or variants of conics, all into the Conics menu.
Pseudoazimuthal is not so precisely defined. Geocart puts anything that is azimuthal, “pseudoazimuthal”, “quasiazimuthal”, retroazimuthal, all into the Azimuthal menu.
Lenticular is not so precisely defined. As Tobias noted, this nomenclature is specific to Geocart. It contains projections that are similar to pseudocylindric but that have parallels that bow toward the poles. The name means “lens-shaped”. It is vaguely descriptive.
Miscellaneous holds the rest.
These divisions in Geocart are not meant to make statements of rigorous classification. They are simply organizational. It would be wasteful of screen real estate to have some categories housing hundreds of projections and others housing just a few, or to proliferate the categories into some unwieldy count of them. And, lastly, many systems of classification exist. They contradict each other, and some of them dump most of the projections people might be interested in into a ‘miscellaneous’ bucket (but usually called something else).
— daan
Cylindric and pseudocylindric are the only two categories that Geocart rigorously observes. Those two categories are precisely, unanimously defined, and they each contain enormous numbers of projections described by the literature.
Pseudoconic is not so precisely defined. Geocart puts anything that is conic, polyconic, “pseudoconic”, cardioid, or variants of conics, all into the Conics menu.
Pseudoazimuthal is not so precisely defined. Geocart puts anything that is azimuthal, “pseudoazimuthal”, “quasiazimuthal”, retroazimuthal, all into the Azimuthal menu.
Lenticular is not so precisely defined. As Tobias noted, this nomenclature is specific to Geocart. It contains projections that are similar to pseudocylindric but that have parallels that bow toward the poles. The name means “lens-shaped”. It is vaguely descriptive.
Miscellaneous holds the rest.
These divisions in Geocart are not meant to make statements of rigorous classification. They are simply organizational. It would be wasteful of screen real estate to have some categories housing hundreds of projections and others housing just a few, or to proliferate the categories into some unwieldy count of them. And, lastly, many systems of classification exist. They contradict each other, and some of them dump most of the projections people might be interested in into a ‘miscellaneous’ bucket (but usually called something else).
— daan