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EdwardLane, thanks for the brilliant start. I have taken the liberty of restructuring considerably. Your foundation faithfully mirrors the state of the articles. Unfortunately, as far as categorization is concerned, the articles lack sources and merely comprise an ad hoc accretion of edits by people of varying interests and knowledge. They just don’t reflect the state of the literature or reality very well.
So, while I understand that my own edits to this template would be considered unsourced, so are the articles from which you developed the first state of this template. My purpose in restructuring is to encourage changes in the articles to better match reality and reduce the ad hoc (and incoherent) nature of their composition.
That said, we’re already beyond the limits of the literature. “Hybrid” and “compromise” are terms that appear in the literature, but not in the context of some taxonomic hierarchy. Hence it was WP:OR—and mistaken at that—for some editor to lump them into “By Surface”.
“By Surface” is already a suspect term: The various “pseudos” are not surfaces and they’re not even “conceptual” surfaces. They are mathematical abstractions that preserve some trait of a surface development while relaxing the remaining traits. I am therefore conflicted about their inclusion in “By Surface”. “Surface” itself is already generalized; it is not as if a cylindric projection is geometrically projected onto a cylinder in the usual case. So we have these terms that are supposed to aid in conceptualizing but they encourage false beliefs because people take them too literally.
I took the liberty of adding “By Construction”, though I do not necessarily like that terminology; it is a little too general. The various “pseudos” more properly belong there than in “By Surface”, but I won’t make that change without discussion.
Thanks, and now you're running beyond the limits of my knowledge, and I know some people are sticklers for wikilawyering content one way of another, but you seem to have a good grasp of the subject, so your opinion of what is 'roughly right' is going to be better than mine. So that will have to do, at least until someone finds a bunch of referenced material giving a nice structure for us to hang the template structure off. Presumably there are some books on 'Varieties of map projection' that have chapter headings and sub headings that might have a structure that could be useful (and 'not original research'). Are you saying that 'more accurately' "by surface" should be "by algorithm" and then "by surface - conical" really ought to be "conical surface approximation algorithms" (obviously piped to something shorter)?
The literature is more sparse than you might imagine. Map projections were not even named systematically, let alone treated as a subject, before d’Azevac’s 1863 Coup d’Oeil Historique sur la Projection des Cartes Géographique. For decades after that time, texts tended to describe just the three surface classes, making occasional (and seeming almost begrudging) references to the few common exceptions. The 20th century is when the huge profusion of projections we see today burst onto the scene. L.P. Lee wrote a detailed paper on classification in 1944 called The Nomenclature and Classification of Map Projections as one of the few primary sources; that’s where pseudoconic first appear. In his conclusion he write, “The foregoing observations reveal that the terminology of map projections is in a state of confusion that would not be tolerated in any other modern science, and a systematization is long overdue.” I’m not sure it’s improved much since then. Soviet-sphere authors put out many proposals over the decades but these have remained largely inaccessible to the West and have made no impact outside the old Soviet Union.
Are you saying that 'more accurately' "by surface" should be "by algorithm" and then "by surface - conical" really ought to be "conical surface approximation algorithms" (obviously piped to something shorter)? Something like that. When the projection is in equatorial aspect, and if the meridians are straight line segments which are or can be extended to radiate from a single point, and if the meridians have constant angle between constant meridian separations, and if the parallels are concentric circular arcs, then you have what we call a conic projection, regardless of the spacing of those circular arcs. In the general case, that spacing is algorithmic rather than perspective or even geometric. You can regard the cone as some convenient “constraint” placed on the development of the projection so that the mathematician had a direction to go in, and you can regard it as a convenience for construction using just ruler and compass, but the significance of those regardings to the notion of map projection, let alone to the purpose of the map, is another matter entirely.
LP Lee did not like the three surfaces, regarding their classical treatment as misleading, writing, “No reference has been made in the above definitions to cylinders, cones or planes. The projections are termed cylindric or conic because they can be regarded as developed on a cylinder or a cone, as the case may be, but it is as well to dispense with picturing cylinders and cones, since they have given rise to much misunderstanding. Particularly is this so with regard to the conic projections with two standard parallels: they may be regarded as developed on cones, but they are cones which bear no simple relationship to the sphere. In reality, cylinders and cones provide us with convenient descriptive terms, but little else.”
Sounds like that Lee quote and the 'then' definition from your paragraph above of "what is a conic projection" needs to get into the Map projection article (and probably the same for each of the other categories of projection). The lack of systemization available might be an issue, if the russians do have some systemization that makes sense, then perhaps a google translate of one of those can be used as a reliable source. But that might be a bit tricky to find. EdwardLane (talk) 10:25, 16 April 2012 (UTC)[reply]
One incidental question are "pseudo azimuthal - hammer" and 'hammer retroazimuthal' meant to be the same projection/not (if so one should be renamed)?
Oh and where you created 'general perspective' it looked like it was including "central cylindric" and "perspective conic" - but I didn't think that was your intention so I added (rather clumsily I'm afraid) 'other perspective'.
Not terrible, but I was hoping there was some way for the hierarchy to adequately display unequal branchings. Grr.
Did I mention you're doing a grand job - and I like the 'by construction section'
Presently the map projection articles and this template refer to “polyhedral projections”, but that is a solecism. They are “projections” onto polyhedra, but the method of projection onto a surface of the polyhedron is independent of the geometry of the polyhedron and how it is unfolded. The projection onto the surface could be identical for many “projections” which are known by different names. For example, many polyhedral schemes use the gnomonic projection for the actual business of projection, yet receive their status as independent “projections” on the basis of the polyhedron chosen and how it is laid out on the plane.
So, we have situations where an inventor has laid out a particular polyhedron geometry and called it a projection, with little thought given to the actual business of projection (Waterman). We have situations where the inventor has proposed a novel projection coupled with a specific polyhedron (Fisher). We have situations where novel projections have been devised suitable for adaptation to “any” polyhedron (Lee). Mess. Strebe (talk) 18:59, 9 April 2012 (UTC)[reply]
Think I under stand the 3 cases here, it sounds like they ought really to have different rows in the table - two under polyhedral arrangements (the fisher and waterman types), with subsections in each case being which (common/novel) projection was used and what polyhedron arrangement, and 1 under polyhedral projections (the Lee types) ? does that make sense ? EdwardLane (talk) 10:13, 16 April 2012 (UTC)[reply]
