Reads like textbook
This article is too big, at the present state it is not at all an encyclopedia article, it is just a piece of a textbook. I think it should be moved to corresponding wiki-book project and here only minimal set of facts should stay. It should not contain proofs, infact I do not think these proofs are interesting enough to be here, but it is ok for a text-book. Tosha 06:52, 15 Apr 2004 (UTC)
I agree. This is...a bit much. The explicit calculations are distracting from getting an overall view. (Anon.)
There is already a place for discussing Moebius transformations and cross-ratio. I suppose some people might prefer the direct computational proof of invariance of cross-ratio; not to my taste. So I think some at least of the projective line material could be moved elsewhere.
Also, the transformation of conics is done in nineteenth-century style. I'm sure there is a better way of expressing it.
Charles Matthews 10:46, 7 May 2004 (UTC)
- If there's no objection, I may try to move some of the proofs over to "proof pages", analogous to others on Category:Article proofs. This should make the page easier to read and quicker to load, without loosing content. linas 03:43, 27 June 2006 (UTC)
Too long and misses the main point: If V and W are vector spaces and T is a linear transformation from V to W, then T defines a projective transformation t from P(V) to P(W) if and only if T is invertible. —Preceding unsigned comment added by 184.108.40.206 (talk) 20:39, 16 February 2008 (UTC)
My view is a little contrary to the idea of stream-lining this article too much. Not so quick: There was the suggestion that it was written "19th century style". And I don't find it a problem at all. I read this article and realised that for the first time I actually got a much better intuition for the Moebius transform and higher dimensional generalisations, and perhaps for the whole idea of projective transformations. I can even see that the "19th century" method was at that point the best way to find the more general theory, namely by someone writing pages of tedious algebra to arrive at something quite powerful and general. Yes, this may be written for a beginner's level, because all it assumes is that you know basic algebraic operations and a little bit linear algebra. Of course, it can be presented in wonderfully compact form. But before you can appreciate the compact, elegant and generalised form, you may need to see the gory detail of this article first. So I would suggest, if someone wants to really rewrite this, he or she should keep the current form almost completely intact in the wiki and refer to it. You can always write another piece of math that represents this in the most compact form you like, but you easily risk to leave anyone uninitiated (like myself) behind. Reiner —Preceding unsigned comment added by 220.127.116.11 (talk) 19:07, 11 July 2009 (UTC)
Agree completely with the comment saying "The explicit calculations are distracting from getting an overall view." E.g., the article never even mentions that it's necessary to adjoin points at infinity; it just casually uses an infinity symbol for the first time somewhere in the middle of a calculation.--18.104.22.168 (talk) 19:38, 22 August 2009 (UTC)
Agreed that this page, while good, is written in textbook style, not encyclopedic. It’s useful content, but not suited for ’pedia (pages like homography and projective linear transformation cover this content in encyclopedia style). I’ve thus marked it to be transwikied to Wikibooks, where it may find a better home.
- It’s been moved to Wikibooks at: wikibooks:Projective Geometry/Classic/Projective Transformations, where it can further be worked on – thanks all!
- —Nils von Barth (nbarth) (talk) 23:13, 6 December 2009 (UTC)
This article has been saved from Redirect to homography because it has content not covered in that article. In particular, correlation (projective geometry) is not referred to. Correlations are peculiar to projective geometry and express the important property of duality (projective geometry) that such spaces possess. The article perspectivity about one of the basic projective transformations is also without reference at Homography.
It is not advisable to lump all Projective transformations into the category of Homographies, particularly since homography (computer vision) has been the primary interpretation of that term in Mathematical Reviews during the last two decades. The terms in the current article provide discrimination among the types, including use of Homography to indicate projective mappings on a Projective line over a ring, such as quaternions, as found in the book by du Val and in Mathematical Reviews.Rgdboer (talk) 21:14, 4 January 2014 (UTC)
- You have no reference that says a correlation is a homography and I can produce several that explicitly state otherwise. You may not like the way terms are used, such as projective transformation being a synonym for homography, but we do not determine the usage, only report on it. When you have reliable secondary sources for what you claim, we'll talk about it. Until then, I'm reverting. Bill Cherowitzo (talk) 03:52, 5 January 2014 (UTC)
But a Correlation (projective geometry) is a projective transformation, thus justifying this page as a stand-alone. Warning: see WP:3RR. Only the 24 hour stipulation has saved you from a violation.Rgdboer (talk) 20:40, 5 January 2014 (UTC)
- No it isn't, which is why this page should remain a redirect. You can prove me wrong by finding a citation which agrees with your unsupported statement and opposes J.W. Young, W.T. Fishback, H. Eves, P. Yale, and Emil Artin, among others, all of whom explicitly state that a projective transformation is an alternate term for a projectivity. You also don't count very well, I've only reverted you twice. Bill Cherowitzo (talk)