Talk:Axonometric projection

Shouldn't Axonometric view be a subheading of auxiliary view

Axonometric view seems pretty much a particular type of auxiliary view where one axis is usually shown as vertical. Shouldnt this be categorized as a type of auxiliary view? —Preceding unsigned comment added by 210.56.14.76 (talk) 10:38, 2 October 2009 (UTC)

Not sure, do we even need the categorization into "main-axis" and "auxiliary" view? E.g. for round objects those make not much sense. In the end, we simply should use whatever is used in other literature. --Allefant (talk) 19:53, 6 October 2009 (UTC)

Axonometric projection at Orthographic projection

Axonometric projection is addressed at Orthographic projection, under Pictorials ... suggest present site might be discontinued Pat Kelso 21:16, Mar 1, 2004 (UTC)

I have incorporated the info from orthographic projection into this article. Warofdreams 17:20, 2 Mar 2004 (UTC)

re: "Axonometric projection is a form of orthographic projection. It is a method for the visual representation of three-dimensional objects in which there are no vanishing points, objects are drawn to the same scale regardless of distance, and all line which are parallel in three-dimensional space are parallel in the two-dimensional picture."

The reference to no vanishing points and the scale being independent of distance is implicit in the definition of orthographic projection and therefore perhaps redundant. The mention of these, however, suggests a comparison with Perspective projection which may be an excellent point of departure for the entire article as it is not strictly addressed else where, to my knowledge.

The "Longer explanation of axonometric projection" is frought with misstatements and technical errors.... suggest it be discontinued.....

...... Pat Kelso 22:01, Mar 2, 2004 (UTC)

New image

I made a new image and put it in the article. I had some issues with the placement, could someone handier with wiki markup fix the placement? Thanks. Phasmatisnox 12:21, 14 September 2007 (UTC)

Placement looks good enough The problem is the navigation box to the right, it takes up the space normally used for images. I at some point moved it down to the bottom, but someone else moved it back up, so would need to first find a consensus to move it down - but the field of descriptive geometry seems somewhat abandoned currently. --Allefant 09:43, 25 September 2007 (UTC)

Header

I think this sentence in the header is wrong. "in which the three coordinate axes appear equally foreshortened." You can have an axonometric view from the top, don't you? and then the scale of the z axis is 0.

I'd say that the common idea to all axonometric projections is that the scale of objects does not change with their distance to the observer, or, in other words, that the drawer is at infinite distance. Please, some specialist take care of this! —Preceding unsigned comment added by Gaianauta (talk • contribs) 09:58, 19 February 2009 (UTC)

Yes, it seems that the previous edit, while improving quite a few stuff, moved this sentence to the wrong place. I reverted it for now, someone indeed should take care of this. I may when I find time, but probably won't. --Allefant (talk) 03:51, 20 February 2009 (UTC)

I tried to fix the problem here. If there is more please let me know. -- Marcel Douwe Dekker (talk) 20:44, 1 March 2009 (UTC)

Proposal to merge Dimetric projection and Trimetric projection here

I would like to propose to merge Dimetric projection and Trimetric projection articles here. In it's current shape they have hardly anything offer anything more, then in the article already explained. -- Marcel Douwe Dekker (talk) 21:43, 2 June 2009 (UTC)

Sounds OK. Just make sure to move the video game related stuff in these articles to Video games with isometric graphics. SharkD (talk) 18:38, 7 June 2009 (UTC)

Thanks. Because there were no further objections in the past two weeks I have merged both articles here. -- Marcel Douwe Dekker (talk) 20:40, 18 June 2009 (UTC)

I’ve restored the video-game relation information lost during the merge. As an aside, I don’t think Diablo used Dimetric projection; it looks isometric to me (each tile is a symmetrical rombic rectangle). Samboy (talk) 21:29, 26 November 2009 (UTC)

I reverted your changes. Use of axonometric projection in video games is discussed in Video games with isometric graphics. SharkD  Talk  05:17, 27 November 2009 (UTC)

I moved a lot of content from Isometric projection to here, so maybe we should merge it as well. SharkD  Talk  09:05, 27 November 2009 (UTC)

I think the Isometric projection article should be a separate article, because it is by far the most important projection method in technical drawing. -- Mdd (talk) 20:55, 27 November 2009 (UTC)

Sure, but minus the (now) duplicated content, it's basically a stub article. SharkD  Talk  23:03, 27 November 2009 (UTC)

I think it is important for Isometric projection to exist as a separate article. I would never have found the isometric information if it were merged into Axonometric projection. I was specifically looking for isometric projection, and have never heard of axonometric before, so I would never have looked at it or even guessed that it contained isometric information. --AridWaste (talk) 23:13, 19 February 2010 (UTC)

The search feature would still have led you here via a redirect. SharkD  Talk  00:05, 20 February 2010 (UTC)

I like most of your changes, but there a couple of issues:

• The cabinet image is helpful. There is no reason to remove it.
  • OK, I see why you did this. Took me a while to find a good place to put it on the page. We really need to add more text from the Isometric projection article. Samboy (talk) 19:51, 27 November 2009 (UTC)
    • The same projections are compared/depicted in the other image. See Talk:Video games with isometric graphics#Cabinet image for discussion regarding the images. SharkD  Talk  23:02, 27 November 2009 (UTC)
• Some sections still do not have references. Please find and add references. Samboy (talk) 16:42, 27 November 2009 (UTC)
  • I had added some references to Parallel projection previously (which is very similar to this article). I copied them over to here. The "Limitations" section is missing some refs, but it uses diagrams that readers can easily refer to. SharkD  Talk  03:40, 28 November 2009 (UTC)

Regarding User:Mdd's deleted comments: While the "History" section begins solely with a discussion of isometry, it ends by discussing axonometry in general. Also, the limitations discussed in the "Limitations" section apply equally well to axonometric projection (or any type of parallel projection for that matter) as to isometric projection. For instance, M. C. Escher's Waterfall (1961) used in the section as an example is drawn in dimetric projection, not isometric projection. SharkD  Talk  03:17, 28 November 2009 (UTC)

Any more support/objections to the merger of isometric projection? I don't think we've reached consensus quite yet. (One for the merger, two against, one unspecified.) SharkD  Talk  01:27, 22 August 2010 (UTC)

I'm against the merger as it tends to hamper expansion. Specifically, for the last couple of months I've been working on one of the methods of creating axonometric projections which involves using vector graphic software. This is where you, in the simplest case, take the face on views of the sides of a cube, and squeeze and skew them appropriately. At this point I have several images and animations describing the more general process. I have also created a spreadsheet where you type in your desired downward viewing angle, horizontal viewing angle, tilt of the wall/plane and horizontal rotation of the wall/plane and then the spreadsheet calculates the necessary squeezes and skews and a 2x2 transformation matrix. I am planning to create in each of the isometric, dimetric and trimetric projection articles, a section devoted to how to create these projections. From my point of view it would not work well to jam it all into a single article. By the way, it is my understanding that there is no way to store and then link to a spreadsheet file in the same way that one can store and then link to a image file in Wikipedia. Am I correct in this view and if so does anyone have any suggestions about the best way to provide access to a spreadsheet file? Dave3457 (talk) 18:03, 13 October 2010 (UTC)

Just a few hours ago I wrote the above comment but have since began writing the text for the images I created and have begun to have second thoughts about my position because I have found myself repeating things more often than I thought I would. I'll hold off on a position until I'm further along.

As the two relevant pages still have merge banners it would be nice for me if this issue could be settled one way or the other before I get to far along in my text. Dave3457 (talk) 21:05, 13 October 2010 (UTC)

Just to say that I agree that the three axonometric projections, trimetric, dimetric, and isometric, should be in this page for the fundamental reason that that is the order that is presented and taught in any proper technical drawing book. Miguelmadruga (talk) 08:34, 30 May 2012 (UTC)

Oppose, the title Isometric seems more familiar to a reader, nevertheless who is reading, rather than Axonometric projection--Dr.pragmatist (talk) 10:53, 31 July 2012 (UTC)

History

The history section seems to be based almost exclusively on this purile article by Krikke which is absolutely ludicrous. Axonometry had been used for centuries before Jesuits came back from China, since most military engineers used them for their drawings at least since the 14th century. Farish might have been the first who explained axonometries in english but Gaspard Monge preceded him undoubtedly and I bet most axonometries had been already described mathematically by Italian geometers (but i'm not sure of that). 93.67.104.181 (talk) 15:03, 20 July 2011 (UTC)Athanasius

Op Art & Escher

The concluding section of the article mentions Op Art and then M C Escher. Escher's work is not usually classed as Op Art (typified by Riley and Vasarely). And the example of his work given (The Waterfall) does not use axonometric projection: it uses true linear perspective, though with weak convergence (the vanishing points are well outside the picture margins) which might not be evident at first glance. It may be true that axonometric projections make this sort of thing more straightforward to devise, but they are not essential. Dayvey (talk) 22:37, 4 December 2014 (UTC)

Is the current wording better? SharkD  Talk  01:24, 19 November 2015 (UTC)

Oblique projection?

Why is oblique projection listed here as a type of axonometric projection? I thought it was separate from these. SharkD  Talk  01:18, 19 November 2015 (UTC)

Types of axonometric projections

I am not familiar how the axonometric projection is dealt in English literature. Here some statements common in German literature (see the German version of axonometric projection):

• 1) An axonometric projection is a scaled parallel projection (Theorem of Pohlke), mostly oblique (for example: military view, cabinet view), in special cases an orthographic projection, sometimes a scaled orthographic projection (Ingenieur-Axonometrie, standard isometry).
• 2) An axonometric projection is determined by 5 parameters: the 3 forshortenings vx.vy,vz and the 2 angles alpha, beta between the x- and z-axis and between the y- and z-axis.
• 3) An axonometric projection is called a) isometric, if vx=vy=vz, b) dimetric, if 2 of the vx,vy,vz are equal and 3) trimetric, if vx,vy,vz are all different. For the popular standard isometry we have besides vx=vy=vz that alpha=beta=120 degree. The standard isometry is a scaled orthographic projection. For the parameters for the military view and the cabinet view see the picture .

In order to get a nice picture You have to be careful while choosing the free parametrs.--Ag2gaeh (talk) 13:44, 20 November 2015 (UTC)

This is weird, because I thought axonometric perspective implied that none of the faces of the object should be parallel to the viewing plane, whereas in oblique projection usually there is one object face which is parallel to the viewing plane. For instance, in military perspective the top face of the object is parallel to the viewing plane, and in cavalier perspective it is the front face. SharkD  Talk  21:10, 20 November 2015 (UTC)

Perhaps I misused the word oblique. I used it in the sence of non orthogonal parallel projection. In German I would say schiefe Parallel-Projektion. By the way, You may draw an axonometric picture of any curve or surface/body, for example a sphere, which has no plane faces. -- Ag2gaeh (talk) 21:54, 20 November 2015 (UTC)

Here is a PDF from a textbook of some sort. On page 515 there is a graphical comparison of the different views as I also understand them. The term oblique here means that the viewing direction and viewing plane are not orthogonal to each other, irrespective of what is being looked at. But it also says that multiviews and axonometric are both sub-types of orthographic projection, which is confusing. Maybe a thorough survey of sources is needed. SharkD  Talk  23:25, 20 November 2015 (UTC)

To the page 515: The subscripts (a) multiview projection and (b) axonometric projection are wrong. The texts within the pictures desribe in both cases an orthographic projection. (c) and (d) are correct. — Preceding unsigned comment added by Ag2gaeh (talk • contribs) 12:46, 23 November 2015 (UTC)

(a) multiview projection refers to multiview orthographic projection. I think the pictures are correct. It is the chapter text below the pictures that I think may be problematic. SharkD  Talk  21:48, 23 November 2015 (UTC)

Survey of sources

I'm going to start listing sources and notes here. Please add any that you find as well. SharkD  Talk  22:06, 23 November 2015 (UTC)

Page 1 of DocsFiles search result (link)

Source	Notes
CHAPTER FOURTEEN AXONOMETRIC PROJECTION	Distinguishes between axonometric and oblique perspectives, but lumps multiview and axonometric perspective together as types of orthographic perspective.
9.Axonometric and Central Projections	I did not read the whole text, but it considers military perspective as a type of isometric perspective.
Lecture 3: Composites, Conventions, Axonometrics	Distinguishes between axonometric and oblique perspectives, but lumps multiview and axonometric perspective together as types of orthographic perspective.
7.1 AXONOMETRIC PROJECTION - McGraw-Hill Education	Distinguishes between axonometric and oblique perspectives. Orthographic perspective is mentioned once, but not defined. It may be defined in an earlier chapter. I think the file is missing a bunch of illustrations.
BST12781 BUILDING COMMUNICATION multi view and single view	Considers oblique perspective a type of axonometric perspective, but considers isometric, dimetric and trimetric perspectives as types of orthographic perspective.
technical drawing	Calls oblique perspective "planometric". Also seems to consider planometric and axonometric as synonyms.
Pictorial Drawings: Axonometric Projection pictorial drawing	Distinguishes between axonometric and oblique perspectives, but lumps multiview and axonometric perspective together as types of orthographic perspective.
Slide Set 3 – Orthographic Projection II – Isometric	Distinguishes between axonometric and oblique perspectives, but lumps multiview and axonometric perspective together as types of orthographic perspective.

Page 1 of Google Books search result (link)

Source	Notes
Architectural Graphics By Francis D. K. Ching	Distinguishes between axonometric and oblique perspectives, but lumps multiview and axonometric perspective together as types of orthographic perspective. Quote, "The term 'axonometric' is often misused to describe paraline drawings of oblique projections or the entire class of paraline drawings."
Axonometric and Oblique Drawing: A 3-D Construction, Rendering and Design Guide by Mohammed Saleh Uddin	Mentions axonometric and oblique projections many times (it is the focus of the entire book) but never to describe the same thing.
Machine Drawing:Includes Autocad By Singh Ajeet	Matches the current state of this article. 04:58, 25 November 2015 (UTC)
A New Approach to Axonometric Projection and Its Application to Shop Drawings by John Gilbert McGuire	Distinguishes between axonometric and oblique projection. I could not view the whole text, so was unable to see how he places them w.r.t. orthographic projection.
By Lorraine Farrelly	Defines axonometric projection as a type of "plan oblique drawing".
Art and Representation: New Principles in the Analysis of Pictures By John Willats	Describes axonometric projection as a variety of "vertical oblique projection". I gather he means military projection.
Practice: Architecture, Technique and Representation By Stan Allen	Talks about axonometric projection, but does not mention oblique projection.
Autodesk VIZ in Manufacturing Design: Autodesk VIZ/3ds Max for Engineering ... By Jon M. Duff	Defines axonometric projection without mentioning oblique projection. Distinguishes between axonometric and "principal orthogonal views (Top, Front, Side, etc.)". Does not define orthographic projection.

Others

Source	Notes
Chapter 5 of an (unnamed in the scans) textbook	Matches the article currently. 04:58, 25 November 2015 (UTC)
Descriptive geometry--pure and applied: with a chapter on higher plane ... By Frederick Newton Willson	Defines axonometric and oblique projections separately.

Thank You for the table and the links in it. At a first glance: Axonometric projection is nowhere defined correctly. Here the definition (used in German literature, see the German site on Axonometrie):

parameters of an axonometric proj. in general

special cases

Definition of an axonometric projection

Axonometric projection is a procedure of descriptive geometry to generate 2d-images of 3d-objects using coordinateaxes and coordinates of single points:

1. Choose the images of the coordinate axes in the drawing plane (no two of them on the same line).
2. Choose forshortenings $v_{x},v_{y},v_{z}$.
3. You get the image of a point P=(x,y,z) by: 1) go from the origin $v_{x}\cdot x$ in x-direction, then 2) $v_{y}\cdot y$ in y-direction then 3) $v_{z}\cdot z$ in z-direction and mark the final point .

Pohlke's thorem says: The image of an object produced by this procedure is a scaled parallel projection. The image is mostly a scaled oblique projection. If You chose the parameters of the axonometric projection suitable, You get an exact orthographic projection (see the German site orthogonale Axonometrie). For special cases see the table. A popular axonometric projection with engineers (in Germany) is the Ingenieur- Axonometrie. It uses simple forshortenings ($v_{x}=0.5,v_{y}=1,v_{z}=1$) and delivers nearly an orthographic projection (scale factor is near 1). Cabinet projection, military projection are always oblique projections. The standard isometric projection with $\alpha =\beta =120^{\circ },v_{x}=v_{y}=v_{z}=1$ is a scaled orthographic projection (scale factor 1.225).--Ag2gaeh (talk) 09:56, 24 November 2015 (UTC)

The German and English literature seem to have different definitions. SharkD  Talk  19:04, 24 November 2015 (UTC)

But what is the mathematicaly exact English definition ? I found a correct English definition of an axonometric projection here on page 38. But it seems to be a Hungarian source. --Ag2gaeh (talk) 22:10, 24 November 2015 (UTC)

By mathematical, do you mean in that it includes formulas? You do know that mathematics can be expressed without formulas, don't you? SharkD  Talk  05:07, 25 November 2015 (UTC)

Since G. Monge descriptive geometry is founded mathematicaly exact without formulas. It is typical for descriptive geometry to solve gemetric 3d-problems without formulas. By the way: Thank You yery much for Your great effort on this topic. --Ag2gaeh (talk) 07:23, 25 November 2015 (UTC)

After looking into the links above and considering Your comments, I would say, an English definition of an axonometric projection may be as follows:

• An axonometric projection is an orthographic projection that shows the picture of a cartesian coordinate system, which is related suitably to the object (cube, building, ...) to be projected, in general position (no two pictures of the axes are contained in a common line).

This definition is rather different from the German one and does not contain cabinet and military projection. The last ones are oblique axonometric projections. The German definition is more general and independent of any object. It depends only on the coordinate axes, and the image of the unit cube (angles,forshortenings) which all can be chosen (nearly) abitrarily. So the German definition comprises scaled orthographic and scaled oblique projections.--Ag2gaeh (talk) 10:30, 25 November 2015 (UTC)

Hence: The English axonometric projection is the German orthogonale Axonometrie. --Ag2gaeh (talk) 11:55, 25 November 2015 (UTC)

Here are the qualities which most of the sources ([1][2][3][4][5] and others) above agree on:

1. The projected rays are parallel to each other. Hence, axonometric projection is a form of parallel projection (or paraline projection).

2. The projected rays are perpendicular (orthogonal) to the projection plane (or picture plane).

However, several sources also say that axonometric projection is a form of orthographic projection. I would disagree with them, and several of the sources agree with me ([6][7][8]), and instead say that:

3. Orthographic projection is limited to top, bottom and side views (or plans and elevations) where the projected rays are perpendicular (or orthogonal) to the faces of the object. Axonometric projection, on the other hand, deals with auxiliary views, or views not parallel to the coordinate axes. SharkD  Talk  19:12, 25 November 2015 (UTC)

I can't find Your restriction of orthographic projcetion in the sources 6,7,8. And the article orthographic projection says it is equivalent to orthogonal parallel projection and not restricted to principle projections (bottom, elevation and side view). So my English definition of axonometric projection (above) complies with the sources. I tried to understand other language sites and think the French and Spanish definitions are equivalent to the German one.--Ag2gaeh (talk) 09:26, 26 November 2015 (UTC)

6: "Orthographic projections show views of the object as seen from the principal directions named as front, top and side view."

7: "...the design-drawing process usually begins with two-dimensional expressions in the form of orthographic sketches and drawings. These multiview drawings are the plan, elevation, and section vocabulary that an architect/designer uses."

8: "When principal orthogonal views (Top, Front, Side, etc.) are rotated, a User view is created. This is 3D Studio's description of an axonometric view."

Also, I don't understand the rest of your comment. What is "it" in your second sentence? How does orthographic projection relate to your definition? Sorry, I was looking at the wrong definition. You are correct. However, it is curious that originally the article did not mention axonometric projection, and limited the views to ones with increments of 90 degree rotation.

SharkD  Talk  03:39, 27 November 2015 (UTC)

OK! If You are right, one should clarify the defintion of orthographic projection. But this is another issue. I still think that the English axonometric projection is equivalent to the German orthogonale Axonometrie. A better English name would be orthogonal axonometric projection. So, there would be space for oblique axonometric projection, which would comprise cabinet, cavalier and military projections. The last ones deal with coordinates and coordinate axes,too, and should bear the name axonometric, too. In both cases (orthogonal and oblique) there exist the three types: isometric, dimetric and trimetric projections.--Ag2gaeh (talk) 10:28, 27 November 2015 (UTC)

Wikipedia is not the place to go making up terminology. We have to go by what the sources tell us. How we feel on that matter is not a concern. I am okay with mentioning in the article that German terminology differs, maybe because Karl Pohlke was himself German. SharkD  Talk  14:11, 27 November 2015 (UTC)

Third Opinion

A third opinion has been requested. Due to the highly technical nature of the subject and the lengthy exchange, it is hard to tell what the question is. I can see that terminology is used differently in English than in German. I will leave the Third Opinion request up for another editor, but would advise the two editors to formulate a concise question. Robert McClenon (talk) 18:26, 28 November 2015 (UTC)

One question might be, "Which definition of axonometric projection should we use in the article? German or English?" SharkD  Talk  18:36, 28 November 2015 (UTC)

If the definitions in English and in German are different, we should state what both definitions are, precisely because this linguistic discrepancy in scholarship can cause confusion. Since this is the English Wikipedia, we should focus on the English definition, but should clarify what the differences are. If that is the question, that is the third opinion. Robert McClenon (talk) 23:32, 1 December 2015 (UTC)

I removed this entry from 3O because it was listed for longer than six days. Erpert ^{blah, blah, blah...} 03:29, 2 December 2015 (UTC)

Hi Ag2gaeh & SharkD, While the third opinion request has expired without anyone picking it up, I'm happy to have a look at the issue and provide an opinion if you think it would be helpful. To assist, could you each put a brief summary of your thoughts in the sections below? - Ryk72 ^'c.s.n.s.' 22:41, 2 December 2015 (UTC)

Third opinion

Ryk72 (talk · contribs) wants to offer a third opinion. To assist with the process, editors are requested to summarize the dispute in a short sentence below.

Viewpoint by (Ag2gaeh)

A) The German/French definition of an axonometric projection (Axonometrie) is rather general and covers orthogonal, oblique and scaled parallel projections. Because the definition is done by a procedure to construct images, it is necessary to prove that it delivers scaled parallel projections. This was done by Pohlke (Pohlke' theorem). The German definition comprises oblique axonometric projections (like cavalier, cabinet and military projection) and scaled projections ( like the Standard-Isometrie, Ingenieur-Axonometrie).

B) The English definition is: an axonometric projection is an orthogonal parallel projection which uses coordinate axes. It does not cover oblique projections (like cavalier,...) or scaled projections ! The English definition needs not Pohlke's theorem, because an axonometric projection is per definition a parallel projection.

I think these essential differences should be mentioned in order to prevent any confusion. --Ag2gaeh (talk) 09:13, 3 December 2015 (UTC)

Viewpoint by (SharkD)

I'm okay with noting the difference between English and German usage in the article. But I'm having trouble understanding Ag2gaeh's definitions. It seems he is simply translating terms from the literal German. It doesn't help that Pohlke is not a well-known mathematician. SharkD  Talk  03:59, 5 December 2015 (UTC)

Third opinion by Ryk72

....

German Definition\Illustrations

parameters of an axonometric proj. in general

special cases

I disagree with these images. In the isometric example, $v_{x},v_{y},v_{z}$ should not equal 1 if $v$ equals 1. In isometric projection, the axes are foreshortened, so they should equal less than 1. The same is true for Ingenieur-Axonometrie; all three axes are foreshortened by some amount. The other two images are okay. Also, I am looking again at the definition you provided. It says, "Choose forshortenings $v_{x},v_{y},v_{z}$" However, military and cavalier perspectives violate this rule; in these perspectives there is no foreshortening for two of the three axes. SharkD  Talk  16:56, 2 December 2015 (UTC)

Also, in the Ingenieur-Axonometry graphic, why is $v_{x}$ equal to 0.5, yet drawn as if it is equal to 1? SharkD  Talk  19:01, 2 December 2015 (UTC)

The first image is in accordance with the German/French/Spanish definition. It does not reflect the English definition. The definitions of cavalier, cabinet and military projection differ slightly in literature, but are in any cases oblique dimetric projections. The simplest case of an isometric projection, named Standard-Isometrie ($v_{x}=v_{y}=v_{z}=1,\alpha =\beta =120^{\circ }$), delivers a scaled orthogonal projection. Scaling is omitted in English literature by choosing the common forshortening 0.816. The Ingenieur-Axonometrie seems not to appear in English literature. It is also a slightly scaled orthogonal projection. Standard-Isometrie and Ingenieur-Axonometrie are very popular, because the forshortenings are so simple. In English literature axonometric projection is always an orthogonal (non scaled) projection and does not contain cabinet, cavalier and military projection in contrary to the more general German definition. Pohlke's theorem is a statement on generaly (German) defined Axonometrie and not on (English) axonometric projections.To the German forshortenings: any positve real number is allowed. So, the word shortening should not be taken literally.--Ag2gaeh (talk) 20:05, 2 December 2015 (UTC)

Survey of sources 2

I'm going to go through the same sources as earlier into more detail to find out exactly what is going on. SharkD  Talk  20:29, 24 April 2017 (UTC)

Schemes

Scheme A	Scheme B	Scheme C	Scheme D
Graphical projection Parallel projection Orthographic projection Multiview projection Plan Elevation Section Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection Perspective projection	Graphical projection Parallel projection Orthographic projection Normal projection Plan Elevation Section Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection Conic/central projection Perspective projection	Graphical projection Multiview projection Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection General oblique projection Perspective projection	Graphical projection Orthographic projection Multiview projection Axonometric projection Isometric projection Regular Reverse Long Dimetric projection Trimetric projection Oblique projection Perspective projection

Scheme E	Scheme F	Scheme G	Scheme H
Graphical projection Parallel projection Orthographic projection Multiview projection First-angle projection Second-angle projection Third-angle projection Fourth-angle projection Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection Perspective projection Linear perspective One point perspective Two point perspective Three point perspective Aerial perspective Aerial perspective	Graphical projection Orthographic projection Multiview projection Axonometric projection Isometric projection (paraline) Dimetric projection (paraline) Trimetric projection (paraline) Oblique projection Plan oblique (paraline) Elevation oblique (paraline) Perspective projection 1-point perspective 2-point perspective 3-point perspective	Pictorial drawing Perspective Axonometric Oblique	Three-dimensional drawing techniques Perspective Axonometric (a.k.a. plan oblique drawing) Isometric

Scheme I	Scheme J	Scheme K
Projection systems Orthogonal/orthographic projection Simple orthogonal projection Top Front Side Isometric projection Dimetric projection Trimetric projection Oblique projection Oblique (front face parallel) Axonometric (top face parallel) Perspective projection Single-point Two-point Three-point	Graphical projection Axonometric projection Orthographic projection Plan Section Perspective projection	Projective geometry Parallel (a.k.a. cylindrical) projection Orthographic (a.k.a. perpendicular, orthogonal, rectangular) projection One-plane descriptive (a.k.a. horizontal) projection Axonometric projection Isometric projection Oblique (a.k.a. clinographic) projection Cavalier projection Cabinet projection Military projection Central (a.k.a. conical, radial, polar) projection

DocsFiles search result (link)

Title	Notes
CHAPTER FOURTEEN AXONOMETRIC PROJECTION	Scheme A
9.Axonometric and Central Projections	Dead link
Lecture 3: Composites, Conventions, Axonometrics	Scheme B
7.1 AXONOMETRIC PROJECTION - McGraw-Hill Education	Scheme C
BST12781 BUILDING COMMUNICATION multi view and single view	Not sure
technical drawing	Not sure
Pictorial Drawings: Axonometric Projection pictorial drawing	Scheme D
Slide Set 3 – Orthographic Projection II – Isometric	Scheme E

Google Books search result (link)

Title	Notes
Architectural Graphics By Francis D. K. Ching	Scheme F
Axonometric and Oblique Drawing: A 3-D Construction, Rendering and Design Guide by Mohammed Saleh Uddin	Can't see much text. Oblique and axonometric seem to be described separately.
Machine Drawing:Includes Autocad By Singh Ajeet	Can't see much text. Quote: "Axonometric projections use only one plane to show an object. Lines of sight are perpendicular to this plane but the object is so oriented such that front, top and side of the object are visible in one view."
A New Approach to Axonometric Projection and Its Application to Shop Drawings by John Gilbert McGuire	Can't see much text. Scheme G
Basics Architecture 01: Representational Techniques By Lorraine Farrelly	Scheme H
Art and Representation: New Principles in the Analysis of Pictures By John Willats	Scheme I. There is second scheme as well, for which the book preview does not show the organization of.
Practice: Architecture, Technique and Representation By Stan Allen	Scheme J. Does not go into much detail, so I had to piece things together.
Autodesk VIZ in Manufacturing Design: Autodesk VIZ/3ds Max for Engineering ... By Jon M. Duff	Not a good source.

Other sources

Title	Notes
Chapter 5 of an (unnamed in the scans) textbook	Dead link.
Descriptive geometry--pure and applied: with a chapter on higher plane ... By Frederick Newton Willson	Scheme K
Technical Graphics Communications	Can't see much text. Quote: "The axonometric projection is produced by multiple parallel lines of sight perpendicular to the plane of projection, with the observer at infinity and the object rotated about an axis to produce a pictorial view."

Later on: The word "Multiview" might not have actually been used in several of those sources. Confusion on my part. Sorry. ➧datumizer  ☎  01:44, 12 May 2021 (UTC)

Lemchastain

1/13/2022 -- just replied to Nje-de at _bottom_ of this section; will go there to edit that reply.

Dec. xy, '21 --I would like to hear from someone that has studied higher dimensions about my generalization. I define a Axonometric Projection of an N-dimensional cube as its (N-1) dimensional image. The general equation that I need feedback on -- from a qualified person will be briefly described below.

22 December 2021 update of my 28 February 2021 comment below. Basically, if this gets printed, then most of the earlier comment can be ignored. I'm back to report some progress on corrections to my Spring 1989 article, "Axonometric Projections". From I brief scan of the article, I am using the English definition; not previously knowing of a German one. [As an aside, I think this topic should refer to the English definition; since German does not have these two words. Their definition is for a similar term in 'Deutshe worten': you can't just translate a term, and expect to carry the precise meaning in the other language to be translated into the English meaning.] & Now, to my reason to struggle back into this article; to report that "Engineering Design Graphics Journal has published a "Correction' to my 1989 article as a D.O.I. on the Internet, in APA style. Since it took 32 years to get to it, I'm glad to catch more than just the old typos. & Please see, http://www.edgj.org/index.php/EDGJ/issue/view/237 and click on the "EDGJ Vol 53 No 2 Spring 1989" button. That will take you to the Correction page. Read this before the actual article, and perhaps print it out for reference when reading that article. Below the Correction, ou should find the full issue. The "Axonometric Projections" article appears on pages 19 - 25.

8 January 2022: I am interested in extending this term into N dimensions, with N from 1 to as high as you need. See the 1989 article for the 3-D case (Digital Object Identifier in paragraph 3 of 22 Dec. '21 entry. Last year I worked on the 4-D case, but believe the findings generalize to higher dimensions. [2-d is equivalent to the Pythagorean Theorem, and 1-d is trivial, but consistent.] At that time someone mentioned Laplace's Four Square Theorem, not as a contradiction, but as indicating that my "all integer" solutions should not be a surprise. Time for dinner; more later, when notation developed. Lemchastain (talk) 02:04, 9 January 2022 (UTC)

Hello Lemchastain, just noticed you mentioned my name here but didn't WP:PING me. That's why I only saw it as you edited the page again and it showed up in my watchlist. Anyway, I am not sure how I can be of assistance here. I reverted your edits back in February 2021 as they came without any references to reliable sources. I am not a professional in axonometric projection though. – NJD-DE (talk) 02:16, 9 January 2022 (UTC)

13 Jan 2022 Dear Njd-de, I'm sorry: I don't know what WP:PING is -- some way to "ping" you? Anyway, the problem (with a source) was that I was talking about _my_ published article, from 1989, but I didn't count as a reliable source. The last paragraph of my 22 Dec. 2021 entry lists the new DOI that EDGJ has since published. Yes, it refers to the 'Correction' they allowed _me_ to make (in APA style), but the "source" is EDGJ, not the author (i.e. me, again).

&

I've also just dropped a comment at the bottom of the talk section of the "Pythagorean Triplets" topic; in case you want to see how little progress I make there. In scanning other sites on that topic, I thought someone would also have come up with my approach by now, but no one seems to want to raise any issues with Euclid. Lobachevsky, Hilbert, et al were brave to question anything in Euclid's marvelous (no sarcasm) books. [Aside: My impression, from the English translation by Heath -- including the Fairplay version of Prop. V -- was that Euclid did not make a mistake that ruled out hyperbolic space: he said, "...if the sum of the two angles is less than 180 degrees, then the lines extended to that side intersect..." -- approximately. He made no claim about what happens if the sum of the angles is not less than 180 degrees. So, he was not wrong; just sticking to planar 2-D geometry.

&

If you have my e-mail address, please give that a try. I check it daily, but rarely look at my own 'Talk' section.

If not leave a note here, but be patient. I might consider putting my address up again (for you), and then editing it out later. Would that work?Lemchastain (talk) 16:59, 13 January 2022 (UTC)

Hi Lemchastain, pinging is a way of notifying people here that there's a message for them on a talkpage. Unfortunately I really can't make any comments of benefit on the subject. Honestly I know nothing about axonometric projection.

Back in February last year I only reverted your edit because there weren't any references to reliable sources, and also the text style was rather unusual for a Wikipedia article. Citing yourself as a subject-matter-expert would possible, however sometimes quickly reverted as it can look like a form of spamming.

Maybe people at the Wikipedia:WikiProject Technology can be of some assistance to you. – NJD-DE (talk) 00:53, 19 January 2022 (UTC)

Lem 18 Jan 2022 -- Dear NJD, I get those in the Alert section; so I may not need to duplicate that for others.

There seems to be a good deal on Axonometric Projections on Wiki-pedia, if you get curious. However, none of those writer's covered my 1989 article;so look for Digital Object Identified, DOI, for it and my recent correction in (what was) last section of Axo. Proj. 'Talk' page. I finally get that an encyclopedia is not the place for new work (32 years vs. 2,000 for Euclid, etc.), but a good place to summarize prior work. — Preceding unsigned comment added by Lemchastain (talk • contribs) 01:13, 19 January 2022 (UTC)

Yes you are right Lemchastain, you get the notifications there. But in order to receive them, the one posting a message needs to "ping" them by adding link to their userpage as part of the message, e.g. {{u|Njd-de}}, and signing the post with four tildes ~~~~.

I might have a look at article on that topic at some time. Wikipedia also covers more recent content of course. The important thing needed is though that references to reliable sources are added. A reliable source could be your work, but as mentioned earlier I am not the right person to say anything about it.– NJD-DE (talk) 01:29, 19 January 2022 (UTC)

Thanks for that explanation, but "tlx"? Meanwhile, someone couldn't let my note in the 'History' section of the 'Article' page stay up even a couple of hours; even though I expressly ask them to let it stay a day or so -- knowing that I might have used a comma instead of a semi-colon, or indented one space too much. Is the objective to be the first one to "get' someone? PS They missed the reference below however -- so far 17:29 EST.Njd-de {{u|Njd-de}} Lemchastain (talk) 22:35, 19 January 2022 (UTC)

You should never add personal comments to article space. They correctly removed that as soon as they saw it. This talk page is the place for discussions about the article or suggestions for improvement. Please don't add such comments to article space again. MrOllie (talk) 23:40, 19 January 2022 (UTC)

I just attempted to get a 'further reading' citation correct this time. It definitely concerns this 'Axonometric Projection' topic. I don't know what was wrong with it last time, and don't know how to get to those archived edits. I don't expect it to stay up long, but some things last for hours. (I did not even try to explain what to do on the the cover page to get to the article, and I noticed the dot at the beginning: click on the Spring issue button on lower left. Oh, the DOI is above, in the paragraph just before the 8 Jan 2022 comment. Goingbatty Lemchastain (talk) 04:39, 20 January 2022 (UTC)

PS Following GoingBatty pointing out a Tearoom mistake in the address of the DOI, I corrected it (added ".org" to "edgj"); then decided to check entry above, and had to change "hppp://" to "http://". I apologize to anyone that had a problem due to either of my errors. Goingbatty Lemchastain (talk) 04:58, 20 January 2022 (UTC)

Per WP:COI you shouldn't be adding your own work to further reading, particularly after multiple other editors have removed it. - MrOllie (talk) MrOllie (talk) 14:41, 20 January 2022 (UTC)

&?? My recent addition to 'Other Reading' on the article page was immediately 'reverted'. I won't even put it there again, but why not _here_ so readers can test their 'reverting'skills: "Never mind!" -- see Whoops below.

    Giesecke, F. E., Mitchell, A., Spencer, H. C., and Hill, I. L., "Technical Drawing", Sixth Edition, Macmillan, New York, NY 1974    (talk) Ljc 23:58, 7 February 2022 (UTC)

Whops! That is how it should look, but there are formatting symbols (i.e. {{ | = etc. ) that I didn't see when I first tried to edit "Other Readings". The "references" section in another topic did show them when I added a book there. I also had a problem seeing any references but the first one for this topic on the article page. (talk) Ljc 00:49, 8 February 2022 (UTC)

Strange header image and description

I am using the mobile app. I just edited the page description; previously it was "consumption of feces", and the main image was a close up photograph of a fly.

Either this was vandalism, or a caching error, as there was nothing in the page history about this. Feel free to revert my change if it was just an issue with my device. Krackpipe (talk) 19:17, 18 April 2023 (UTC)