Talk:Axonometric projection

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Shouldn't Axonometric view be a subheading of auxiliary view[edit]

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 (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[edit]

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[edit]

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)


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 (talkcontribs) 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[edit]

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.
  • 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)


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). (talk) 15:03, 20 July 2011 (UTC)Athanasius

Op Art & Escher[edit]

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?[edit]

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[edit]

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 (talkcontribs) 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[edit]

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)[edit]

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)[edit]

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.


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[edit]

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 .
  3. You get the image of a point P=(x,y,z) by: 1) go from the origin in x-direction, then 2) in y-direction then 3) 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 () and delivers nearly an orthographic projection (scale factor is near 1). Cabinet projection, military projection are always oblique projections. The standard isometric projection with 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[edit]

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[edit]

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[edit]

parameters of an axonometric proj. in general
special cases

I disagree with these images. In the isometric example, should not equal 1 if 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 " 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 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 (), 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)