Iso Metric Grid layout -- Possible Problem?

[jclements]

Technically speaking, in an Isometric drawing (Iso meaning equal) the angle between the x, y, and z axis which define the Isometric plans are equal. 360 degrees/3 = 120 degrees (or 30 degrees from a horizontal line).

When I checked out Xara's Isometric grid, it seems its angles are 116.57, 116.57, and 126.86 (or 26.57 degrees from a horizontal line). Which I believe is a Dimetric configuration.

I just noticed this when I imported some isometric drawings made in another application. It may be an important issue for some people.

I would appreciate it if those interested would check it out for themselves and verify if what I have posted is valid. Thanks.

[jclements]

Technically speaking, in an Isometric drawing (Iso meaning equal) the angle between the x, y, and z axis which define the Isometric plans are equal. 360 degrees/3 = 120 degrees (or 30 degrees from a horizontal line).

When I checked out Xara's Isometric grid, it seems its angles are 116.57, 116.57, and 126.86 (or 26.57 degrees from a horizontal line). Which I believe is a Dimetric configuration.

I just noticed this when I imported some isometric drawings made in another application. It may be an important issue for some people.

I would appreciate it if those interested would check it out for themselves and verify if what I have posted is valid. Thanks.

[Soquili]

Hi John,

You are right, the isometric grid isn't 120 degrees between axis, as the attachment will show. The XaraX protractor I drew isn't calibrated to 100th of degrees but it is to 1 degree.

Soquili [img]/infopop/emoticons/icon_smile.gif[/img]

[Soquili]

If anyone is interested, the .xar file for the protractor is attached.

Soquili [img]/infopop/emoticons/icon_smile.gif[/img]

[bputnam]

The isometric grid seems to be stretched in the X direction so that the height (in the X direction) of the triangles is equal to the length of the sides in the Y direction. The result is that the triangles are not equilateral. If I were Xara, I'd want to fix that.

Bryan

[jclements]

Soquili, thanks for the protractor. I downloaded it. I hope you did not draw just for this posting and I hope it was not an inconvenience.

Mark, thanks for your comments as well. I amcurious to see how many responses might develop.

Regards, John

[Big Frank]

Isometric is a perspective where given 3 lines that are of equal length in 3 axes their length will appear equal. What this means in simplified terms is that if you have three 1 foot sticks and you place one pointing upwards, one pointing away from you and one pointing directly to your right they will all look the same length from your perspective. Such a perspective would be said to be in a 1:1 ratio because it is as long as it is wide in 2D-pixel format.

Quote from http://www.lupinegames.com/articles/isoeng4u.htm

Therefore this does not necessarily mean that the angles are equal, just the lenths of the perspective lines and the distance of the outers from the perpendicular.

Quod erat demonstrandum

Just my tuppence worth. Feel free to shoot me down in flames: [img]/infopop/emoticons/icon_razz.gif[/img]

[Soquili]

John, I did draw the protractor for your post. It only took about 20 minutes using techniques I learned from Gary's June 2000 tutorial "Pushing the Envelope"

After uploading the protractor, I discovered that I had left out the crosshairs in the center. I'm attaching the updated protractor here.


Big Frank, thanks for the link. The info helped jog my memory. It's amazing how much you forget when you pass 50. It seems I forget more each year. [img]/infopop/emoticons/icon_biggrin.gif[/img]

Soquili [img]/infopop/emoticons/icon_smile.gif[/img]

[This message was edited by Soquili on March 09, 2001 at 07:08 PM.]

[bputnam]

I thought an isometric grid normally consisted of equilateral triangles and that the resulting diagonal lines were 30 degrees with repect to the horizontal. At least when the grid is drawn on paper.

Now, after thinking about this some more, perhaps Xara made the correct compromise within the constraints of a pixel display. Otherwise the major spacing and number of subdivisions would lose some meaning. For example, it's probably meaningless to talk of a distance of "100pix" along a diagonal, in fact the endpoint of the line might not even land on a pixel. Furthermore, the marks specifying subdivisions wouldn't be well determined. (?)

Bryan

[jclements]

Hi Frank,

I don't claim be an expert nor I am very good at the written word, but here's what my understanding is. I think its just a matter of semantics. Probably Ross MacIntosh could do a better job of explaining than I.

See the book, "Graphic Science, Engineering Drawing, Descriptive Geometry, Graphic Solutions", McGraw Hill, 1958; Chapter 8, Pictorial Drawing.

Also, see Nick Wilkinson's WWW.IsoCalc.com or contact him at support@IsoCalc.com. He DOES know this stuff inside and out.

By DEFINITION a 3 axis drawing (Axonometric projection) in which only two axis-angles are equal is called a Dimetric Projection (which is what you've described in your posting); if none of the axis-angles are equal it would be called a Trimetric Projection. Sometimes people describe all non-perspection, 3-sided projections as Isometrics when (again by DEFINITION) they are Axonometrics.

The 3 isometric axes are "all FORESHORTENED equally because they are at the same angle to the picture plane", otherwise, measurements taken from the 3 planes would not necessarily be of the same scale and that is one of the reasons for the popularity of Isometric Projection ... that 1:1 measurements can be taken directly off them and it makes the drawing process much easier than the remaining Axonometric Projection types. In digital drawing it is especially convenient because one can draw along the vertical axis taking advantage of a program's drawing tools which can easily stretch and size objects and measure distances. The results can then be rotated clockwise or counter clockwise 120 degrees for a representation in one of the other two planes.

The overall Isometric Projection can; however, be rotated to any angle and it is still considered an "Isometric" because the angles of each of its 3 PLANES ARE STILL PERPENDICULAR to each other in 3D space or 120 degrees in flat paper space.

Anyway, that's my understanding from what I've read and what I've learned from Mr. Witt my shop teacher and from Nick Wilkinson's site and his application, IsoCalc. [img]/infopop/emoticons/icon_smile.gif[/img]

[This message was edited by John Clements on March 09, 2001 at 07:12 PM.]