[OTish} Isometric scale

I've been playing with Hotdoor CADtools which is a very nifty Illustrator
plug-in. When objects are projected isometrically by Cadtools they are
foreshortened to 81.65%. Is this right? It's a long time since I was schooled
in the basics of technical drawing, but I was taught that isometric
projections should be drawn to actual scale - that was the point of
isometric. Have the rules changed when I wasn't looking?

--
Michael

mhp at o2 dot ie

but I was taught that isometric projections should be drawn to actual
scale - that was the point of
isometric. Have the rules changed when I wasn't looking?





The rules have not changed; you're just looking at "half" the rules. ;-)

Fact is, earlier versions of CAD tools (actually, their Perspective product) committed all kinds of atrocities in "isometric" drawing. The foreshortening factor you notice is correct for isometric projection.

The distinction you are missing is the difference between isometric drawing (the method you are accustomed to) and isometric projection (the method represented by the foreshortened axes).

You recall that in the days of drawing on the board, you used true measure along the isometric axes. But you will also recall that you did not use ordinary drafting ellipse templates; you used special isometric templates, which were larger in size. That is, a 1" 35-degree drafting ellipse template measures 1" across its major diameter. But an isometric (35'16") 1" template measured approximately 1.24" across its major diameter. When you think about it, it is quite logical: In order for the isometric template to be in proportion with your drawing when you are using true-measure along the axes, the ellipse template would have to be enlarged enough so that it measured true not along its major diameter, but along its 30' and 150' diameters.

Isometric projection takes the inverse approach. Instead of using true measure along the axes, and proportionally-enlarged ellipses, isometric projection uses true-measure ellipses and scaled-down axis measure.

Believe it or not, even in the "on the board" days, you could purchase from the same vendors from whom you bought your templates an isometric scale, which was--you guessed it--about 82% of true measure. This facilitated drawing isometric projections. Cumbersome? Not really. Here's why:

If you are drawing objects which have many off-axis surfaces and angles, it is hugely advantageous to be able to use ordinary drafting templates, available at 5-degree increments of "tilt". Drawing in projection mode lets you use ordinary drafting templates--say, a 25-degree ellipse to not just draw tilted holes and circles, but to step off measures along tilted surfaces and thrust lines.

But what about nowadays? In mainstream drawing software, which method makes most sense? Consider:

When you doubleClick Illustrator's ellipse tool and enter values for an ellipse, you are entering values for its extrema--its major and minor diameters. You cannot tell Illustrator "I want a 35'16" ellipse that measures 1" along its 30' diameter."

Consider also: In the "on the board" days, even if you worked full time drawing isos, chances are you might have had a general understanding of dimetric and trimetric, but seldom if ever actually used it.

Well, it's not that way anymore. Drawing in software (even in software that so often feels downright antagonistic toward technical drawing like Illustrator), it is just as easy to draw in dimetric and trimetric as in isometric orientations. (Or you might say, the programs are no more friendly to isometric than they are to dimetric or trimetric.)

But if you make it your habit to draw isometric projections instead of isometric drawings, you can use the same habits when you want to draw dimetric or trimetric. And (more commonly) you don't have to mentally "shift gears" when constructing the parts of your isos which involve simple and compound rotations. (Few things in the world have surfaces, edges, thrust lines, orientation, and assembly which are only and always at 90 degree angles.)

Now, of course, if illustrator simply had a properly-implemented user-customizable ruler scales feature as do all the other programs in its category, then you could set the scale to whatever you want as you draw in order to use true measure along your drawing axes, even when building isometric projections.

JET

Thanks for the thorough and very interesting essay, James. I checked a couple
of old ('60s) textbooks - one states that isometric projections are always
same scale, the other states the isometric scale to be root 2 divided by root
3 (which is the scale that Hotdoor uses). I've learned something new!
I've been in touch with Hotdoor and am told that in the next version of
Cadtools a foreshortening on/off option will be added.

--
Michael

mhp at o2 dot ie

Michael,

The axis foreshortening factor of 81.65% is due to the fact that .8165 is cosine of 35 degrees, 16 minutes (the isometric tilt angle).

You may have never thought about it this way, but...

A "25 degee ellipse" is one which is representative of a circle which you view edge-on, and then tilt up toward your line of sight 25 degrees. If you draw (or imagine) a side view of this, you'll see that the amount of "rise" of the back edge of the circle is the sine of 25 degrees. If you measure the minor diameter of a 1" 25 degree ellipse, you'll find that it is the sine of 25 degrees.

Well, it's that way with any "angle" ellipse. The isometric ellipse represents a circle which is "tilted up toward you" 35 degrees, 16 minutes. The height of a projection of a 1" circle which is tilted at that angle measures the sine of that angle. The perpendicular to that (the "thrust line" of the ellipse, or the "front vertical edge" of a 1" isometric projection cube) is therefore the cosine of the same tilt angle (.8166).

Again, this is all according to simple orthographic projection. The oversizing of ellipses which are labeled "isometric ellipses" is just an artificial accomodation to allow using true scale for measures along the iso axes.

Why 35'16"? because that's the angle of tilt which causes the three sides of a cube to make the same angle with the line of sight--and that is the whole point of isometric; that all three axes are foreshortened equally--regardless of whether the scale being used is 1:1 or 1:.86 (or any other scale).

one states that isometric projections are always same scale





That would be kind of a sloppy way to define it. You can draw an isometric drawing at any scale. The rule is simple: if you use true-measure along the axes, you MUST use oversize ellipses. If you use true-measure ellipses (major diameter), you MUST use foreshortened axis measure.

BTW, if you are interested in axonometric drawing (and certainly if you have much occasion to do it) be sure to take a look at Corel Designer 12, which has a proper and well-integrated feature set specifically designed for the purpose.

JET

On Tue, 8 Nov 2005 23:09:58 +0000, James_E._Talmage@adobeforums.com wrote
(in article <3bbd24e2.2@webx.la2eafNXanI>):

> BTW, if you are interested in axonometric drawing (and certainly if you have
> much occasion to do it) be sure to take a look at Corel Designer 12, which
> has a proper and well-integrated feature set specifically designed for the
> purpose.

Not available for Mac, unfortunately.

--
Michael

mhp at o2 dot ie

Not available for Mac




Oops. Sorry.

JET