# How to make a cube using isometric style drawing?

#### Wendy

Joined Mar 24, 2008
22,205
Way back when I was taking engineering courses I was introduced to the concept of isometric drawing. This is not a hard concept. The traditional method of drawing a cub is a prime example of isometric drawing. Recently I tasked myself with the project of drawing a 8" X 3" box, and I realized I had no clue how long to make the diagonal lines (z axis). I tried using the Pythagorean theorem, which for the stated dimensions is 8.54", at this point it gets muddy. I can do it by eye and get in the ball park, how do I figure out the x,y numbers that will match a 45° angle?

As you can see it is way too long. This is what it looks like when I do it by eye...

Oops the part on the drawing labeled Part B should be Part C. No matter the question stands.

Last edited:

#### MrChips

Joined Oct 2, 2009
22,499
Are you sure you want isometric view and not perspective view?

#### SamR

Joined Mar 19, 2019
2,897
You need and 30/60/90 triangle to start with... And your drawing is missing and edge line where parts A&B join. Isometric view/projection and orthographic projection. Z-axis vertical, X-axis -60° from Z, Y-axis +60° from Z. Part marked C should be 7.5" if there is .25" on each side of it.

#### Wendy

Joined Mar 24, 2008
22,205
I am using Paint. I scaled the drawings I did to 50 px/inch. to keep the drawing in perspective. Think 0°, 45°, and 90°. I can fake it, and do quite regularly. It just seems I can use a notepad to calculate the x/y dimensions for a 45° line. to match a scaled distance similar to what I can do with X or Y. So, am I spitting into the wind or does a simple method exist?

Remember, I cut my teeth on 8 bit computers and their pixelated graphics. This is just more of the same.

If you re-examine my monitor stand drawing the dimensions are all there (and scaled to each other).

#### Wendy

Joined Mar 24, 2008
22,205
Here is the revised drawing...

Oops, had to do more touch up after a second look.

#### djsfantasi

Joined Apr 11, 2010
7,209

Never could draw on a computer, a perspective drawing of an object.

When I need a perspective drawing, I do it the old fashioned way. On a drafting table with a straightedge. Perhaps an extended ruler (I don’t remembet what they’re called).

#### Wendy

Joined Mar 24, 2008
22,205
Yardstick? I'm a bit weird, I use machinist scales, which are marked in decimal inches.

#### Wendy

Joined Mar 24, 2008
22,205
A possible solution has just occurred to me. Treat the horizontal line (8") as a radius, the diagonal is another 8" radius with a 45° angle. It now becomes a relatively simple trig problem, solve for X and Y and the diagonal should be the right length. I'll be back after I work out the details.

Using the Law of sines I get
X/sin(45°) = r/ sin(90°) = Y/sin(45°)
which simplifies to
X/0.707 = r/1 = Y/0.707
X = Y = .707r

A little better, don'tcha think? Still a little long for my tastes. It is probably a perspective problem

Last edited:

#### SamR

Joined Mar 19, 2019
2,897
I use machinist scales, which are marked in decimal inches.
Those are what we call Engineering scales marked in decimal. Architect scales are marked in 1/16ths even though Engineers use them for Piping and Structural Drawing among others. I probably used 16ths more than decimal as a Project Engineer as those are the standard for most shop drawings. Most Engineers use Architectural scales and Civil Engineers mostly use Engineering scales. Odd... Unless it's Metric then it's always decimal.

#### Wendy

Joined Mar 24, 2008
22,205
Or to show it another way

I really like M\$ Paint. Linux has some almost as good, but I haven't figured out how to turn its aliasing off, so it is a no go for PaintCAD.

#### Attachments

• 4 KB Views: 2
Last edited:

#### WBahn

Joined Mar 31, 2012
26,398
I'm not quite sure what it is you are trying to achieve.

You are not doing an isometric drawing in the first place (as I understand it). It looks more like you are doing a cabinet projection, which is one type of oblique parallel projection.

An isometric projection uses three axes set 120° apart. The first (usually called the z-axis) is vertical. The one that is clockwise 30° from the upward vertical is the x-axis and the one that is counterclockwise is the y-axis.

In general, there is no way to calculate the point on a piece of paper that corresponds to a particular point in 3-D space because the mapping is not unique. The path you take can put you at different points on the drawing. This is the basis for any number of optical illusions.

#### SamR

Joined Mar 19, 2019
2,897
Here is one we used to play with in high school only we would actually thread the rods. Drawing Isometric threads is not an easy task.

xox