Isometric view from Top Viewport

Grasshopper
#1

Hi everyone!

I have been trying to rotate my model (any model actually) in order for it to be baked and be able to run Make2D directly from Top view.

According to this Wikipedia article, there are 2 rotations to achieve Isometric View,:

For example, with a cube, this is done by first looking straight towards one face. Next, the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately 35.264° (precisely arcsin ​1⁄√3 or arctan ​1⁄√2, which is related to the Magic angle) about the horizontal axis.

But I must be missing something…

iso
iso.png1717×480 49.5 KB

Isometric.gh (6.0 KB)

#2

Use plane YZ instead of XZ for the second Rotate:

Isometric_2019Nov9a
Isometric_2019Nov9a.png773×213 11.8 KB

Isometric_2019Nov9a.gh (9.8 KB)

#3

Hi Joseph, thank you.

Unfortunately I tried that too and it doesn’t seem to do it either

The angle here is supposed to be 120 degrees.

iso2
iso2.png1478×548 42.8 KB

#4

OK, your angle is wrong. I did a quick experiment and determined that the three lines you refer to (“101.54”), projected to World XY, become equal in length when the angle is ~54 degrees. As explained in the Wikipedia citation:

Isometric_2019Nov9b2

Which is \text{arctan}(\sqrt{2}), not \text{arctan}\!\left(\frac{1}{\sqrt{2}}\right):

Isometric_2019Nov9b
Isometric_2019Nov9b.png965×267 14.5 KB

Isometric_2019Nov9b.gh (10.5 KB)

FYI, here is the “test jig” I rigged up; I was intending to measure the angles between these three lines, then realized that they would be of equal length which is more expedient to measure:

Isometric_2019Nov9aa
Isometric_2019Nov9aa.png1206×470 24.6 KB

Isometric_2019Nov9aa.gh (16.6 KB)

Isometric views take me way back to mechanical drawing classes in high school, where X and Y lines were drawn at 30 degrees using a plastic triangle and T-square.

#5

Thanks Joseph,

Hmm thats weird. Wikipedia explicitly says

approximately 35.264° (precisely arcsin ​1⁄√3 or arctan ​1⁄√2, which is related to the Magic angle.

Meaning it is related to 54.73 but not the one used to create an isometric.

Oh well, it seems to work, thank you.

#6

Ah, I was looking at this page for “Magic Angle”:

and you are citing this page for “Isometric projection”, which appears to be wrong!