My brain is hearting trying to figure this out, just wondering if anyone has already encountered and solved this or is up for a challenge.
Basically: given two random vectors on a plane build a new 3d plane, where the projected vectors would be 90° to each other and would have the same length. you would have tho possible planes as solutions, one being mirrored version of the other.
Is this what you’re looking for? The idea is that you’re starting out with two vectors in the XY plane and so the question is how much “Z” (the white in the image) do you add to each to meet these two conditions:
The two resulting vectors are orthogonal, IOW their dot product =0
Their lengths are equal.,
I won’t go through the algebra, which isn’t that bad, but it results in a quadratic equation for the length of one of the additional “Z”'s squared. Knowing that, you can solve for the other “Z” . As you noted, the mirror image is also a solution…
project planes.gh (16.8 KB)
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So simple!
no matrix, no trigonometry. it just works!
BTW your art is out of this world! @akilli
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Thanks, you just made my day!