Grasshopper

algorithmic modeling for Rhino

# Inscribed rectangle proof

A quick recreation of the Inscribed Rectangle Proof by the magnificent 3Blue1Brown: https://www.youtube.com/watch?v=AmgkSdhK4K8

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Comment by David Rutten on November 5, 2016 at 5:19pm

I can't get the mesh to be valid either, I'm pretty sure it's the underlying mobiusness of the topology that messes it up.

Comment by Laurent DELRIEU on November 5, 2016 at 5:09pm

Certainly not as simple as David's script but it seems to work with no duplicate meshes. Just need a weld and unify mesh.

Next step evaluate self intersection of mesh and find the positions of rectangles !

Comment by Laurent DELRIEU on November 5, 2016 at 4:50pm

It is weird because there is not some curve intersection but just on point but that worked well.

As seen on the render I have a problem with meshes near the curve. It is because I use Hollistic cross reference and after that I used quad, quad on the curves are quad with 2 points equals. I also add double quad everywhere.

I change a bit my definition to have just the mesh where necessary.

Comment by David Rutten on November 5, 2016 at 4:14pm

@Laurent, nice! Circles are a weird limit case aren't they?

Comment by Laurent DELRIEU on November 5, 2016 at 3:08pm

Also some recreation on this nice problem, some test with mesh of this surface.

Comment by Pieter Segeren on November 5, 2016 at 4:46am

@ David, yes, I'd say that definitely would have been better. Now the method seems to claim to be proving something that doesn't get proved.
Either that, or my understanding of what 'inscribed' means is off.

Comment by David Rutten on November 5, 2016 at 4:10am

@Pieter, I wondered about that as well. Perhaps vertex-coincident would have been better.

Comment by Pieter Segeren on November 5, 2016 at 3:59am

Really interesting video, thanks for the link David. I wonder: is the word 'inscribed' justified if there's pieces of the loop inside the rectangle?

Comment by Mateusz Zwierzycki on November 4, 2016 at 6:47pm

The elegance of this proof... I'm in awe. Wonder about the square case, I guess a bit different abstraction would be necessary - given we would have to care both about the diagonals ratio and the angle between them I'm betting the map itself should be of a higher dimension (?)

by June Lee

by June Lee