Grasshopper

algorithmic modeling for Rhino

# Manhattan 3d

voronoi

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Comment by Shkattii on May 12, 2015 at 1:33am

Very interesting! This is exactly what I wanted to do for my project which it can creates unique interior spaces. Would you be able to share on how you got it to work in 3D, it would be much appreciated if you can share the definition with me. Thanks

Comment by taz on April 4, 2013 at 3:55pm

Well, now at least I know where the name comes from but, yeah, Wikipedia is more like a black hole once you move beyond general definitions...

Comment by Christos Antonopoulos on April 4, 2013 at 3:16pm

@Vicente That is great!It looks more complicated than I would think. Certainly I would not be able to develop smt like that. I will do it myself too. Thanks a lot!

Comment by Vicente Soler on April 4, 2013 at 2:51pm

The geometrical version I can't get it quite as simple:

Comment by Vicente Soler on April 4, 2013 at 12:02pm

Comment by taz on April 4, 2013 at 11:19am

Thank goodness for Wikipedia or I wouldn't understand anything!

Comment by Vicente Soler on April 4, 2013 at 11:04am

Btw, after actually looking at the article the max norm is not really the rectilinear distance but the maximum distance to one of the axis. It looks similar but it's not the Manhattan voronoi.

Comment by Arie-Willem de Jongh on April 4, 2013 at 10:18am

Really nice Mateusz!

Comment by Christos Antonopoulos on April 4, 2013 at 10:02am

@Vicente Now I understand it more. Thanks for the components view too. I will give it a go myself to understand its logic. Thanks again!

Comment by Vicente Soler on April 4, 2013 at 7:32am

Christos, if you don't mind the raster method of doing it (how I presume the images in your link were generated), it's very easy using simple components:

The 'max norm' they are referring is just the rectilinear distance. Rather than applying the Pythagorean theorem to find the distance between two points, you just add up the absolute values of each axis of the vector between the two. For example, if I have a vector {1,2,0} the 'max norm' distance is 3.