Manhattan Voronoi

Some experiments on Manhattan Voronoi. I had to test 3 strategies in order to have descent quality and speed. I used Delaunay Triangulation, then Brep intersections (with pyramids) then the last using RTree and CreateBooleanIntersection
https://developer.rhino3d.com/api/RhinoCommon/html/M_Rhino_Geometry_Curve_CreateBooleanIntersection_1.htm
Manahattan Voronoi







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may i ask what this was/is aimed for?

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It is another type of Voronoi, named Manhattan voronoi because it is good at creating city type plots.

https://www.shadertoy.com/view/ltV3R3

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It is just a different distance used to calculate this Voronoi Tessellation, here the Manhattan distance between 2 points in plane XY P1(x1, y1) , P2(x2, y2)
d(P1, P2) = |x1-x2|+|y1-y2|

Classical distance is
d(P1, P2) = (|x1-x2|²+|y1-y2|²)^0.5

For the use it is a Tessellation, mainly for design.

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Might add it’s called Manhattan as the distance is calculated in an orthogonal manner, so it’s like going from one point to another in Manhattan (where the city plan is grid-like)

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Nice! Would be interesting to see this on meshes, somehow applying it for planarization similar to this : https://github.com/formateng/giraffe

Wouldn’t be that hard to use them for generative floor plans also.

@Petras_Vestartas and @felipegutierrezduque i don’t see many uses as it is just a slightly different tessellations from classical Voronoi. Meanwhile The Manhattan and Chebychev distance are already in Grasshopper.

Voronoi => intersection of cones


Manhattan => Intersection of pyramids


Chebychev => Intersection of pyramids


Equilateral => Intersection of cubes (rotated 45° then Atan(1/sqrt(2))


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I’m trying to understand too and I’m not completely clear

It’s possible to align every “pyramid” to a local plane?

As it is a 3d object the answer is yes. I included rotation and non uniform scale to make anisotropy. But as the result must be projected in a plane I don’t add rotation in X or Y.

Dont know why but all these make me feel satisfied…

Hello Laurent,
I didn’t know Manhattan distance Voronoi can be created using pyramide intersections, thank you for the hint!

Is Delaunay triangulation method geometrically correct or does it only produce similar looking results? Would you share your script with me or point me in a direction to help me create my own?

Cheers
Jonas

Hi. @laurent_delrieu I been wondering if you have an example file for the Manhattan Voronoi.
I believe it can be use for splitting building floor plans, and to get a better “equal” area partitions.