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

# Manhattan Voronoi

may i ask what this was/is aimed for?

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

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.

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)

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.