Louvre Abu Dhabi

[Chris Kitrick]

For anyone interested in domes I suggest checking out the new Louve Abu Dhabi, which just opened this month. It is not a standard geodesic dome but it is complex and very visually intriguing. Some links below.

Jean Nouvel’s Louvre Abu Dhabi featuring giant geometric-patterned dome set to open on November 11
http://worldarchitecture.org/architecture-news/cvgcp/jean_nouvel_s_louvre_abu_dhabi_featuring_giant_geometricpatterned_dome_set_to_open_on_november_11.html

The 3D Geometry of Louvre Abu Dhabi
https://channel9.msdn.com/Events/FSharp-Events/fsharpConf-2016/The-3D-Geometry-of-Louvre-Abu-Dhabi

Cheers

[Adrian Rossiter]

Hi Chris and All

On Sat, 18 Nov 2017, Chris Kitrick wrote:
> For anyone interested in domes I suggest checking out the new Louve Abu
> Dhabi, which just opened this month. It is not a standard geodesic dome but
> it is complex and very visually intriguing. Some links below.

Thanks for posting this. I skipped through the video quickly for now
but will look at the software techniques later.

It is of interest as I have been looking at tiling recently and have
come up with constructive notation that can be used to create these
sort of tiling patterns from a base tiling.

The external pattern seen in the photo can be described in this
notation by

[V2F,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2

In the photo it is applied to a square base tiling, but it could
be applied to any tiling. I have attached images of the pattern
applied to a square grid dome (proj_dome.py is in
https://github.com/antiprism/antiprism_python) and a geodesic sphere

proj_dome.py -t s -p -4.5 6 5 | wythoff -p [2FV,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2 | antiview
wythoff -p [2FV,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2 geo_3 | antiview

The wythoff program will be available in the next release of Antiprism,
or is avaiable now if building Antiprism from the Github repository. I
have included some of the program help below as it describes the notation.

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

wythoff - Wythoff-style constructions

The polyhedron faces are divided by a 'meta' operation into triangles
each having vertices which are a vertex V, edge centre E and face centre F.
A start point is positioned on one of these triangles, the next point is
found by using the pattern to step between triangles, leading to a circuit.
If input_file is not given the program reads from standard input.


-p <pat> pattern in form: [Coords0:Coords1:...]Path0,Path1...
Coordinates are barycentric, in form aVbEcF:
VEF element letters, and a,b,c are barycentric coordinates
corresponding to the following element letter. Ommiting a
an element letter and coordinate sets the coordinate to zero.
Ommitting just the coordinate sets the coordinate to 1. E.g
V = (1,0,0), VE = (1,1,0), V2E3F = (1,2,3)
Paths are in the form: TrisPidx0Move0Pidx1Move1...
Tris: one of +-* (default +) indicating that paths should
start for positive, negative or both kinds of triangles.
Pidx: an index number of a point from the coordinates list
Move: an operation for stepping to the next triangle, given
as a series of characters from the following:
_ - no move, stay on the same triangle
v,e,f - step over side opposite V,E,F
V,E,F - step two trianglesi, rotating about V,E,F,
according to: V=ef, E=fv, F=ve
Paths can start with either a move or a point, but cannot both
start and end with a move

Notes

wythoff expands on the ideas behind the Wythoff symbol to create a
specified tiling pattern from any suitable triangular tiling.
Triangle tilings are created, by default, from the input model by the
Conway 'meta' operation. This consists of all triangles that join a face
centre to one of its vertices and a neighbouring edge centre. With regard
to starting triangles, the meta triangle (Vn, En, F) is labelled -/black,
and the meta triangle (Vn+1, En, F) is labelled +/white.

The output tiling will not necesarily be planar, or have equal edge
lengths. The output of 'spherical' tilings can be processed with the
canonical program.

In the final model, vertices are coloured according to which elements are
involved in the pattern coordinates: V=0/red, E=1/green, F=2/blue,
VE=3/yellow, EF=4/cyan, FE=5/magenta, VEF=6/grey. Faces are coloured
according to their corresponding position in the pattern.

[Adrian Rossiter]

Hi All

On Sun, 19 Nov 2017, Adrian Rossiter wrote:
> It is of interest as I have been looking at tiling recently and have
> come up with constructive notation that can be used to create these
> sort of tiling patterns from a base tiling.
>
> The external pattern seen in the photo can be described in this
> notation by
>
> [V2F,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2
>
> In the photo it is applied to a square base tiling, but it could
> be applied to any tiling. I have attached images of the pattern
> applied to a square grid dome (proj_dome.py is in
> https://github.com/antiprism/antiprism_python) and a geodesic sphere
>
> proj_dome.py -t s -p -4.5 6 5 | wythoff -p [2FV,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2 | antiview
> wythoff -p [2FV,2VE,E]0F,1V,*0_1_2,0e1e1,0v0v2 geo_3 | antiview
>
> The wythoff program will be available in the next release of Antiprism,

I have just released Antiprism 0.25.1, which includes the new wythoff
program

http://www.antiprism.com/download/