1-vector/2-vector

[Michael Ewert]

Wanted to add an example for barycentric coordinates to your tutorial section ( as suggested on bivector.net). Ran into a problem.

julia> basis"3"

julia> a = 0v1
0v₁

julia> b = 1v1
1v₁

julia> c = 1v2
1v₂

julia> ab = b-a
1v₁

julia> ca = a-c
0v₁ - 1v₂ + 0v₃

julia> bc = c-b
-1v₁ + 1v₂ + 0v₃

julia> A = -ab∧ca
1v₁₂ + 0v₁₃ + 0v₂₃

julia> bc∧ca
1v₁₂ + 0v₁₃ + 0v₂₃

julia> bc∧ca/A
ERROR: DimensionMismatch("No precise constructor for SArray{Tuple{8},Int64,1,8} found. Length of input was 3.")
Stacktrace:
[1] SArray{Tuple{8},Int64,1,8}(::Tuple{Tuple{Tuple{Tuple{Int64,Int64,Int64}}}}) at /Users/mewert/.julia/packages/StaticArrays/1g9bq/src/convert.jl:1
[2] StaticArray at /Users/mewert/.julia/packages/StaticArrays/1g9bq/src/convert.jl:4 [inlined] (repeats 3 times)
[3] macro expansion at /Users/mewert/.julia/packages/StaticArrays/1g9bq/src/convert.jl:4 [inlined]
[4] reverse(::Chain{⟨+++⟩,2,Int64,3}) at /Users/mewert/.julia/packages/Grassmann/OeTVc/src/products.jl:531
[5] ~ at /Users/mewert/.julia/packages/DirectSum/Ofduh/src/generic.jl:242 [inlined]
[6] inv(::Chain{⟨+++⟩,2,Int64,3}) at /Users/mewert/.julia/packages/Grassmann/OeTVc/src/algebra.jl:671
[7] /(::Chain{⟨+++⟩,2,Int64,3}, ::Chain{⟨+++⟩,2,Int64,3}) at /Users/mewert/.julia/packages/AbstractTensors/cHS7X/src/AbstractTensors.jl:156
[8] top-level scope at REPL[31]:1

Seems to be the zero elements

julia> A
1v₁₂ + 0v₁₃ + 0v₂₃

julia> (bc∧ca)/1v12
1.0v⃖

[Dream Scatter]

Yes, I'm aware of that issue, I fixed it locally a few days ago but didn't push it yet. The fix is now pushed to the master branch.

As for barycenters you can use the barycenters function on a mesh without any hassle:

julia> p,e,t = initmesh(2:0.1:8)
(Λ¹⟨++⟩×61, Λ¹Λ¹⟨_+⟩×61×2, I¹Λ¹⟨++⟩×61×60)

julia> barycenters(t)

This example is for a 1 dimensional mesh, but the same function works for any dimension.

[Michael Ewert]

yeah, the intention for the barycentre function was to follow the suggestion on bivector.net, not to use grassmann.jl api.

[Dream Scatter]

Let me know what you come up with then!

[Alok Singh]

Yes, I'm aware of that issue, I fixed it locally a few days ago but didn't push it yet. The fix is now pushed to the master branch.

As for barycenters you can use the barycenters function on a mesh without any hassle:

julia> p,e,t = initmesh(2:0.1:8)
(Λ¹⟨++⟩×61, Λ¹Λ¹⟨_+⟩×61×2, I¹Λ¹⟨++⟩×61×60)

julia> barycenters(t)

This example is for a 1 dimensional mesh, but the same function works for any dimension.

barycenters no longer works, using the latest version of grassmann. barycenter does work though, giving 1.0v₁ + 1.0327868852459017v₂.