improved various mesh & plotting methods

Project.toml

@@ -1,7 +1,7 @@
 name = "Grassmann"
 uuid = "4df31cd9-4c27-5bea-88d0-e6a7146666d8"
 authors = ["Michael Reed"]
-version = "0.5.15"
+version = "0.5.16"
 
 [deps]
 AbstractTensors = "a8e43f4a-99b7-5565-8bf1-0165161caaea"
@@ -17,7 +17,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 [compat]
 julia = "1"
 Leibniz = "0.0.5"
-DirectSum = "0.5.8"
+DirectSum = "0.5.11"
 AbstractTensors = "0.4.9"
 ComputedFieldTypes = "0.1"
 StaticArrays = "0"

src/Grassmann.jl

@@ -167,7 +167,7 @@ end
 
 ## skeleton / subcomplex
 
-export skeleton, 𝒫, collapse, subcomplex, chain, path
+export skeleton, 𝒫, collapse, subcomplex, chain, path, pointset, column, columns
 
 absym(t) = abs(t)
 absym(t::SubManifold) = t
@@ -241,7 +241,7 @@ columns(t,i=1,j=ndims(t)) = column.(Ref(value(t)),list(i,j))
 function edges(t,cols=columns(t))
     ndims(t) == 2 && (return t)
     np,N = length(points(t)),ndims(Manifold(t))
-    A = spzeros(np,np),points(t)(list(N-1,N)...)
+    A,M = spzeros(np,np),points(t)(list(N-1,N)...)
     for c ∈ combo(N,2)
         A += sparse(cols[c[1]],cols[c[2]],1,np,np)
     end
@@ -401,22 +401,35 @@ function __init__()
         AbstractPlotting.arrows(p::Vector{<:Chain{V}},v;args...) where V = AbstractPlotting.arrows(GeometryBasics.Point.(↓(V).(p)),GeometryBasics.Point.(value(v));args...)
         AbstractPlotting.arrows!(p::Vector{<:Chain{V}},v;args...) where V = AbstractPlotting.arrows!(GeometryBasics.Point.(↓(V).(p)),GeometryBasics.Point.(value(v));args...)
         AbstractPlotting.scatter(p::ChainBundle,x,;args...) = AbstractPlotting.scatter(submesh(p)[:,1],x;args...)
-        AbstractPlotting.scatter!(p::Vector{<:Chain},x,;args...) = AbstractPlotting.scatter!(submesh(p)[:,1],x;args...)
-        AbstractPlotting.scatter(p::Vector{<:Chain},x,;args...) = AbstractPlotting.scatter(submesh(p)[:,1],x;args...)
         AbstractPlotting.scatter!(p::ChainBundle,x,;args...) = AbstractPlotting.scatter!(submesh(p)[:,1],x;args...)
-        AbstractPlotting.mesh(t::ChainBundle;args...) = AbstractPlotting.mesh(points(t),t;args...)
+        AbstractPlotting.scatter(p::Vector{<:Chain},x,;args...) = AbstractPlotting.scatter(submesh(p)[:,1],x;args...)
+        AbstractPlotting.scatter!(p::Vector{<:Chain},x,;args...) = AbstractPlotting.scatter!(submesh(p)[:,1],x;args...)
+        AbstractPlotting.lines(p::ChainBundle,args...) = AbstractPlotting.lines(value(p),args...)
+        AbstractPlotting.lines!(p::ChainBundle,args...) = AbstractPlotting.lines!(value(p),args...)
         AbstractPlotting.lines(p::Vector{<:TensorAlgebra},args...) = AbstractPlotting.lines(GeometryBasics.Point.(p),args...)
-        AbstractPlotting.linesegments(e::Vector{<:Chain},args...) = (p=points(e); AbstractPlotting.linesegments(pointpair.(p[e],↓(Manifold(p))),args...))
-        AbstractPlotting.linesegments!(e::Vector{<:Chain},args...) = (p=points(e); AbstractPlotting.linesegments!(pointpair.(p[e],↓(Manifold(p))),args...))
+        AbstractPlotting.lines!(p::Vector{<:TensorAlgebra},args...) = AbstractPlotting.lines!(GeometryBasics.Point.(p),args...)
         AbstractPlotting.linesegments(e::ChainBundle,args...) = AbstractPlotting.linesegments(value(e),args...)
         AbstractPlotting.linesegments!(e::ChainBundle,args...) = AbstractPlotting.linesegments!(value(e),args...)
-        function AbstractPlotting.mesh(p::ChainBundle,t::ChainBundle;args...)
+        AbstractPlotting.linesegments(e::Vector{<:Chain},args...) = (p=points(e); AbstractPlotting.linesegments(pointpair.(p[e],↓(Manifold(p))),args...))
+        AbstractPlotting.linesegments!(e::Vector{<:Chain},args...) = (p=points(e); AbstractPlotting.linesegments!(pointpair.(p[e],↓(Manifold(p))),args...))
+        AbstractPlotting.mesh(t::ChainBundle;args...) = AbstractPlotting.mesh(points(t),t;args...)
+        AbstractPlotting.mesh!(t::ChainBundle;args...) = AbstractPlotting.mesh!(points(t),t;args...)
+        AbstractPlotting.mesh(t::Vector{<:Chain};args...) = AbstractPlotting.mesh(points(t),t;args...)
+        AbstractPlotting.mesh!(t::Vector{<:Chain};args...) = AbstractPlotting.mesh!(points(t),t;args...)
+        function AbstractPlotting.mesh(p::ChainBundle,t;args...)
             if ndims(p) == 2
                 AbstractPlotting.plot(submesh(p)[:,1],args[:color])
             else
                 AbstractPlotting.mesh(submesh(p),array(t);args...)
             end
         end
+        function AbstractPlotting.mesh!(p::ChainBundle,t;args...)
+            if ndims(p) == 2
+                AbstractPlotting.plot!(submesh(p)[:,1],args[:color])
+            else
+                AbstractPlotting.mesh!(submesh(p),array(t);args...)
+            end
+        end
     end
     #@require Makie="ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" nothing
     @require MiniQhull="978d7f02-9e05-4691-894f-ae31a51d76ca" begin

src/algebra.jl

@@ -348,6 +348,8 @@ Exterior product as defined by the anti-symmetric quotient Λ≡⊗/~
 @inline ∧(a::UniformScaling{T},b::TensorAlgebra{V}) where {V,T<:Field} = V(a)∧b
 @generated ∧(t::T) where T<:SVector = Expr(:call,:∧,[:(t[$k]) for k ∈ 1:length(t)]...)
 @generated ∧(t::T) where T<:SizedVector = Expr(:call,:∧,[:(t[$k]) for k ∈ 1:length(t)]...)
+∧(::SVector{0,<:Chain{V}}) where V = one(V) # ∧() = 1
+∧(::SizedVector{0,<:Chain{V}}) where V = one(V)
 ∧(t::Chain{V,1,<:Chain} where V) = ∧(value(t))
 ∧(a::X,b::Y,c::Z...) where {X<:TensorAlgebra,Y<:TensorAlgebra,Z<:TensorAlgebra} = ∧(a∧b,c...)
 

src/composite.jl

@@ -392,7 +392,7 @@ INV(m::Chain{V,1,<:Chain{V,1}}) where V = Chain{V,1,Chain{V,1}}(inv(SMatrix(m)))
         Chain{M,1}.($(Expr(:.,:SVector,v)))
     end
 end
-@pure list(a,b) = SVector(a:b...)
+@pure list(a::Int,b::Int) = SVector{max(0,b-a+1),Int}(a:b...)
 vectors(x::SVector{N,<:Chain{V}},y=x[1]) where {N,V} = ↓(V).(x[list(2,N)].-y)
 vectors(x::Chain{V,1},y=x[1]) where V = vectors(value(x),y)
 #point(x,y=x[1]) = y∧∧(vectors(x))
@@ -451,8 +451,15 @@ curl(m::T) where T<:TensorAlgebra = Manifold(m)(∇)×m
 LinearAlgebra.det(t::Chain{V,1,<:Chain} where V) = ∧(t)
 LinearAlgebra.det(m::Vector{<:Chain{V}}) where V = ∧(m)
 LinearAlgebra.det(m::ChainBundle) = ∧(m)
-∧(m::Vector{<:Chain{V}}) where V = .∧(points(m)[m])
 ∧(m::ChainBundle) = ∧(value(m))
+function ∧(m::Vector{<:Chain{V}}) where V
+    p = points(m); pm = p[m]
+    if ndims(p)>ndims(V)
+        .∧(vectors.(pm))
+    else
+        Chain{↓(Manifold(V)),ndims(V)-1}.(value.(.∧(pm)))
+    end
+end
 for op ∈ (:mean,:barycenter,:curl)
     ops = Symbol(op,:s)
     @eval begin
@@ -488,11 +495,12 @@ function refinemesh!(::R,p::ChainBundle{W},e,t,η,_=nothing) where {W,R<:Abstrac
 end
 
 const array_cache = (Array{T,2} where T)[]
+array(m::Vector{<:Chain}) = [m[i][j] for i∈1:length(m),j∈1:ndims(Manifold(m))]
 function array(m::ChainBundle{V,G,T,B} where {V,G,T}) where B
     for k ∈ length(array_cache):B
         push!(array_cache,Array{Any,2}(undef,0,0))
     end
-    isempty(array_cache[B]) && (array_cache[B] = [m[i][j] for i∈1:length(m),j∈1:ndims(m)])
+    isempty(array_cache[B]) && (array_cache[B] = array(value(m)))
     return array_cache[B]
 end
 function array!(m::ChainBundle{V,G,T,B} where {V,G,T}) where B

src/forms.jl

@@ -44,7 +44,7 @@
             :(@inbounds Chain{w,1,T}(b.v[$ind]))
         else quote
             out,N = zeros(choicevec(M,G,valuetype(b))),ndims(V)
-            ib,S = indexbasis(N,G),bits(W)
+            ib,S = indexbasis(N,G),bits(w)
             for k ∈ 1:length(ib)
                 @inbounds if b[k] ≠ 0
                     @inbounds if count_ones(ib[k]&S) == G