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generalized TensorField product topology
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@chakravala
chakravala committed Aug 1, 2023
1 parent bf7c629 commit 3481cd8
Showing 1 changed file with 171 additions and 27 deletions.
198 changes: 171 additions & 27 deletions src/Adapode.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -28,11 +28,10 @@ import AbstractTensors: Scalar, GradedVector, Bivector, Trivector
export Values, odesolve
export initmesh, pdegrad

export ElementFunction, IntervalMap, PlaneCurve, SpaceCurve, Surface, ParametricMap
export ElementFunction, IntervalMap, PlaneCurve, SpaceCurve, GridSurface, GridParametric
export TensorField, ScalarField, VectorField, BivectorField, TrivectorField
export RealFunction, ComplexMap, ComplexMapping, SpinorField, CliffordField
#export QuaternionField # PhasorField

export MeshFunction, QuaternionField # PhasorField
export Section, FiberBundle

struct Section{R,T} <: Number
Expand All @@ -51,6 +50,8 @@ Base.:/(a::Section{R},b::Section{R}) where R = a.v.first==b.v.first ? Section(a.
Base.:*(a::Number,b::Section) = Section(b.v.first,a*b.v.second)
Base.:*(a::Section,b::Number) = Section(a.v.first,a.v.second*b)
Base.:/(a::Section,b::Number) = Section(a.v.first,a.v.second/b)
Base.abs(a::Section) = Section(a.v.first,abs(a.v.second))
Grassmann.value(a::Section) = Section(a.v.first,value(a.v.second))

abstract type FiberBundle{T,N} <: AbstractArray{T,N} end
Base.@pure isfiber(::FiberBundle) = true
Expand All @@ -61,31 +62,36 @@ struct TensorField{R,B,T,N} <: FiberBundle{Section{R,T},N}
cod::Array{T,N}
TensorField{R}(dom::B,cod::Array{T,N}) where {R,B,T,N} = new{R,B,T,N}(dom,cod)
TensorField(dom::B,cod::Array{T,N}) where {N,R,B<:AbstractArray{R,N},T} = new{R,B,T,N}(dom,cod)
TensorField(dom::B,cod::Vector{T}) where {B<:ChainBundle,T} = new{eltype(value(points(dom))),B,T,1}(dom,cod)
end


#const ParametricMesh{T<:AbstractVector{<:Chain},S} = TensorField{T,S,1}
const MeshFunction{R,B<:ChainBundle,T<:Real} = TensorField{R,B,T,1}
const ElementFunction{R,B<:AbstractVector{R},T<:Real} = TensorField{R,B,T,1}
const IntervalMap{R<:Real,B<:AbstractVector{R},T} = TensorField{R,B,T,1}
const RealFunction{R<:Real,B<:AbstractVector{R},T<:Union{Real,Single,Chain{V,G,<:Real,1} where {V,G}}} = ElementFunction{R,B,T}
const PlaneCurve{R<:Real,B<:AbstractVector{R},T<:Chain{V,G,Q,2} where {V,G,Q}} = TensorField{R,B,T,1}
const SpaceCurve{R<:Real,B<:AbstractVector{R},T<:Chain{V,G,Q,3} where {V,G,Q}} = TensorField{R,B,T,1}
const Surface{R,B<:AbstractMatrix{R},T<:Real} = TensorField{R,B,T,2}
const ParametricMap{R<:Real,B<:AbstractArray{R},T,N} = TensorField{R,B,T,N}
const GridSurface{R,B<:AbstractMatrix{R},T<:Real} = TensorField{R,B,T,2}
const GridParametric{R,B<:AbstractArray{R},T<:Real,N} = TensorField{R,B,T,N}
const ComplexMapping{R,B,T<:Complex,N} = TensorField{R,B,T,N}
const ComplexMap{R,B,T<:Couple,N} = TensorField{R,B,T,N}
const ScalarField{R,B,T<:Single,N} = TensorField{R,B,T,N}
const VectorField{R,B,T<:Chain{V,1} where V,N} = TensorField{R,B,T,N}
const SpinorField{R,B,T<:Spinor,N} = TensorField{R,B,T,N}
#const PhasorField{R,B,T<:Phasor,N} = TensorField{R,B,T,N}
#const QuaternionField{R,B,T<:Quaternion,N} = TensorField{R,B,T,N}
const QuaternionField{R,B,T<:Quaternion,N} = TensorField{R,B,T,N}
const CliffordField{R,B,T<:Multivector,N} = TensorField{R,B,T,N}
const BivectorField{R,B,T<:Chain{V,2} where V,N} = TensorField{R,B,T,N}
const TrivectorField{R,B,T<:Chain{V,3} where V,N} = TensorField{R,B,T,N}

TensorField(dom::AbstractArray,fun::Function) = TensorField(dom,fun.(dom))
TensorField(dom::ChainBundle,fun::Function) = TensorField(dom,fun.(value(points(dom))))

Base.size(m::TensorField) = size(m.cod)
Base.getindex(m::TensorField,i::Vararg{Int}) = Section(getindex(m.dom,i...),getindex(m.cod,i...))
Base.getindex(m::TensorField,i::Vararg{Int}) = Section(getindex(domain(m),i...),getindex(codomain(m),i...))
Base.getindex(m::ElementFunction{R,<:ChainBundle} where R,i::Vararg{Int}) = Section(getindex(value(points(domain(m))),i...),getindex(codomain(m),i...))
@pure Base.eltype(::Type{TensorField{R,B,T}}) where {R,B,T} = Section{R,T}

function (m::IntervalMap{Float64,Vector{Float64}})(t)
Expand All @@ -100,10 +106,36 @@ function parametric(t,m,d=diff(codomain(m))./diff(domain(m)))
codomain(m)[i]+(t-domain(m)[i])*d[i]
end

function (m::TensorField{R,<:ChainBundle} where R)(t)
i = domain(m)[findfirst(t,domain(m))]
(codomain(m)[i])⋅(points(domain(m))[i]/t)
end

export domain, codomain
domain(t::TensorField) = t.dom
codomain(t::TensorField) = t.cod

Base.:*(n::Number,t::TensorField) = TensorField(domain(t),n*codomain(t))
Base.:*(t::TensorField,n::Number) = TensorField(domain(t),codomain(t)*n)
Base.:/(n::Number,t::TensorField) = TensorField(domain(t),n./codomain(t))
Base.:/(t::TensorField,n::Number) = TensorField(domain(t),codomain(t)/n)
Base.:+(n::Number,t::TensorField) = TensorField(domain(t),n.+codomain(t))
Base.:+(t::TensorField,n::Number) = TensorField(domain(t),codomain(t).+n)
Base.:-(n::Number,t::TensorField) = TensorField(domain(t),n.-codomain(t))
Base.:-(t::TensorField,n::Number) = TensorField(domain(t),codomain(t).-n)
Base.:*(a::TensorField,b::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).*codomain(b))
Base.:/(a::TensorField,t::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a)./codomain(b))
Base.:+(a::TensorField,b::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).+codomain(b))
Base.:-(a::TensorField,b::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).-codomain(b))
Grassmann.:∧(a::TensorField,b::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).∧codomain(b))
Grassmann.:∨(a::TensorField,t::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).∨codomain(b))
Grassmann.:⋅(a::TensorField,b::TensorField) = checkdomain(a,b) && TensorField(domain(t),codomain(a).⋅codomain(b))
Base.abs(t::TensorField) = TensorField(domain(t),abs.(codomain(t)))
Grassmann.value(t::TensorField) = TensorField(domain(t),value.(codomain(t)))
absvalue(t::TensorField) = TensorField(domain(t),value.(abs.(codomain(t))))

checkdomain(a::TensorField,b::TensorField) = domain(a)≠domain(b) ? error("TensorField domains not equal") : true

centraldiff_fast(f::Vector,dt::Float64,l=length(f)) = [centraldiff_fast(i,f,l)/centraldiff_fast(i,dt,l) for i ∈ 1:l]
centraldiff_fast(f::Vector,dt::Vector,l=length(f)) = [centraldiff_fast(i,f,l)/dt[i] for i ∈ 1:l]
centraldiff_fast(f::Vector,l=length(f)) = [centraldiff_fast(i,f,l) for i ∈ 1:l]
Expand All @@ -121,10 +153,8 @@ centraldiff_fast(dt::Float64,l::Int) = [centraldiff_fast(i,dt,l) for i ∈ 1:l]
centraldiff_fast(i::Int,dt::Float64,l::Int) = i∈(1,l) ? 6dt : 2dt
#centraldiff_fast(i::Int,dt::Float64,l::Int) = 2dt

centraldiff(f::Vector,dt::Float64,l=length(f)) = [centraldiff(i,f,l)/centraldiff(i,dt,l) for i ∈ 1:l]
#=centraldiff(f::Vector,dt::Float64,l=length(f)) = [centraldiff(i,f,l)/centraldiff(i,dt,l) for i ∈ 1:l]
centraldiff(f::Vector,dt::Vector,l=length(f)) = [centraldiff(i,f,l)/dt[i] for i ∈ 1:l]
centraldiffdiff(f,dt,l) = centraldiff(centraldiff(f,dt,l),dt,l)
centraldiffdiff(f::Vector,dt) = centraldiffdiff(f,dt,length(f))
centraldiff(f::Vector,l=length(f)) = [centraldiff(i,f,l) for i ∈ 1:l]
function centraldiff(i::Int,f::Vector,l::Int=length(f))
if isone(i)
Expand All @@ -138,6 +168,50 @@ function centraldiff(i::Int,f::Vector,l::Int=length(f))
else
f[i-2]+8f[i+1]-8f[i-1]-f[i+2]
end
end=#

export Grid

struct Grid{N,T,A<:AbstractArray{T,N}}
v::A
end

Base.size(m::Grid) = size(m.v)

@generated function Base.getindex(g::Grid{M},j::Int,::Val{N},i::Vararg{Int}) where {M,N}
:(Base.getindex(g.v,$([k≠N ? :(i[$k]) : :(i[$k]+j) for k ∈ 1:M]...)))
end

centraldiffdiff(f,dt,l) = centraldiff(centraldiff(f,dt,l),dt,l)
centraldiffdiff(f,dt) = centraldiffdiff(f,dt,size(f))
centraldiff(f::AbstractArray,args...) = centraldiff(Grid(f),args...)

centraldiff(f::Grid{1},dt::Float64,l=size(f.v)) = [centraldiff(f,l,i)/centraldiff(i,dt,l) for i ∈ 1:l]
centraldiff(f::Grid{1},dt::Vector,l=size(f.v)) = [centraldiff(f,l,i)/dt[i] for i ∈ 1:l[1]]
centraldiff(f::Grid{1},l=size(f.v)) = [centraldiff(f,l,i) for i ∈ 1:l[1]]

centraldiff(f::Grid{2},dt::AbstractMatrix,l::Tuple=size(f.v)) = [Chain(centraldiff(f,l,i,j).v./(dt[i,j].v)) for i ∈ 1:l[1], j ∈ 1:l[2]]
centraldiff(f::Grid{2},l::Tuple=size(f.v)) = [centraldiff(f,l,i,j) for i ∈ 1:l[1], j ∈ 1:l[2]]

centraldiff(f::Grid{3},dt::AbstractArray{T,3} where T,l::Tuple=size(f.v)) = [Chain(centraldiff(f,l,i,j,k).v./(dt[i,j,k].v)) for i ∈ 1:l[1], j ∈ 1:l[2], k ∈ 1:l[3]]
centraldiff(f::Grid{3},l::Tuple=size(f.v)) = [centraldiff(f,l,i,j,k) for i ∈ 1:l[1], j ∈ 1:l[2], k ∈ 1:l[3]]

centraldiff(f::Grid{1},l,i::Int) = centraldiff(f,l[1],Val(1),i)
@generated function centraldiff(f::Grid{M},l,i::Vararg{Int}) where M
:(Chain($([:(centraldiff(f,l[$k],Val($k),i...)) for k ∈ 1:M]...)))
end
function centraldiff(f::Grid,l,k::Val{N},i::Vararg{Int}) where N #l=size(f)[N]
if isone(i[N])
18f[1,k,i...]-9f[2,k,i...]+2f[3,k,i...]-11f.v[i...]
elseif i[N]==l
11f.v[i...]-18f[-1,k,i...]+9f[-2,k,i...]-2f[-3,k,i...]
elseif i[N]==2
6f[1,k,i...]-f[2,k,i...]-3f.v[i...]-2f[-1,k,i...]
elseif i[N]==l-1
3f.v[i...]-6f[-1,k,i...]+f[-2,k,i...]+2f[1,k,i...]
else
f[-2,k,i...]+8f[1,k,i...]-8f[-1,k,i...]-f[2,k,i...]
end
end

centraldiff(f::StepRangeLen,l=length(f)) = [centraldiff(i,Float64(f.step),l) for i ∈ 1:l]
Expand Down Expand Up @@ -191,9 +265,19 @@ end
function tangent(f::IntervalMap,d=centraldiff(domain(f)))
TensorField(domain(f),centraldiff(codomain(f),d))
end
function tangent(f::GridParametric,d=centraldiff(domain(f)))
TensorField(domain(f),centraldiff(Grid(codomain(f)),d))
end
function tangent(f::MeshFunction)
TensorField(domain(f),interp(domain(f),gradient(domain(f),codomain(f))))
end
function unittangent(f::IntervalMap,d=centraldiff(domain(f)),t=centraldiff(codomain(f),d))
TensorField(domain(f),t./abs.(t))
end
function unittangent(f::MeshFunction)
t = interp(domain(f),gradient(domain(f),codomain(f)))
TensorField(domain(f),t./abs.(t))
end
function speed(f::IntervalMap,d=centraldiff(domain(f)),t=centraldiff(codomain(f),d))
TensorField(domain(f),abs.(t))
end
Expand Down Expand Up @@ -280,7 +364,7 @@ end
#bishoppolar(f::TensorField) = TensorField(f.dom,Chain.(value.(curvature(f).cod),getindex.(trapz(torsion(f)).cod,1)))
#bishop(f::TensorField,κ=value.(curvature(f).cod),θ=getindex.(trapz(torsion(f)).cod,1)) = TensorField(f.dom,Chain.(κ.*cos.(θ),κ.*sin.(θ)))

export ProductSpace, RealProductSpace, ⧺
export ProductSpace, RealRegion, Interval, Rectangle, Hyperrectangle, ⧺
import DirectSum: ⊕

struct ProductSpace{V,T,N,M,S} <: AbstractArray{Chain{V,1,T,N},N}
Expand All @@ -289,17 +373,42 @@ struct ProductSpace{V,T,N,M,S} <: AbstractArray{Chain{V,1,T,N},N}
ProductSpace{V,T}(v::Values{M,S}) where {V,T,M,S} = new{V,T,mdims(V),M,S}(v)
end

const RealProductSpace{V,T<:Real,N,S<:AbstractVector{T}} = ProductSpace{V,T,N,N,S}
RealProductSpace{V}(v::Values{N,S}) where {V,T<:Real,N,S<:AbstractVector{T}} = ProductSpace{V,T,N}(v)
RealProductSpace(v::Values{N,S}) where {T<:Real,N,S<:AbstractVector{T}} = ProductSpace{ℝ^N,T,N}(v)
const RealRegion{V,T<:Real,N,S<:AbstractVector{T}} = ProductSpace{V,T,N,N,S}
const Interval{V,T,S} = RealRegion{V,T,1,S}
const Rectangle{V,T,S} = RealRegion{V,T,2,S}
const Hyperrectangle{V,T,S} = RealRegion{V,T,3,S}
RealRegion{V}(v::Values{N,S}) where {V,T<:Real,N,S<:AbstractVector{T}} = ProductSpace{V,T,N}(v)
RealRegion(v::Values{N,S}) where {T<:Real,N,S<:AbstractVector{T}} = ProductSpace{ℝ^N,T,N}(v)
ProductSpace{V}(v::Values{N,S}) where {V,T<:Real,N,S<:AbstractVector{T}} = ProductSpace{V,T,N}(v)
ProductSpace(v::Values{N,S}) where {T<:Real,N,S<:AbstractVector{T}} = ProductSpace{ℝ^N,T,N}(v)

@generated Base.size(m::RealProductSpace{V}) where V = :(($([:(size(m.v[$i])...) for i ∈ 1:mdims(V)]...),))
@generated Base.getindex(m::RealProductSpace{V,T,N},i::Vararg{Int}) where {V,T,N} = :(Chain{V,1,T}($([:(m.v[$j][i[$j]]) for j ∈ 1:N]...)))
@generated Base.size(m::RealRegion{V}) where V = :(($([:(size(m.v[$i])...) for i ∈ 1:mdims(V)]...),))
@generated Base.getindex(m::RealRegion{V,T,N},i::Vararg{Int}) where {V,T,N} = :(Chain{V,1,T}($([:(m.v[$j][i[$j]]) for j ∈ 1:N]...)))
@pure Base.eltype(::Type{ProductSpace{V,T,N}}) where {V,T,N} = Chain{V,1,T,N}

⊕(a::AbstractVector{A},b::AbstractVector{B}) where {A<:Real,B<:Real} = RealProductSpace(Values(a,b))
centraldiff(f::RealRegion) = ProductSpace(centraldiff.(f.v))

function (m::TensorField{R,<:Rectangle} where R)(t)
x,y = domain(m).v[1],domain(m).v[2]
i,j = searchsortedfirst(x,t[1])-1,searchsortedfirst(y,t[2])-1
f1 = m.cod[i,j]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j]-m.cod[i,j])
f2 = m.cod[i,j+1]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j+1]-m.cod[i,j+1])
f1+(t[2]-y[i])/(y[i+1]-y[i])*(f2-f1)
end

function (m::TensorField{R,<:Hyperrectangle} where R)(t)
x,y,z = domain(m).v[1],domain(m).v[2],domain(m).v[3]
i,j,k = searchsortedfirst(x,t[1])-1,searchsortedfirst(y,t[2])-1,searchsortedfirst(z,t[3])-1
f1 = m.cod[i,j,k]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j,k]-m.cod[i,j,k])
f2 = m.cod[i,j+1,k]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j+1,k]-m.cod[i,j+1,k])
g1 = f1+(t[2]-y[i])/(y[i+1]-y[i])*(f2-f1)
f3 = m.cod[i,j,k+1]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j,k+1]-m.cod[i,j,k+1])
f4 = m.cod[i,j+1,k+1]+(t[1]-x[i])/(x[i+1]-x[i])*(m.cod[i+1,j+1,k+1]-m.cod[i,j+1,k+1])
g2 = f3+(t[2]-y[i])/(y[i+1]-y[i])*(f4-f3)
g1+(t[3]-z[i])/(z[i+1]-z[i])*(g2-g1)
end

⊕(a::AbstractVector{A},b::AbstractVector{B}) where {A<:Real,B<:Real} = RealRegion(Values(a,b))

@generated ⧺(a::Real...) = :(Chain($([:(a[$i]) for i ∈ 1:length(a)]...)))
@generated ⧺(a::Complex...) = :(Chain($([:(a[$i]) for i ∈ 1:length(a)]...)))
Expand Down Expand Up @@ -484,16 +593,51 @@ show_progress(x,t,b) = t.i%75000 == 11 && println(time(x[t.i])," out of ",b)

function __init__()
@require Makie="ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" begin
Makie.lines(t::IntervalMap) = Makie.lines(t.cod,color=value.(speed(t).cod))
Makie.lines(t::RealFunction) = Makie.lines(t.dom,getindex.(value.(t.cod),1),color=value.(speed(t).cod))
Makie.linesegments(t::IntervalMap) = Makie.linesegments(t.cod,color=value.(speed(t).cod))
Makie.linesegments(t::RealFunction) = Makie.linesegments(t.dom,getindex.(value.(t.cod),1),color=value.(speed(t).cod))
Makie.surface(t::Surface{<:RealProductSpace}) = Makie.surface(t.dom.v[1],t.dom.v[2],t.cod)
Makie.contour(t::Surface{<:RealProductSpace}) = Makie.contour(t.dom.v[1],t.dom.v[2],t.cod)
Makie.contourf(t::Surface{<:RealProductSpace}) = Makie.contourf(t.dom.v[1],t.dom.v[2],t.cod)
Makie.heatmap(t::Surface{<:RealProductSpace}) = Makie.heatmap(t.dom.v[1],t.dom.v[2],t.cod)
Makie.wireframe(t::Surface{<:RealProductSpace}) = Makie.wireframe(t.dom.v[1],t.dom.v[2],t.cod)
Makie.spy(t::Surface{<:RealProductSpace}) = Makie.spy(t.dom.v[1],t.dom.v[2],t.cod)
Makie.lines(t::SpaceCurve;args...) = Makie.lines(t.cod;color=value.(speed(t).cod),args...)
Makie.lines(t::PlaneCurve;args...) = Makie.lines(t.cod;color=value.(speed(t).cod),args...)
Makie.lines(t::RealFunction;args...) = Makie.lines(t.dom,getindex.(value.(t.cod),1);color=value.(speed(t).cod),args...)
Makie.linesegments(t::SpaceCurve;args...) = Makie.linesegments(t.cod;color=value.(speed(t).cod),args...)
Makie.linesegments(t::PlaneCurve;args...) = Makie.linesegments(t.cod;color=value.(speed(t).cod),args...)
Makie.linesegments(t::RealFunction;args...) = Makie.linesegments(t.dom,getindex.(value.(t.cod),1);color=value.(speed(t).cod),args...)
Makie.volume(t::GridParametric{<:Chain,<:Hyperrectangle};args...) = Makie.volume(t.dom.v[1],t.dom.v[2],t.dom.v[3],t.cod;args...)
Makie.volumeslices(t::GridParametric{<:Chain,<:Hyperrectangle};args...) = Makie.volumeslices(t.dom.v[1],t.dom.v[2],t.dom.v[3],t.cod;args...)
Makie.surface(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.surface(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.contour(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.contour(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.contourf(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.contourf(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.contour3d(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.contour3d(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.heatmap(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.heatmap(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.wireframe(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.wireframe(t.dom.v[1],t.dom.v[2],t.cod;args...)
#Makie.spy(t::GridSurface{<:Chain,<:RealRegion};args...) = Makie.spy(t.dom.v[1],t.dom.v[2],t.cod;args...)
Makie.streamplot(f::Function,t::Rectangle;args...) = Makie.streamplot(f,t.v[1],t.v[2];args...)
Makie.streamplot(f::Function,t::Hyperrectangle;args...) = Makie.streamplot(f,t.v[1],t.v[2],t.v[3];args...)
Makie.streamplot(m::TensorField{R,<:RealRegion,<:Real} where R;args...) = Makie.streamplot(tangent(m);args...)
Makie.streamplot(m::TensorField{R,<:ChainBundle,<:Real} where R,dims...;args...) = Makie.streamplot(tangent(m),dims...;args...)
Makie.streamplot(m::VectorField{R,<:ChainBundle} where R,dims...;args...) = Makie.streamplot(p->Makie.Point(m(Chain(one(eltype(p)),p.data...))),dims...;args...)
Makie.streamplot(m::VectorField{R,<:RealRegion} where R;args...) = Makie.streamplot(p->Makie.Point(m(Chain(p.data...))),domain(m).v...;args...)
Makie.arrows(t::VectorField{<:Chain,<:Rectangle};args...) = Makie.arrows(t.dom.v[1],t.dom.v[2],getindex.(t.cod,1),getindex.(t.cod,2);args...)
Makie.arrows!(t::VectorField{<:Chain,<:Rectangle};args...) = Makie.arrows!(t.dom.v[1],t.dom.v[2],getindex.(t.cod,1),getindex.(t.cod,2);args...)
Makie.arrows(t::VectorField{<:Chain,<:Hyperrectangle};args...) = Makie.arrows(Makie.Point.(domain(t))[:],Makie.Point.(codomain(t))[:];args...)
Makie.arrows!(t::VectorField{<:Chain,<:Hyperrectangle};args...) = Makie.arrows!(Makie.Point.(domain(t))[:],Makie.Point.(codomain(t))[:];args...)
Makie.arrows(t::Rectangle,f::Function;args...) = Makie.arrows(t.v[1],t.v[2],f;args...)
Makie.arrows!(t::Rectangle,f::Function;args...) = Makie.arrows!(t.v[1],t.v[2],f;args...)
Makie.arrows(t::Hyperrectangle,f::Function;args...) = Makie.arrows(t.v[1],t.v[2],t.v[3],f;args...)
Makie.arrows!(t::Hyperrectangle,f::Function;args...) = Makie.arrows!(t.v[1],t.v[2],t.v[3],f;args...)
Makie.arrows(t::MeshFunction;args...) = Makie.arrows(points(domain(t)),codomain(t);args...)
Makie.arrows!(t::MeshFunction;args...) = Makie.arrows!(points(domain(t)),codomain(t);args...)
Makie.mesh(t::ElementFunction;args...) = Makie.mesh(domain(t);color=codomain(t),args...)
Makie.mesh!(t::ElementFunction;args...) = Makie.mesh!(domain(t);color=codomain(t),args...)
Makie.mesh(t::MeshFunction;args...) = Makie.mesh(domain(t);color=codomain(t),args...)
Makie.mesh!(t::MeshFunction;args...) = Makie.mesh!(domain(t);color=codomain(t),args...)
Makie.wireframe(t::ElementFunction;args...) = Makie.wireframe(value(domain(t));color=codomain(t),args...)
Makie.wireframe!(t::ElementFunction;args...) = Makie.wireframe!(value(domain(t));color=codomain(t),args...)
end
@requires UnicodePlots="b8865327-cd53-5732-bb35-84acbb429228" begin
UnicodePlots.lineplot(t::PlaneCurve;args...) = UnicodePlots.lineplot(getindex.(t.cod,1),getindex.(t.cod,2);args...)
UnicodePlots.lineplot(t::RealFunction;args...) = UnicodePlots.lineplot(t.dom,getindex.(value.(t.cod),1);args...)
UnicodePlots.contourplot(t::GridSurface{<:Chain,<:RealRegion};args...) = UnicodePlots.contourplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
UnicodePlots.surfaceplot(t::GridSurface{<:Chain,<:RealRegion};args...) = UnicodePlots.surfaceplot(t.dom.v[1][2:end-1],t.dom.v[2][2:end-1],(x,y)->t(Chain(x,y));args...)
UnicodePlots.spy(t::GridSurface{<:Chain,<:RealRegion};args...) = UnicodePlots.spy(t.cod;args...)
UnicodePlots.heatmap(t::GridSurface{<:Chain,<:RealRegion};args...) = UnicodePlots.heatmap(t.cod;args...)
end
end

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