implemented FiberProduct structure

README.md

@@ -15,23 +15,27 @@
 Provides `TensorField{B,F,N} <: GlobalFiber{LocalTensor{B,F},N}` implementation for both a local `ProductSpace` and general `ImmersedTopology` specifications on any `AbstractFrameBundle` expressed with [Grassmann.jl](https://github.com/chakravala/Grassmann.jl) algebra.
 Many of these modular methods can work on input meshes or product topologies of any dimension, although there are some methods which are specialized.
 Building on this, `Cartan` provides an algebra for any `GlobalSection` and associated bundles on a manifold, such as general `Connection` and `CovariantDerivative` operators in terms of `Grassmann` elements.
+Calculus of `Variation` fields can also be generated with the combined topology of a `FiberProductBundle`.
+Furthermore, the `FiberProduct` structure enables construction of `HomotopyBundle` types.
 Utility package for differential geometry and tensor calculus intended for [Adapode.jl](https://github.com/chakravala/Adapode.jl).
 
 The `Cartan` package is intended to standardize the composition of various methods and functors applied to specialized categories transformed with a unified representation over a product topology, especially having fibers of the `Grassmann` algebra.
 Initial topologies include `ProductSpace` types and in general the `ImmersedTopology`.
 ```
 Positions{P, G} where {P<:Chain, G} (alias for AbstractArray{<:Coordinate{P, G}, 1} where {P<:Chain, G})
 Interval{P, G} where {P<:AbstractReal, G} (alias for AbstractArray{<:Coordinate{P, G}, 1} where {P<:Union{Real, Single{V, G, B, <:Real} where {V, G, B}, Chain{V, G, <:Real, 1} where {V, G}}, G})
-IntervalRange (alias for GridFrameBundle{P, G, 1, PA, GA} where {P<:Real, G, PA<:AbstractRange, GA})
+IntervalRange{P, G, PA, GA} where {P<:Real, G, PA<:AbstractRange, GA} (alias for GridFrameBundle{Coordinate{P, G}, 1, <:PointArray{P, G, 1, PA, GA}} where {P<:Real, G, PA<:AbstractRange, GA})
 Rectangle (alias for ProductSpace{V, T, 2, 2} where {V, T})
 Hyperrectangle (alias for ProductSpace{V, T, 3, 3} where {V, T})
 RealRegion{V, T} where {V, T<:Real} (alias for ProductSpace{V, T, N, N, S} where {V, T<:Real, N, S<:AbstractArray{T, 1}})
 RealSpace{N} where N (alias for AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})
-AlignedRegion{N} where N (alias for GridFrameBundle{P, G, N, PA, GA} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA<:Global})
-AlignedSpace{N} where N (alias for GridFrameBundle{P, G, N, PA, GA} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA})
+AlignedRegion{N} where N (alias for GridFrameBundle{Coordinate{P, G}, N, PointArray{P, G, N, PA, GA}} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA<:Global})
+AlignedSpace{N} where N (alias for GridFrameBundle{Coordinate{P, G}, N, PointArray{P, G, N, PA, GA}} where {N, P<:Chain, G<:InducedMetric, PA<:(ProductSpace{V, <:Real, N, N, <:AbstractRange} where V), GA})
 GridFrameBundle{P,G,N,PA<:AbstractArray{P,N},GA<:AbstractArray{G,N}} <: AbstractFrameBundle{Coordinate{P,G},N}
 SimplexFrameBundle{P,G,PA<:AbstractVector{P},GA<:AbstractVector{G},TA<:ImmersedTopology} <: AbstractFrameBundle{Coordinate{P,G},1}
 FacetFrameBundle{P,G,PA,GA,TA<:ImmersedTopology} <: AbstractFrameBundle{Coordinate{P,G},1}
+FiberProductBundle{P,N,SA<:AbstractArray,PA<:AbstractArray} <: AbstractFrameBundle{Coordinate{P,InducedMetric},N}
+HomotopyBundle{P,N,PA<:AbstractArray{F,N} where F,FA<:AbstractArray,TA<:ImmersedTopology} <: AbstractFrameBundle{Coordinate{P,InducedMetric},N}
 AbstractFrameBundle{Coordinate{B,F},N} where {B,F,N}
 ```
 Visualizing `TensorField` reperesentations can be standardized in combination with [Makie.jl](https://github.com/MakieOrg/Makie.jl) or [UnicodePlots.jl](https://github.com/JuliaPlots/UnicodePlots.jl).
@@ -43,6 +47,7 @@ IntervalMap (alias for TensorField{B, F, 1, P} where {B, F, P<:(AbstractArray{<:
 RectangleMap (alias for TensorField{B, F, 2, P} where {B, F, P<:(AbstractMatrix{<:Coordinate{P, G}} where {P<:(Chain{V, 1, <:Real} where V), G})})
 HyperrectangleMap (alias for TensorField{B, F, 3, P} where {B, F, P<:(AbstractArray{<:Coordinate{P, G}, 3} where {P<:(Chain{V, 1, <:Real} where V), G})})
 ParametricMap (alias for TensorField{B, F, N, P} where {B, F, N, P<:(AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})})
+Variation (alias for TensorField{B, F, N, P} where {B, F<:TensorField, N, P})
 RealFunction (alias for TensorField{B, F, 1, PA} where {B, F<:AbstractReal, PA<:(AbstractVector{<:AbstractReal})})
 PlaneCurve (alias for ParametricMap (alias for TensorField{B, F, N, P} where {B, F, N, P<:(AbstractArray{<:Coordinate{P, G}, N} where {N, P<:(Chain{V, 1, <:Real} where V), G})}))
 SpaceCurve (alias for TensorField{B, F, 1, P} where {B, F<:(Chain{V, G, Q, 3} where {V, G, Q}), P<:(AbstractVector{<:Coordinate{P, G}} where {P<:AbstractReal, G})})