--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Grids/parameter_space.jl	Sat Feb 01 22:12:53 2025 +0100
@@ -0,0 +1,88 @@
+"""
+    ParameterSpace{D}
+
+A space of parameters of dimension `D`. Used with `Chart` to indicate which
+parameters are valid for that chart.
+
+Common parameter spaces are created using the functions unit sized spaces
+* `unitinterval`
+* `unitrectangle`
+* `unitbox`
+* `unittriangle`
+* `unittetrahedron`
+* `unithyperbox`
+* `unitsimplex`
+
+See also: [`Interval`](@ref), [`Rectangle`](@ref), [`Box`](@ref),
+[`Triangle`](@ref), [`Tetrahedron`](@ref), [`HyperBox`](@ref),
+[`Simplex`](@ref),
+"""
+abstract type ParameterSpace{D} end
+Base.ndims(::ParameterSpace{D}) where D = D
+
+struct Interval{T} <: ParameterSpace{1}
+    a::T
+    b::T
+
+    function Interval(a,b)
+        a, b = promote(a, b)
+        new{typeof(a)}(a,b)
+    end
+end
+
+limits(i::Interval) = (i.a, i.b)
+
+unitinterval(T=Float64) = Interval(zero(T), one(T))
+
+
+struct HyperBox{T,D} <: ParameterSpace{D}
+    a::SVector{D,T}
+    b::SVector{D,T}
+end
+
+function HyperBox(a,b)
+    ET = promote_type(eltype(a),eltype(b))
+    T = SVector{length(a),ET}
+    HyperBox(convert(T,a), convert(T,b))
+end
+
+Rectangle{T} = HyperBox{T,2}
+Box{T} = HyperBox{T,3}
+
+limits(box::HyperBox, d) = (box.a[d], box.b[d])
+limits(box::HyperBox) = (box.a, box.b)
+
+unitsquare(T=Float64) = unithyperbox(T,2)
+unitcube(T=Float64) = unithyperbox(T,3)
+unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D)))
+unithyperbox(D) = unithyperbox(Float64,D)
+
+
+struct Simplex{T,D,NV} <: ParameterSpace{D}
+    verticies::NTuple{NV,SVector{D,T}}
+
+    Simplex(verticies::Tuple{SVector{D,T}, Vararg{SVector{D,T},N}}) where {T,D,N} = new{T,D,N+1}(verticies)
+    Simplex(::Tuple{}) = throw(ArgumentError("Must provide at least one vertex."))
+end
+
+function Simplex(verticies::Vararg{AbstractArray})
+    ET = mapreduce(eltype,promote_type,verticies)
+    T = SVector{length(verticies[1]),ET}
+
+    return Simplex(Tuple(convert(T,v) for v ∈ verticies))
+end
+
+verticies(s::Simplex) = s.verticies
+
+Triangle{T} = Simplex{T,2}
+Tetrahedron{T} = Simplex{T,3}
+
+unittriangle(T=Float64) = unitsimplex(T,2)
+unittetrahedron(T=Float64) = unitsimplex(T,3)
+function unitsimplex(T,D)
+    z = @SVector zeros(T,D)
+    unitelement = one(eltype(z))
+    verticies = ntuple(i->setindex(z, unitelement, i), D)
+    return Simplex((z,verticies...))
+end
+unitsimplex(D) = unitsimplex(Float64, D)