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annotate src/Grids/manifolds.jl @ 1576:a7245343eb98 feature/grids/manifolds
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| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 25 Apr 2024 21:52:22 +0200 |
| parents | bbb9065834ce |
| children | d5aa72662161 |
| rev | line source |
|---|---|
| 1558 | 1 """ |
| 2 ParameterSpace{D} | |
| 3 | |
| 4 A space of parameters of dimension `D`. Used with `Chart` to indicate which | |
| 5 parameters are valid for that chart. | |
| 6 | |
| 7 Common parameter spaces are created using the functions unit sized spaces | |
| 8 * `unitinterval` | |
| 9 * `unitrectangle` | |
| 10 * `unitbox` | |
| 11 * `unittriangle` | |
| 12 * `unittetrahedron` | |
| 13 * `unithyperbox` | |
| 14 * `unitsimplex` | |
| 15 | |
| 16 See also: [`Interval`](@ref), [`Rectangle`](@ref), [`Box`](@ref), | |
| 17 [`Triangle`](@ref), [`Tetrahedron`](@ref), [`HyperBox`](@ref), | |
| 18 [`Simplex`](@ref), | |
| 19 """ | |
| 20 abstract type ParameterSpace{D} end | |
| 21 | |
| 22 struct HyperBox{T,D} <: ParameterSpace{D} | |
| 23 a::SVector{D,T} | |
| 24 b::SVector{D,T} | |
| 25 end | |
| 26 | |
| 27 function HyperBox(a,b) | |
| 28 T = SVector{length(a)} | |
| 29 HyperBox(convert(T,a), convert(T,b)) | |
| 30 end | |
| 31 | |
| 32 Interval{T} = HyperBox{T,1} | |
| 33 Rectangle{T} = HyperBox{T,2} | |
| 34 Box{T} = HyperBox{T,3} | |
| 35 | |
| 36 limits(box::HyperBox, d) = (box.a[d], box.b[d]) | |
| 37 limits(box::HyperBox) = (box.a, box.b) | |
| 38 | |
| 39 unitinterval(T=Float64) = unithyperbox(T,1) | |
| 40 unitsquare(T=Float64) = unithyperbox(T,2) | |
| 41 unitcube(T=Float64) = unithyperbox(T,3) | |
| 42 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D))) | |
| 43 unithyperbox(D) = unithyperbox(Float64,D) | |
| 44 | |
| 45 | |
| 46 struct Simplex{T,D} <: ParameterSpace{D} | |
| 47 verticies::NTuple{D,SVector{D,T}} | |
| 48 end | |
| 49 | |
|
1564
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
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50 Simplex(verticies::Vararg{AbstractArray}) = Simplex(Tuple(SVector(v...) for v ∈ verticies)) |
|
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
|
51 |
| 1558 | 52 Triangle{T} = Simplex{T,2} |
| 53 Tetrahedron{T} = Simplex{T,3} | |
| 54 | |
| 55 unittriangle(T) = unitsimplex(T,2) | |
| 56 unittetrahedron(T) = unitsimplex(T,3) | |
| 57 function unitsimplex(T,D) | |
| 58 z = @SVector zeros(T,D) | |
| 59 unitelement = one(eltype(z)) | |
| 60 verticies = ntuple(i->setindex(z, unitelement, i), 4) | |
| 61 return Simplex(verticies) | |
| 62 end | |
| 63 | |
| 64 | |
| 65 """ | |
| 66 | |
| 67 A parametrized description of a manifold or part of a manifold. | |
| 68 | |
| 69 Should implement a methods for | |
| 70 * `parameterspace` | |
| 71 * `(::Chart)(ξs...)` | |
| 72 """ | |
| 73 abstract type Chart{D} end | |
| 74 # abstract type Chart{D,R} end | |
| 75 | |
| 76 domain_dim(::Chart{D}) where D = D | |
| 77 # range_dim(::Chart{D,R}) where {D,R} = R | |
| 78 | |
| 79 """ | |
| 80 The parameterspace of a chart | |
| 81 """ | |
| 82 function parameterspace end | |
| 83 | |
| 84 | |
| 1568 | 85 # TODO: Add trait for if there is a jacobian available? |
| 86 # Add package extension to allow calling the getter function anyway if it's not available | |
| 87 # And can we add an informative error that ForwardDiff could be loaded to make it work? | |
| 88 # Or can we handle this be custom implementations? For sometypes in the library it can be implemented explicitly. | |
| 89 # And as an example for ConcreteChart it can be implemented by the user like | |
| 90 # c = ConcreteChart(...) | |
| 91 # jacobian(c::typeof(c)) = ... | |
| 92 | |
|
1564
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
|
93 struct ConcreteChart{D, PST<:ParameterSpace{D}, MT} <: Chart{D} |
|
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
|
94 mapping::MT |
| 1558 | 95 parameterspace::PST |
| 96 end | |
| 97 | |
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157c43966b06
Add some tests and implement parameterspace for ConcreteChart
Jonatan Werpers <jonatan@werpers.com>
parents:
1568
diff
changeset
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98 (c::ConcreteChart)(x̄) = c.mapping(x̄) |
|
157c43966b06
Add some tests and implement parameterspace for ConcreteChart
Jonatan Werpers <jonatan@werpers.com>
parents:
1568
diff
changeset
|
99 parameterspace(c::ConcreteChart) = c.parameterspace |
| 1558 | 100 |
| 101 | |
| 102 """ | |
| 103 Atlas | |
| 104 | |
| 105 A collection of charts and their connections. | |
| 106 Should implement methods for `charts` and | |
| 107 """ | |
| 108 abstract type Atlas end | |
| 109 | |
| 110 """ | |
| 111 charts(::Atlas) | |
| 112 | |
| 113 The colloction of charts in the atlas. | |
| 114 """ | |
| 115 function charts end | |
| 116 | |
| 117 """ | |
| 118 connections | |
| 119 | |
| 120 TBD: What exactly should this return? | |
| 121 | |
| 122 """ | |
| 123 | |
| 124 struct CartesianAtlas <: Atlas | |
| 125 charts::Matrix{Chart} | |
| 126 end | |
| 127 | |
| 128 charts(a::CartesianAtlas) = a.charts | |
| 129 | |
| 130 struct UnstructuredAtlas <: Atlas | |
| 131 charts::Vector{Chart} | |
| 132 connections | |
| 133 end | |
| 134 | |
| 135 charts(a::UnstructuredAtlas) = a.charts | |
| 136 | |
| 137 | |
| 138 ### | |
| 139 # Geometry | |
| 140 ### | |
| 141 | |
| 142 abstract type Curve end | |
| 143 abstract type Surface end | |
| 144 | |
| 145 | |
| 146 struct Line{PT} <: Curve | |
| 147 p::PT | |
| 148 tangent::PT | |
| 149 end | |
| 150 | |
| 151 (c::Line)(s) = c.p + s*c.tangent | |
| 152 | |
| 153 | |
| 154 struct LineSegment{PT} <: Curve | |
| 155 a::PT | |
| 156 b::PT | |
| 157 end | |
| 158 | |
| 159 (c::LineSegment)(s) = (1-s)*c.a + s*c.b | |
| 160 | |
| 161 | |
| 162 struct Circle{T,PT} <: Curve | |
| 163 c::PT | |
| 164 r::T | |
| 165 end | |
| 166 | |
| 167 (c::Circle)(θ) = c.c + r*@SVector[cos(Θ), sin(Θ)] | |
| 168 | |
| 169 struct TransfiniteInterpolationSurface{T1,T2,T3,T4} <: Surface | |
| 170 c₁::T1 | |
| 171 c₂::T2 | |
| 172 c₃::T3 | |
| 173 c₄::T4 | |
| 174 end | |
| 175 | |
| 176 function (s::TransfiniteInterpolationSurface)(u,v) | |
| 177 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄ | |
| 178 P₀₀ = c₁(0) | |
| 179 P₁₀ = c₂(0) | |
| 180 P₁₁ = c₃(0) | |
| 181 P₀₁ = c₄(0) | |
| 182 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - ( | |
| 183 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁ | |
| 184 ) | |
| 185 end | |
| 186 | |
| 187 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray) | |
| 188 s(ξ̄...) | |
| 189 end | |
| 190 | |
| 191 | |
| 192 function polygon_sides(Ps...) | |
| 193 n = length(Ps) | |
| 194 return [t->line(t,Ps[i],Ps[mod1(i+1,n)]) for i ∈ eachindex(Ps)] | |
| 195 end |