Mercurial > repos > public > sbplib_julia
annotate src/Grids/manifolds.jl @ 1913:e97f4352b8d0 feature/grids/manifolds
Merge feature/grids/parameter_spaces
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Sat, 01 Feb 2025 23:20:31 +0100 |
| parents | 04c251bccbd4 |
| children | e7f8d11c4670 |
| rev | line source |
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| 1558 | 1 """ |
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2 Chart{D} |
| 1558 | 3 |
| 4 A parametrized description of a manifold or part of a manifold. | |
| 5 """ | |
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6 struct Chart{D, PST<:ParameterSpace{D}, MT} |
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7 mapping::MT |
| 1558 | 8 parameterspace::PST |
| 9 end | |
| 10 | |
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11 Base.ndims(::Chart{D}) where D = D |
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12 (c::Chart)(ξ) = c.mapping(ξ) |
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13 parameterspace(c::Chart) = c.parameterspace |
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14 |
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15 """ |
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16 jacobian(c::Chart, ξ) |
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18 The jacobian of the mapping evaluated at `ξ`. This defers to the |
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19 implementation of `jacobian` for the mapping itself. If no implementation is |
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20 available one can easily be specified for either the mapping function or the |
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21 chart itself. |
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22 ```julia |
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23 c = Chart(f, ps) |
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24 jacobian(f::typeof(f), ξ) = f′(ξ) |
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25 ``` |
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26 or |
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27 ```julia |
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28 c = Chart(f, ps) |
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29 jacobian(c::typeof(c),ξ) = f′(ξ) |
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30 ``` |
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31 which will both allow calling `jacobian(c,ξ)`. |
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32 """ |
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33 jacobian(c::Chart, ξ) = jacobian(c.mapping, ξ) |
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34 # TBD: Can we register a error hint for when jacobian is called with a function that doesn't have a registered jacobian? |
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35 |
| 1558 | 36 |
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37 # TBD: Should Charts, parameterspaces, Atlases, have boundary names? |
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38 |
| 1558 | 39 """ |
| 40 Atlas | |
| 41 | |
| 42 A collection of charts and their connections. | |
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43 Should implement methods for `charts` and `connections`. |
| 1558 | 44 """ |
| 45 abstract type Atlas end | |
| 46 | |
| 47 """ | |
| 48 charts(::Atlas) | |
| 49 | |
| 50 The colloction of charts in the atlas. | |
| 51 """ | |
| 52 function charts end | |
| 53 | |
| 54 """ | |
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55 connections(::Atlas) |
| 1558 | 56 |
| 57 TBD: What exactly should this return? | |
| 58 """ | |
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59 function connections end |
| 1558 | 60 |
| 61 struct CartesianAtlas <: Atlas | |
| 62 charts::Matrix{Chart} | |
| 63 end | |
| 64 | |
| 65 charts(a::CartesianAtlas) = a.charts | |
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66 connections(a::CartesianAtlas) = nothing |
| 1558 | 67 |
| 68 struct UnstructuredAtlas <: Atlas | |
| 69 charts::Vector{Chart} | |
| 70 connections | |
| 71 end | |
| 72 | |
| 73 charts(a::UnstructuredAtlas) = a.charts | |
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74 connections(a::UnstructuredAtlas) = nothing |
| 1558 | 75 |
| 76 | |
| 77 ### | |
| 78 # Geometry | |
| 79 ### | |
| 80 | |
| 81 abstract type Curve end | |
| 82 abstract type Surface end | |
| 83 | |
| 84 | |
| 85 struct Line{PT} <: Curve | |
| 86 p::PT | |
| 87 tangent::PT | |
| 88 end | |
| 89 | |
| 90 (c::Line)(s) = c.p + s*c.tangent | |
| 91 | |
| 92 | |
| 93 struct LineSegment{PT} <: Curve | |
| 94 a::PT | |
| 95 b::PT | |
| 96 end | |
| 97 | |
| 98 (c::LineSegment)(s) = (1-s)*c.a + s*c.b | |
| 99 | |
| 100 | |
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101 function linesegments(ps...) |
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102 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1] |
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103 end |
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104 |
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105 |
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106 function polygon_edges(ps...) |
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107 n = length(ps) |
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108 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)] |
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109 end |
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110 |
| 1558 | 111 struct Circle{T,PT} <: Curve |
| 112 c::PT | |
| 113 r::T | |
| 114 end | |
| 115 | |
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116 function (C::Circle)(θ) |
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117 (;c, r) = C |
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118 c + r*@SVector[cos(θ), sin(θ)] |
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119 end |
| 1558 | 120 |
| 121 struct TransfiniteInterpolationSurface{T1,T2,T3,T4} <: Surface | |
| 122 c₁::T1 | |
| 123 c₂::T2 | |
| 124 c₃::T3 | |
| 125 c₄::T4 | |
| 126 end | |
| 127 | |
| 128 function (s::TransfiniteInterpolationSurface)(u,v) | |
| 129 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄ | |
| 130 P₀₀ = c₁(0) | |
| 131 P₁₀ = c₂(0) | |
| 132 P₁₁ = c₃(0) | |
| 133 P₀₁ = c₄(0) | |
| 134 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - ( | |
| 135 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁ | |
| 136 ) | |
| 137 end | |
| 138 | |
| 139 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray) | |
| 140 s(ξ̄...) | |
| 141 end | |
| 142 | |
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143 # TODO: Implement jacobian() for the different mapping helpers |
| 1558 | 144 |