Mercurial > repos > public > sbplib_julia
annotate src/Grids/manifolds.jl @ 1625:84c3b9d71218 feature/grids/manifolds
Add linesegments function
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Fri, 14 Jun 2024 13:09:00 +0200 |
| parents | f77c5309dd2b |
| children | e213bd857f3f |
| 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 | |
|
1580
fdee60ab8c4e
Add ndims method for ParameterSpace
Jonatan Werpers <jonatan@werpers.com>
parents:
1579
diff
changeset
|
21 Base.ndims(::ParameterSpace{D}) where D = D |
| 1558 | 22 |
| 23 struct HyperBox{T,D} <: ParameterSpace{D} | |
| 24 a::SVector{D,T} | |
| 25 b::SVector{D,T} | |
| 26 end | |
| 27 | |
| 28 function HyperBox(a,b) | |
| 29 T = SVector{length(a)} | |
| 30 HyperBox(convert(T,a), convert(T,b)) | |
| 31 end | |
| 32 | |
| 33 Interval{T} = HyperBox{T,1} | |
| 34 Rectangle{T} = HyperBox{T,2} | |
| 35 Box{T} = HyperBox{T,3} | |
| 36 | |
| 37 limits(box::HyperBox, d) = (box.a[d], box.b[d]) | |
| 38 limits(box::HyperBox) = (box.a, box.b) | |
| 39 | |
| 40 unitinterval(T=Float64) = unithyperbox(T,1) | |
| 41 unitsquare(T=Float64) = unithyperbox(T,2) | |
| 42 unitcube(T=Float64) = unithyperbox(T,3) | |
| 43 unithyperbox(T, D) = HyperBox((@SVector zeros(T,D)), (@SVector ones(T,D))) | |
| 44 unithyperbox(D) = unithyperbox(Float64,D) | |
| 45 | |
| 46 | |
|
1579
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
47 struct Simplex{T,D,NV} <: ParameterSpace{D} |
|
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
48 verticies::NTuple{NV,SVector{D,T}} |
| 1558 | 49 end |
| 50 | |
|
1564
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
|
51 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
|
52 |
|
1579
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
53 verticies(s::Simplex) = s.verticies |
|
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
54 |
| 1558 | 55 Triangle{T} = Simplex{T,2} |
| 56 Tetrahedron{T} = Simplex{T,3} | |
| 57 | |
|
1579
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
58 unittriangle(T=Float64) = unitsimplex(T,2) |
|
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
59 unittetrahedron(T=Float64) = unitsimplex(T,3) |
| 1558 | 60 function unitsimplex(T,D) |
| 61 z = @SVector zeros(T,D) | |
| 62 unitelement = one(eltype(z)) | |
|
1579
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
63 verticies = ntuple(i->setindex(z, unitelement, i), D) |
|
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
64 return Simplex((z,verticies...)) |
| 1558 | 65 end |
|
1579
14d79b13b54f
Add tests, fix bugs, add exports, for Simplex and friends
Jonatan Werpers <jonatan@werpers.com>
parents:
1578
diff
changeset
|
66 unitsimplex(D) = unitsimplex(Float64, D) |
| 1558 | 67 |
| 68 """ | |
|
1581
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
69 Chart{D} |
| 1558 | 70 |
| 71 A parametrized description of a manifold or part of a manifold. | |
| 72 """ | |
|
1581
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
73 struct Chart{D, PST<:ParameterSpace{D}, MT} |
|
1564
35fe4375b35f
Export things and fix ConcreteChart and Simplex
Jonatan Werpers <jonatan@werpers.com>
parents:
1558
diff
changeset
|
74 mapping::MT |
| 1558 | 75 parameterspace::PST |
| 76 end | |
| 77 | |
|
1581
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
78 domain_dim(::Chart{D}) where D = D |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
79 (c::Chart)(ξ) = c.mapping(ξ) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
80 parameterspace(c::Chart) = c.parameterspace |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
81 |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
82 """ |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
83 jacobian(c::Chart, ξ) |
| 1558 | 84 |
|
1581
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
85 The jacobian of the mapping evaluated at `ξ`. This defers to the |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
86 implementation of `jacobian` for the mapping itself. If no implementation is |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
87 available one can easily be specified for either the mapping function or the |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
88 chart itself. |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
89 ```julia |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
90 c = Chart(f, ps) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
91 jacobian(f::typeof(f), ξ) = f′(ξ) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
92 ``` |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
93 or |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
94 ```julia |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
95 c = Chart(f, ps) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
96 jacobian(c::typeof(c),ξ) = f′(ξ) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
97 ``` |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
98 which will both allow calling `jacobian(c,ξ)`. |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
99 """ |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
100 jacobian(c::Chart, ξ) = jacobian(c.mapping, ξ) |
|
f77c5309dd2b
Rename ConcreteChart to Chart and remove the abstarct chart type
Jonatan Werpers <jonatan@werpers.com>
parents:
1580
diff
changeset
|
101 |
| 1558 | 102 |
| 103 """ | |
| 104 Atlas | |
| 105 | |
| 106 A collection of charts and their connections. | |
| 107 Should implement methods for `charts` and | |
| 108 """ | |
| 109 abstract type Atlas end | |
| 110 | |
| 111 """ | |
| 112 charts(::Atlas) | |
| 113 | |
| 114 The colloction of charts in the atlas. | |
| 115 """ | |
| 116 function charts end | |
| 117 | |
| 118 """ | |
| 119 connections | |
| 120 | |
| 121 TBD: What exactly should this return? | |
| 122 | |
| 123 """ | |
| 124 | |
| 125 struct CartesianAtlas <: Atlas | |
| 126 charts::Matrix{Chart} | |
| 127 end | |
| 128 | |
| 129 charts(a::CartesianAtlas) = a.charts | |
| 130 | |
| 131 struct UnstructuredAtlas <: Atlas | |
| 132 charts::Vector{Chart} | |
| 133 connections | |
| 134 end | |
| 135 | |
| 136 charts(a::UnstructuredAtlas) = a.charts | |
| 137 | |
| 138 | |
| 139 ### | |
| 140 # Geometry | |
| 141 ### | |
| 142 | |
| 143 abstract type Curve end | |
| 144 abstract type Surface end | |
| 145 | |
| 146 | |
| 147 struct Line{PT} <: Curve | |
| 148 p::PT | |
| 149 tangent::PT | |
| 150 end | |
| 151 | |
| 152 (c::Line)(s) = c.p + s*c.tangent | |
| 153 | |
| 154 | |
| 155 struct LineSegment{PT} <: Curve | |
| 156 a::PT | |
| 157 b::PT | |
| 158 end | |
| 159 | |
| 160 (c::LineSegment)(s) = (1-s)*c.a + s*c.b | |
| 161 | |
| 162 | |
|
1625
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
163 function linesegments(ps...) |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
164 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1] |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
165 end |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
166 |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
167 |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
168 function polygon_edges(ps...) |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
169 n = length(ps) |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
170 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(Ps)] |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
171 end |
|
84c3b9d71218
Add linesegments function
Jonatan Werpers <jonatan@werpers.com>
parents:
1581
diff
changeset
|
172 |
| 1558 | 173 struct Circle{T,PT} <: Curve |
| 174 c::PT | |
| 175 r::T | |
| 176 end | |
| 177 | |
| 178 (c::Circle)(θ) = c.c + r*@SVector[cos(Θ), sin(Θ)] | |
| 179 | |
| 180 struct TransfiniteInterpolationSurface{T1,T2,T3,T4} <: Surface | |
| 181 c₁::T1 | |
| 182 c₂::T2 | |
| 183 c₃::T3 | |
| 184 c₄::T4 | |
| 185 end | |
| 186 | |
| 187 function (s::TransfiniteInterpolationSurface)(u,v) | |
| 188 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄ | |
| 189 P₀₀ = c₁(0) | |
| 190 P₁₀ = c₂(0) | |
| 191 P₁₁ = c₃(0) | |
| 192 P₀₁ = c₄(0) | |
| 193 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - ( | |
| 194 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁ | |
| 195 ) | |
| 196 end | |
| 197 | |
| 198 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray) | |
| 199 s(ξ̄...) | |
| 200 end | |
| 201 | |
| 202 |