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annotate src/Grids/geometry.jl @ 1977:270675bb97be feature/grids/geometry_functions

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Implement Grids.jacobian for TransfiniteInterpolationSurface
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 25 Feb 2025 23:33:56 +0100
parents 34a7e3919e9a
children d7a5129517d9
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1 struct Line{PT}
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2 p::PT
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3 tangent::PT
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4
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5 Line{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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6 end
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7
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8 function Line(p, t)
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9 p = SVector{length(p)}(p)
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10 t = SVector{length(t)}(t)
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11 p, t = promote(p, t)
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12
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13 return Line{typeof(p)}(p,t)
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14 end
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15
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16 (c::Line)(s) = c.p + s*c.tangent
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17
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18 Grids.jacobian(l::Line, t) = l.tangent
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19
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20 struct LineSegment{PT}
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21 a::PT
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22 b::PT
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23
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24 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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25 end
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26
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27 function LineSegment(a, b)
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28 a = SVector{length(a)}(a)
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29 b = SVector{length(b)}(b)
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30 a, b = promote(a, b)
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31
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32 return LineSegment{typeof(a)}(a,b)
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33 end
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34
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35 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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36
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37 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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38
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39 function linesegments(ps...)
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40 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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41 end
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42
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43
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44 function polygon_edges(ps...)
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45 n = length(ps)
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46 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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47 end
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48
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49 struct Circle{PT,T}
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50 c::PT
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51 r::T
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52
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53 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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54 end
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55
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56 function Circle(c,r)
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57 c = SVector{2}(c)
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58 return Circle{typeof(c), typeof(r)}(c,r)
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59 end
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60
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61 function (C::Circle)(θ)
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62 (;c, r) = C
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63 c + r*@SVector[cos(θ), sin(θ)]
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64 end
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65
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66 function Grids.jacobian(C::Circle, θ)
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67 (;r) = C
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68 r*@SVector[-sin(θ), cos(θ)]
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69 end
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70
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71 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
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72 c₁::T1
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73 c₂::T2
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74 c₃::T3
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75 c₄::T4
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76 end
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77
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78 function (s::TransfiniteInterpolationSurface)(u,v)
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79 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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80 P₀₀ = c₁(0)
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81 P₁₀ = c₂(0)
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82 P₁₁ = c₃(0)
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83 P₀₁ = c₄(0)
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84 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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85 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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86 )
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87 end
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88
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89 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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90 s(ξ̄...)
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91 end
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92
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93 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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94 if check_transfiniteinterpolation(Bool, s)
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95 return nothing
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96 else
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97 error("The end of each curve in the transfinite interpolation should be the same as the beginning of the next curve.")
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98 end
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99 end
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100
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101 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
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102 if !isapprox(s.c₁(1), s.c₂(0))
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103 return false
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104 end
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105
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106 if !isapprox(s.c₂(1), s.c₃(0))
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107 return false
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108 end
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109
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110 if !isapprox(s.c₃(1), s.c₄(0))
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111 return false
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112 end
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113
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114 if !isapprox(s.c₄(1), s.c₁(0))
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115 return false
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116 end
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117
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118 return true
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119 end
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120
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121 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
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122 u, v = ξ̄
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123
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124 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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125 P₀₀ = c₁(0)
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126 P₁₀ = c₂(0)
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127 P₁₁ = c₃(0)
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128 P₀₁ = c₄(0)
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129
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130 ∂x̄∂ξ₁ = (1-v)*jacobian(c₁,u) + c₂(v) - v*jacobian(c₃,1-u) -c₄(1-v) - (
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131 -(1-v)*P₀₀ + (1-v)*P₁₀ + v*P₁₁ - v*P₀₁
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132 )
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133
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134
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135 (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
136 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
137 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
138
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
139
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
140 ∂x̄∂ξ₂ = -c₁(u) + u*jacobian(c₂,v) + c₃(1-u) - (1-u)*jacobian(c₄,1-v) - (
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
141 -(1-u)*P₀₀ - u*P₁₀ + u*P₁₁ + (1-u)*P₀₁
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
142 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
143
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
144 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
145 end
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
146
1915
c003685d9926 Add geometry functions removed from feature/grids/manifolds
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
147 # TODO: Implement jacobian() for the different mapping helpers
1971
9e89084cbba4 Add some todos
Jonatan Werpers <jonatan@werpers.com>
parents: 1970
diff changeset
148 # TODO: Add doc strings