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annotate src/Grids/geometry.jl @ 2013:7895b509f9bf feature/grids/geometry_functions

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Implement Grids.jacobian for Arc
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 07 May 2025 15:25:25 +0200
parents 4617e4b74b82
children 6478c29effce
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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 """
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9 Line(p,t)
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10
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11 A line, as a callable object, starting at `p` with tangent `t`.
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12
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13 # Example
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14 ```julia-repl
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15 julia> l = Grids.Line([1,1],[2,1])
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16 Diffinitive.Grids.Line{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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17
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18 julia> l(0)
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19 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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20 1
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21 1
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22
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23 julia> l(1)
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24 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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25 3
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26 2
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27 ```
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28
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29 See also: [`LineSegment`](@ref).
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30 """
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31 function Line(p, t)
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32 p = SVector{length(p)}(p)
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33 t = SVector{length(t)}(t)
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34 p, t = promote(p, t)
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35
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36 return Line{typeof(p)}(p,t)
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37 end
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38
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39 (c::Line)(s) = c.p + s*c.tangent
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40
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41 Grids.jacobian(l::Line, t) = l.tangent
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42
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43 struct LineSegment{PT}
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44 a::PT
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45 b::PT
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46
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47 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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48 end
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49
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50 """
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51 LineSegment(a,b)
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52
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53 A line segment, as a callable object, from `a` to `b`.
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54
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55 # Example
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56 ```julia-repl
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57 julia> l = Grids.LineSegment([1,1],[2,1])
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58 Diffinitive.Grids.LineSegment{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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59
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60 julia> l(0)
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61 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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62 1
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63 1
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64
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65 julia> l(0.5)
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66 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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67 1.5
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68 1.0
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69
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70 julia> l(1)
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71 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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72 2
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73 1
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74 ```
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75
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76 See also: [`Line`](@ref).
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77 """
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78 function LineSegment(a, b)
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79 a = SVector{length(a)}(a)
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80 b = SVector{length(b)}(b)
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81 a, b = promote(a, b)
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82
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83 return LineSegment{typeof(a)}(a,b)
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84 end
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85
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86 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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87
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88 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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89
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90 """
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91 linesegments(ps...)
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92
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93 An array of line segments between the points `ps[1]`, `ps[2]`, and so on.
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94
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95 See also: [`polygon_edges`](@ref).
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96 """
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97 function linesegments(ps...)
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98 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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99 end
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100
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101
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102 """
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103 polygon_edges(ps...)
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104
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105 An array of line segments between the points `ps[1]`, `ps[2]`, and so on
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106 including the segment between `ps[end]` and `ps[1]`.
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107
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108 See also: [`linesegments`](@ref).
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109 """
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110 function polygon_edges(ps...)
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111 n = length(ps)
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112 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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113 end
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114
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115 struct Circle{PT,T}
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116 c::PT
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117 r::T
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118
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119 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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120 end
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121
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122 """
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123 Circle(c,r)
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124
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125 A circle with center `c` and radius `r` paramatrized with the angle to the x-axis.
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126
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127 # Example
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128 ```julia-repl
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129 julia> c = Grids.Circle([1,1], 2)
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130 Diffinitive.Grids.Circle{StaticArraysCore.SVector{2, Int64}, Int64}([1, 1], 2)
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131
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132 julia> c(0)
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133 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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134 3.0
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135 1.0
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136
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137 julia> c(π/2)
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138 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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139 1.0000000000000002
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140 3.0
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141 ```
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142 """
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143 function Circle(c,r)
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144 c = SVector{2}(c)
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145 return Circle{typeof(c), typeof(r)}(c,r)
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146 end
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147
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148 function (C::Circle)(θ)
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149 (;c, r) = C
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150 c + r*@SVector[cos(θ), sin(θ)]
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151 end
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152
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153 function Grids.jacobian(C::Circle, θ)
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154 (;r) = C
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155 r*@SVector[-sin(θ), cos(θ)]
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156 end
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Jonatan Werpers <jonatan@werpers.com>
parents: 1975
diff changeset
157
2011
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
158 struct Arc{PT,T}
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Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
159 c::Circle{PT,T}
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diff changeset
160 θ₀::T
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
161 θ₁::T
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
162 end
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
163
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
164 """
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
165 Arc(C::Circle, θ₀, θ₁)
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
166
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
167 # TODO
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
168 """
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
169 function Arc(C, θ₀, θ₁)
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parents: 1983
diff changeset
170 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
d0b6c63c506e Add Arc type for representing partial circles
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diff changeset
171
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diff changeset
172 return Arc(Circle(C.c, r), θ₀, θ₁)
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
173 end
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
174
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
175 function (A::Arc)(t)
d0b6c63c506e Add Arc type for representing partial circles
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diff changeset
176 (; θ₀, θ₁) = A
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diff changeset
177 return A.c((1-t)*θ₀ + t*θ₁)
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
178 end
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
179
2013
7895b509f9bf Implement Grids.jacobian for Arc
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parents: 2012
diff changeset
180 function Grids.jacobian(A::Arc, t)
7895b509f9bf Implement Grids.jacobian for Arc
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diff changeset
181 (;c, θ₀, θ₁) = A
7895b509f9bf Implement Grids.jacobian for Arc
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diff changeset
182 return (θ₁-θ₀)*jacobian(c, t)
2011
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
183 end
d0b6c63c506e Add Arc type for representing partial circles
Jonatan Werpers <jonatan@werpers.com>
parents: 1983
diff changeset
184
2012
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
185
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
186 """
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
187 arc(a,b,r)
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diff changeset
188
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
189 # TODO
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
190 """
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
191 function arc(a,b,r)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
192 if abs(r) < norm(b-a)/2
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diff changeset
193 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
194 end
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
195
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
196 R̂ = @SMatrix[0 -1; 1 0]
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diff changeset
197
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
198 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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diff changeset
199 t̂ = R̂*(b-a)/norm(b-a)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
200
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
201 c = (a+b)/2 + α*t̂
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parents: 2011
diff changeset
202
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
203 ca = a-c
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diff changeset
204 cb = b-c
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parents: 2011
diff changeset
205 θₐ = atan(ca[2],ca[1])
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diff changeset
206 θᵦ = atan(cb[2],cb[1])
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
207
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
208 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
209
4617e4b74b82 Add arc() for constructing circle arcs between two points
Jonatan Werpers <jonatan@werpers.com>
parents: 2011
diff changeset
210 if r > 0
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
211 Δθ = abs(Δθ)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
212 else
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
213 Δθ = -abs(Δθ)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
214 end
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
215
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
216 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
217 end
4617e4b74b82 Add arc() for constructing circle arcs between two points
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parents: 2011
diff changeset
218
1978
d7a5129517d9 Add docstrings
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diff changeset
219 """
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diff changeset
220 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
d7a5129517d9 Add docstrings
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diff changeset
221
d7a5129517d9 Add docstrings
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diff changeset
222 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
d7a5129517d9 Add docstrings
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diff changeset
223 """
1916
6859089b361e Remove abstract types for Curve and surface
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parents: 1915
diff changeset
224 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
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225 c₁::T1
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parents:
diff changeset
226 c₂::T2
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227 c₃::T3
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parents:
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228 c₄::T4
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parents:
diff changeset
229 end
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parents:
diff changeset
230
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
diff changeset
231 function (s::TransfiniteInterpolationSurface)(u,v)
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parents:
diff changeset
232 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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233 P₀₀ = c₁(0)
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parents:
diff changeset
234 P₁₀ = c₂(0)
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parents:
diff changeset
235 P₁₁ = c₃(0)
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parents:
diff changeset
236 P₀₁ = c₄(0)
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parents:
diff changeset
237 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
diff changeset
238 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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parents:
diff changeset
239 )
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
diff changeset
240 end
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
diff changeset
241
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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parents:
diff changeset
242 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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parents:
diff changeset
243 s(ξ̄...)
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parents:
diff changeset
244 end
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parents:
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245
1978
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
246 """
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
247 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
248
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
249 Throw an error if the ends of the curves in the transfinite interpolation do not match.
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
250 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
251 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
252 if check_transfiniteinterpolation(Bool, s)
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
253 return nothing
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
254 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
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parents: 1979
diff changeset
255 throw(ArgumentError("The end of each curve in the transfinite interpolation should be the same as the beginning of the next curve."))
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
256 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
257 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
258
1978
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
259 """
1983
730c9848ad0b Update docstring for check_transfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1982
diff changeset
260 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
1978
d7a5129517d9 Add docstrings
Jonatan Werpers <jonatan@werpers.com>
parents: 1977
diff changeset
261
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
262 Return true if the ends of the curves in the transfinite interpolation match.
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
263 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
264 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
265 if !isapprox(s.c₁(1), s.c₂(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
266 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
267 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
268
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
269 if !isapprox(s.c₂(1), s.c₃(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
270 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
271 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
272
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
273 if !isapprox(s.c₃(1), s.c₄(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
274 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
275 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
276
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
277 if !isapprox(s.c₄(1), s.c₁(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
278 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
279 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
280
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
281 return true
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
282 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
283
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
284 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
285 u, v = ξ̄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
286
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
287 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
288 P₀₀ = c₁(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
289 P₁₀ = c₂(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
290 P₁₁ = c₃(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
291 P₀₁ = c₄(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
292
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
293 ∂x̄∂ξ₁ = (1-v)*jacobian(c₁,u) + c₂(v) - v*jacobian(c₃,1-u) -c₄(1-v) - (
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
294 -(1-v)*P₀₀ + (1-v)*P₁₀ + v*P₁₁ - v*P₀₁
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
295 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
296
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
297 ∂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
298 -(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
299 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
300
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
301 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
302 end