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annotate src/Grids/geometry.jl @ 2011:d0b6c63c506e feature/grids/geometry_functions

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Add Arc type for representing partial circles
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 07 May 2025 08:38:35 +0200
parents 730c9848ad0b
children 4617e4b74b82
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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157
2011
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158 struct Arc{PT,T}
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159 c::Circle{PT,T}
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160 θ₀::T
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161 θ₁::T
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162 end
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163
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164 """
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165 Arc(C::Circle, θ₀, θ₁)
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166
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167 # TODO
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168 """
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169 function Arc(C, θ₀, θ₁)
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170 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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171
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172 return Arc(Circle(C.c, r), θ₀, θ₁)
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173 end
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174
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175 function (A::Arc)(t)
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176 (; θ₀, θ₁) = A
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177 return A.c((1-t)*θ₀ + t*θ₁)
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178 end
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179
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180 function Grids.jacobian(a::Arc, t)
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181 return nothing
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182 end
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183
1978
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184 """
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185 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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186
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187 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
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188 """
1916
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189 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
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190 c₁::T1
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191 c₂::T2
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192 c₃::T3
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193 c₄::T4
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194 end
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195
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196 function (s::TransfiniteInterpolationSurface)(u,v)
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197 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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198 P₀₀ = c₁(0)
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199 P₁₀ = c₂(0)
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200 P₁₁ = c₃(0)
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201 P₀₁ = c₄(0)
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202 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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203 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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204 )
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205 end
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206
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207 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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208 s(ξ̄...)
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209 end
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210
1978
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211 """
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212 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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213
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214 Throw an error if the ends of the curves in the transfinite interpolation do not match.
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215 """
1973
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216 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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217 if check_transfiniteinterpolation(Bool, s)
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218 return nothing
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219 else
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220 throw(ArgumentError("The end of each curve in the transfinite interpolation should be the same as the beginning of the next curve."))
1973
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221 end
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222 end
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223
1978
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224 """
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225 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
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226
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227 Return true if the ends of the curves in the transfinite interpolation match.
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228 """
1973
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229 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
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230 if !isapprox(s.c₁(1), s.c₂(0))
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231 return false
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232 end
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233
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234 if !isapprox(s.c₂(1), s.c₃(0))
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235 return false
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236 end
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237
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238 if !isapprox(s.c₃(1), s.c₄(0))
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239 return false
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240 end
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241
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242 if !isapprox(s.c₄(1), s.c₁(0))
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243 return false
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244 end
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245
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246 return true
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247 end
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248
1977
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249 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
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250 u, v = ξ̄
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251
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252 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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253 P₀₀ = c₁(0)
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254 P₁₀ = c₂(0)
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255 P₁₁ = c₃(0)
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256 P₀₁ = c₄(0)
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257
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258 ∂x̄∂ξ₁ = (1-v)*jacobian(c₁,u) + c₂(v) - v*jacobian(c₃,1-u) -c₄(1-v) - (
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259 -(1-v)*P₀₀ + (1-v)*P₁₀ + v*P₁₁ - v*P₀₁
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260 )
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261
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262 ∂x̄∂ξ₂ = -c₁(u) + u*jacobian(c₂,v) + c₃(1-u) - (1-u)*jacobian(c₄,1-v) - (
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263 -(1-u)*P₀₀ - u*P₁₀ + u*P₁₁ + (1-u)*P₀₁
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264 )
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265
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266 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
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267 end