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annotate src/Grids/geometry.jl @ 2056:00b274a118e0 feature/grids/geometry_functions tip

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author Vidar Stiernström <vidar.stiernstrom@gmail.com>
date Thu, 12 Feb 2026 14:04:22 +0100
parents 6478c29effce
children
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 # REVIEW:
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10 # 1. Explain the parametrization, i.e., l(1) = p + s*t
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11 # 2. Now, if p and t are ints, l(1) returns an int
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12 # while l(0.5) returns a float. Is this intended/desirable?
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13 """
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14 Line(p,t)
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15
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16 A line, as a callable object, starting at `p` with tangent `t`.
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17
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18 # Example
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19 ```julia-repl
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20 julia> l = Grids.Line([1,1],[2,1])
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21 Diffinitive.Grids.Line{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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22
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23 julia> l(0)
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24 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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25 1
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26 1
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27
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28 julia> l(1)
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29 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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30 3
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31 2
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32 ```
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33
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34 See also: [`LineSegment`](@ref).
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35 """
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36 function Line(p, t)
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37 p = SVector{length(p)}(p)
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38 t = SVector{length(t)}(t)
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39 p, t = promote(p, t)
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40
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41 return Line{typeof(p)}(p,t)
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42 end
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43
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44 (c::Line)(s) = c.p + s*c.tangent
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45
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46 Grids.jacobian(l::Line, t) = l.tangent
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47
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48 struct LineSegment{PT}
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49 a::PT
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50 b::PT
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51
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52 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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53 end
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54
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55
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56 # REVIEW:
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57 # 1. Explain the parametrization.
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58 # 2. Now, if a and b are ints, l(1) returns an int
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59 # while l(0.5) returns a float. Is this intended/desirable?
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60 # 3. Do we want s in [0, 1]? Currently the line segment
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61 # can return values "outside" of the interval [a,b].
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62 """
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63 LineSegment(a,b)
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64
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65 A line segment, as a callable object, from `a` to `b`.
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66
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67 # Example
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68 ```julia-repl
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69 julia> l = Grids.LineSegment([1,1],[2,1])
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70 Diffinitive.Grids.LineSegment{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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71
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72 julia> l(0)
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73 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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74 1
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75 1
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76
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77 julia> l(0.5)
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78 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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79 1.5
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80 1.0
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81
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82 julia> l(1)
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83 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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84 2
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85 1
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86 ```
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87
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88 See also: [`Line`](@ref).
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89 """
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90 function LineSegment(a, b)
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91 a = SVector{length(a)}(a)
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92 b = SVector{length(b)}(b)
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93 a, b = promote(a, b)
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94
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95 return LineSegment{typeof(a)}(a,b)
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96 end
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97
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98 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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99
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100 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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101
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102
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103 """
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104 linesegments(ps...)
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105
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106 An array of line segments between the points `ps[1]`, `ps[2]`, and so on.
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107
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108 See also: [`polygon_edges`](@ref).
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109 """
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110 function linesegments(ps...)
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111 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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112 end
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114
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115 """
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116 polygon_edges(ps...)
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117
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118 An array of line segments between the points `ps[1]`, `ps[2]`, and so on
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119 including the segment between `ps[end]` and `ps[1]`.
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120
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121 See also: [`linesegments`](@ref).
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122 """
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123 function polygon_edges(ps...)
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124 n = length(ps)
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125 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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126 end
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127
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128
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129 struct Circle{PT,T}
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130 c::PT
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131 r::T
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132
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133 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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134 end
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135
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136 """
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137 Circle(c,r)
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138
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139 A circle with center `c` and radius `r` paramatrized with the angle to the x-axis.
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140
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141 # Example
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142 ```julia-repl
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143 julia> c = Grids.Circle([1,1], 2)
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144 Diffinitive.Grids.Circle{StaticArraysCore.SVector{2, Int64}, Int64}([1, 1], 2)
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145
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146 julia> c(0)
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147 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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148 3.0
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149 1.0
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150
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151 julia> c(π/2)
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152 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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153 1.0000000000000002
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154 3.0
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155 ```
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156 """
1969
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157 function Circle(c,r)
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158 c = SVector{2}(c)
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159 return Circle{typeof(c), typeof(r)}(c,r)
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160 end
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161
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162 function (C::Circle)(θ)
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163 (;c, r) = C
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164 c + r*@SVector[cos(θ), sin(θ)]
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165 end
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166
1976
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167 function Grids.jacobian(C::Circle, θ)
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168 (;r) = C
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169 r*@SVector[-sin(θ), cos(θ)]
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170 end
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171
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172
2011
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173 struct Arc{PT,T}
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174 c::Circle{PT,T}
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175 θ₀::T
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176 θ₁::T
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177 end
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178
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179 """
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180 Arc(C::Circle, θ₀, θ₁)
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181
2014
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182 A circular arc as a callable object. The arc is around the circle `C` between
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183 angles `θ₀` and `θ₁` and is paramatrized between 0 and 1.
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184
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185 See also: [`arc`](@ref), [`Circle`](@ref).
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186 """
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187 function Arc(C, θ₀, θ₁)
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188 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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189
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190 return Arc(Circle(C.c, r), θ₀, θ₁)
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191 end
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192
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193 function (A::Arc)(t)
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194 (; θ₀, θ₁) = A
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195 return A.c((1-t)*θ₀ + t*θ₁)
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196 end
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197
2013
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198 function Grids.jacobian(A::Arc, t)
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199 (;c, θ₀, θ₁) = A
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200 return (θ₁-θ₀)*jacobian(c, t)
2011
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201 end
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202
2012
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203
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204 """
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205 arc(a,b,r)
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206
2014
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207 A circular arc between the points `a` and `b` with radius `abs(r)`. If `r > 0`
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208 the arc goes counter clockwise and if `r<0` the arc goes clockwise. The arc is
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209 parametrized such that if `A = arc(a,b,r)` then `A(0)` corresponds to `a` and
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210 `A(1)` to `b`.
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211
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212 See also: [`Arc`](@ref), [`Circle`](@ref).
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213 """
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214 function arc(a,b,r)
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215 if abs(r) < norm(b-a)/2
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216 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
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217 end
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218
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219 R̂ = @SMatrix[0 -1; 1 0]
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220
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221 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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222 t̂ = R̂*(b-a)/norm(b-a)
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223
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224 c = (a+b)/2 + α*t̂
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225
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226 ca = a-c
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227 cb = b-c
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228 θₐ = atan(ca[2],ca[1])
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229 θᵦ = atan(cb[2],cb[1])
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230
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231 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
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232
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233 if r > 0
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234 Δθ = abs(Δθ)
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235 else
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236 Δθ = -abs(Δθ)
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237 end
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238
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239 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
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240 end
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241
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242 # REVIEW:
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243 # 1. Explain parametrisation
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244 # 2. Boundscheck for the parametrisation argumetns, i.e. within [0,1]?
1978
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245 """
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246 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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247
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248 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
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249 """
1916
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diff changeset
250 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
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251 c₁::T1
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252 c₂::T2
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253 c₃::T3
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254 c₄::T4
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255 end
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256
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257 function (s::TransfiniteInterpolationSurface)(u,v)
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258 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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259 P₀₀ = c₁(0)
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260 P₁₀ = c₂(0)
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261 P₁₁ = c₃(0)
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262 P₀₁ = c₄(0)
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263 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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264 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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265 )
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266 end
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267
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268 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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269 s(ξ̄...)
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270 end
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271
1978
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272 """
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273 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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274
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275 Throw an error if the ends of the curves in the transfinite interpolation do not match.
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276 """
1973
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diff changeset
277 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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diff changeset
278 if check_transfiniteinterpolation(Bool, s)
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279 return nothing
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280 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
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diff changeset
281 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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diff changeset
282 end
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diff changeset
283 end
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284
1978
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285 """
1983
730c9848ad0b Update docstring for check_transfiniteinterpolation
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parents: 1982
diff changeset
286 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
1978
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diff changeset
287
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288 Return true if the ends of the curves in the transfinite interpolation match.
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289 """
1973
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diff changeset
290 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
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diff changeset
291 if !isapprox(s.c₁(1), s.c₂(0))
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diff changeset
292 return false
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diff changeset
293 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
294
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diff changeset
295 if !isapprox(s.c₂(1), s.c₃(0))
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diff changeset
296 return false
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diff changeset
297 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
298
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299 if !isapprox(s.c₃(1), s.c₄(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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300 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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301 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
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302
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
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303 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
304 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
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305 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
306
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
307 return true
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
308 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
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309
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
310 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
311 u, v = ξ̄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
312
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
313 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
314 P₀₀ = c₁(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
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315 P₁₀ = c₂(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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316 P₁₁ = c₃(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
317 P₀₁ = c₄(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
318
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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319 ∂x̄∂ξ₁ = (1-v)*jacobian(c₁,u) + c₂(v) - v*jacobian(c₃,1-u) -c₄(1-v) - (
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
320 -(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
321 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
322
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
323 ∂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
324 -(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
325 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
326
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
327 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
328 end