Mercurial > repos > public > sbplib_julia

annotate src/Grids/geometry.jl @ 2073:bc09d0bfac65 feature/grids/geometry_functions tip

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Remove resolved review comment
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 17 Feb 2026 20:40:53 +0100
parents c36812de3f2d
children
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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 """
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10 Line(p,t)
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11
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12 A line, as a callable object, starting at `p` with tangent `t`.
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13 The parametrization is ``l(s) = p + st``.
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14
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15 # Example
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16 ```julia-repl
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17 julia> l = Grids.Line([1,1],[2,1])
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18 Diffinitive.Grids.Line{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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19
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20 julia> l(0)
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21 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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22 1
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23 1
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24
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25 julia> l(1)
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26 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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27 3
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28 2
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29 ```
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30
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31 See also: [`LineSegment`](@ref).
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32 """
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33 function Line(p, t)
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34 p = SVector{length(p)}(p)
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35 t = SVector{length(t)}(t)
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36 p, t = promote(p, t)
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37
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38 return Line{typeof(p)}(p,t)
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39 end
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40
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41 (c::Line)(s) = c.p + s*c.tangent
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42
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43 Grids.jacobian(l::Line, t) = l.tangent
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44
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45 struct LineSegment{PT}
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46 a::PT
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47 b::PT
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48
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49 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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50 end
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51
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52
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53 """
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54 LineSegment(a,b)
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55
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56 A line segment, as a callable object, from `a` to `b`.
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57 The parametrization is ``l(s) = (1-s)a + s*b`` where ``s∈(0,1)``.
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58
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59 # Example
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60 ```julia-repl
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61 julia> l = Grids.LineSegment([1,1],[2,1])
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62 Diffinitive.Grids.LineSegment{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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63
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64 julia> l(0)
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65 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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66 1
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67 1
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68
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69 julia> l(0.5)
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70 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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71 1.5
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72 1.0
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73
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74 julia> l(1)
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75 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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76 2
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77 1
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78 ```
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79
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80 See also: [`Line`](@ref).
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81 """
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82 function LineSegment(a, b)
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83 a = SVector{length(a)}(a)
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84 b = SVector{length(b)}(b)
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85 a, b = promote(a, b)
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86
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87 return LineSegment{typeof(a)}(a,b)
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88 end
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89
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90 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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91
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92 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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93
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94
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95 """
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96 linesegments(ps...)
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97
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98 An array of line segments between the points `ps[1]`, `ps[2]`, and so on.
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99
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100 See also: [`polygon_edges`](@ref).
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101 """
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102 function linesegments(ps...)
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103 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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104 end
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105
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106
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107 """
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108 polygon_edges(ps...)
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109
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110 An array of line segments between the points `ps[1]`, `ps[2]`, and so on
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111 including the segment between `ps[end]` and `ps[1]`.
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112
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113 See also: [`linesegments`](@ref).
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114 """
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115 function polygon_edges(ps...)
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116 n = length(ps)
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117 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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118 end
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119
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120
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121 struct Circle{PT,T}
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122 c::PT
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123 r::T
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124
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125 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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126 end
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127
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128 """
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129 Circle(c,r)
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130
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131 A circle with center `c` and radius `r` paramatrized with the angle to the x-axis.
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132
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133 # Example
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134 ```julia-repl
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135 julia> c = Grids.Circle([1,1], 2)
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136 Diffinitive.Grids.Circle{StaticArraysCore.SVector{2, Int64}, Int64}([1, 1], 2)
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137
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138 julia> c(0)
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139 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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140 3.0
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141 1.0
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142
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143 julia> c(π/2)
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144 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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145 1.0000000000000002
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146 3.0
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147 ```
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148 """
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149 function Circle(c,r)
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150 c = SVector{2}(c)
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151 return Circle{typeof(c), typeof(r)}(c,r)
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152 end
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153
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154 function (C::Circle)(θ)
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155 (;c, r) = C
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156 c + r*@SVector[cos(θ), sin(θ)]
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157 end
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158
1976
34a7e3919e9a Implement Grids.jacobian for Circle
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diff changeset
159 function Grids.jacobian(C::Circle, θ)
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diff changeset
160 (;r) = C
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parents: 1975
diff changeset
161 r*@SVector[-sin(θ), cos(θ)]
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parents: 1975
diff changeset
162 end
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diff changeset
163
2056
00b274a118e0 Add review comments
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164
2011
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diff changeset
165 struct Arc{PT,T}
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diff changeset
166 c::Circle{PT,T}
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diff changeset
167 θ₀::T
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168 θ₁::T
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169 end
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170
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171 """
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172 Arc(C::Circle, θ₀, θ₁)
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173
2014
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174 A circular arc as a callable object. The arc is around the circle `C` between
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175 angles `θ₀` and `θ₁` and is paramatrized between 0 and 1.
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176
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177 See also: [`arc`](@ref), [`Circle`](@ref).
2011
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178 """
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179 function Arc(C, θ₀, θ₁)
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180 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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181
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182 return Arc(Circle(C.c, r), θ₀, θ₁)
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183 end
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184
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185 function (A::Arc)(t)
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186 (; θ₀, θ₁) = A
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187 return A.c((1-t)*θ₀ + t*θ₁)
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188 end
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189
2013
7895b509f9bf Implement Grids.jacobian for Arc
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190 function Grids.jacobian(A::Arc, t)
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191 (;c, θ₀, θ₁) = A
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192 return (θ₁-θ₀)*jacobian(c, t)
2011
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193 end
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194
2012
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195
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196 """
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197 arc(a,b,r)
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198
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199 A circular arc between the points `a` and `b` with radius `abs(r)`. If `r > 0`
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200 the arc goes counter clockwise and if `r<0` the arc goes clockwise. The arc is
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diff changeset
201 parametrized such that if `A = arc(a,b,r)` then `A(0)` corresponds to `a` and
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202 `A(1)` to `b`.
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203
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diff changeset
204 See also: [`Arc`](@ref), [`Circle`](@ref).
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205 """
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206 function arc(a,b,r)
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diff changeset
207 if abs(r) < norm(b-a)/2
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208 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
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209 end
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210
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diff changeset
211 R̂ = @SMatrix[0 -1; 1 0]
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diff changeset
212
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213 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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214 t̂ = R̂*(b-a)/norm(b-a)
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215
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216 c = (a+b)/2 + α*t̂
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217
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218 ca = a-c
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219 cb = b-c
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220 θₐ = atan(ca[2],ca[1])
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221 θᵦ = atan(cb[2],cb[1])
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222
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223 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
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224
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225 if r > 0
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226 Δθ = abs(Δθ)
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227 else
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228 Δθ = -abs(Δθ)
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229 end
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230
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231 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
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232 end
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233
1978
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234 """
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235 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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236
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diff changeset
237 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
2070
c68fa6c74477 Explain parametrizations in docstrings
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parents: 2069
diff changeset
238 The transfinite interpolation maps the unit square ([0,1]⊗[0,1]) to the patch delimited by the given curves.
c68fa6c74477 Explain parametrizations in docstrings
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diff changeset
239 The curves should encircle the patch counterclockwise.
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240
c68fa6c74477 Explain parametrizations in docstrings
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241 See https://en.wikipedia.org/wiki/Transfinite_interpolation for more information on transfinite interpolation.
1978
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diff changeset
242 """
1916
6859089b361e Remove abstract types for Curve and surface
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parents: 1915
diff changeset
243 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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244 c₁::T1
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245 c₂::T2
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246 c₃::T3
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247 c₄::T4
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248 end
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249
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250 function (s::TransfiniteInterpolationSurface)(u,v)
2071
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parents: 2070
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251 if (u,v) ∉ unitsquare()
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diff changeset
252 throw(DomainError((u,v), "Transfinite interpolation was called with parameters outside the unit square."))
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diff changeset
253 end
1915
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254 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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255 P₀₀ = c₁(0)
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256 P₁₀ = c₂(0)
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257 P₁₁ = c₃(0)
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258 P₀₁ = c₄(0)
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259 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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260 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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parents:
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261 )
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parents:
diff changeset
262 end
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parents:
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263
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parents:
diff changeset
264 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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parents:
diff changeset
265 s(ξ̄...)
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266 end
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parents:
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267
1978
d7a5129517d9 Add docstrings
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diff changeset
268 """
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diff changeset
269 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
270
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
271 Throw an error if the ends of the curves in the transfinite interpolation do not match.
d7a5129517d9 Add docstrings
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diff changeset
272 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
273 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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parents: 1971
diff changeset
274 if check_transfiniteinterpolation(Bool, s)
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diff changeset
275 return nothing
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parents: 1971
diff changeset
276 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
Jonatan Werpers <jonatan@werpers.com>
parents: 1979
diff changeset
277 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
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parents: 1971
diff changeset
278 end
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parents: 1971
diff changeset
279 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
280
1978
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diff changeset
281 """
1983
730c9848ad0b Update docstring for check_transfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1982
diff changeset
282 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
1978
d7a5129517d9 Add docstrings
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parents: 1977
diff changeset
283
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parents: 1977
diff changeset
284 Return true if the ends of the curves in the transfinite interpolation match.
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diff changeset
285 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
286 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
287 if !isapprox(s.c₁(1), s.c₂(0))
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parents: 1971
diff changeset
288 return false
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parents: 1971
diff changeset
289 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
290
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
291 if !isapprox(s.c₂(1), s.c₃(0))
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parents: 1971
diff changeset
292 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
293 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
294
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
295 if !isapprox(s.c₃(1), s.c₄(0))
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parents: 1971
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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parents: 1971
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298
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
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299 if !isapprox(s.c₄(1), s.c₁(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
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300 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
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301 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
302
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
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303 return true
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
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304 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
305
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
306 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
2072
c36812de3f2d Add parameter validation when evaluating jacobian for transfinite interpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 2071
diff changeset
307 if ξ̄ ∉ unitsquare()
c36812de3f2d Add parameter validation when evaluating jacobian for transfinite interpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 2071
diff changeset
308 throw(DomainError(ξ̄, "Transfinite interpolation was called with parameters outside the unit square."))
c36812de3f2d Add parameter validation when evaluating jacobian for transfinite interpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 2071
diff changeset
309 end
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
310 u, v = ξ̄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
311
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
312 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
313 P₀₀ = c₁(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
314 P₁₀ = c₂(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
315 P₁₁ = c₃(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
316 P₀₁ = c₄(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
317
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
318 ∂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
319 -(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
320 )
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 ∂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
323 -(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
324 )
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 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
327 end