Mercurial > repos > public > sbplib_julia

annotate src/Grids/geometry.jl @ 2069:15f27fea9929 feature/grids/geometry_functions

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Remove review comments about output types.
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 17 Feb 2026 20:15:37 +0100
parents 00b274a118e0
children c68fa6c74477
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rev   line source
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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 """
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12 Line(p,t)
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13
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14 A line, as a callable object, starting at `p` with tangent `t`.
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15
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16 # Example
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17 ```julia-repl
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18 julia> l = Grids.Line([1,1],[2,1])
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19 Diffinitive.Grids.Line{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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20
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21 julia> l(0)
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22 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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23 1
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24 1
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25
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26 julia> l(1)
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27 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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28 3
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29 2
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30 ```
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31
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32 See also: [`LineSegment`](@ref).
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33 """
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34 function Line(p, t)
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35 p = SVector{length(p)}(p)
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36 t = SVector{length(t)}(t)
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37 p, t = promote(p, t)
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38
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39 return Line{typeof(p)}(p,t)
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40 end
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41
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42 (c::Line)(s) = c.p + s*c.tangent
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43
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44 Grids.jacobian(l::Line, t) = l.tangent
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45
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46 struct LineSegment{PT}
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47 a::PT
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48 b::PT
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49
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50 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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51 end
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52
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53
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54 # REVIEW:
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55 # 1. Explain the parametrization.
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56 # 3. Do we want s in [0, 1]? Currently the line segment
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57 # can return values "outside" of the interval [a,b].
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58 """
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59 LineSegment(a,b)
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60
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61 A line segment, as a callable object, from `a` to `b`.
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62
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63 # Example
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64 ```julia-repl
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65 julia> l = Grids.LineSegment([1,1],[2,1])
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66 Diffinitive.Grids.LineSegment{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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67
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68 julia> l(0)
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69 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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70 1
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71 1
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72
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73 julia> l(0.5)
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74 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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75 1.5
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76 1.0
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77
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78 julia> l(1)
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79 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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80 2
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81 1
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82 ```
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83
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84 See also: [`Line`](@ref).
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85 """
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86 function LineSegment(a, b)
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87 a = SVector{length(a)}(a)
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88 b = SVector{length(b)}(b)
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89 a, b = promote(a, b)
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90
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91 return LineSegment{typeof(a)}(a,b)
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92 end
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93
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94 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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95
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96 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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97
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98
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99 """
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100 linesegments(ps...)
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101
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102 An array of line segments between the points `ps[1]`, `ps[2]`, and so on.
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103
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104 See also: [`polygon_edges`](@ref).
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105 """
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106 function linesegments(ps...)
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107 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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108 end
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109
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110
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111 """
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112 polygon_edges(ps...)
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113
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114 An array of line segments between the points `ps[1]`, `ps[2]`, and so on
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115 including the segment between `ps[end]` and `ps[1]`.
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116
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117 See also: [`linesegments`](@ref).
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118 """
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119 function polygon_edges(ps...)
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120 n = length(ps)
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121 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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122 end
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123
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124
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125 struct Circle{PT,T}
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126 c::PT
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127 r::T
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128
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129 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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130 end
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131
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132 """
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133 Circle(c,r)
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134
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135 A circle with center `c` and radius `r` paramatrized with the angle to the x-axis.
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136
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137 # Example
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138 ```julia-repl
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139 julia> c = Grids.Circle([1,1], 2)
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140 Diffinitive.Grids.Circle{StaticArraysCore.SVector{2, Int64}, Int64}([1, 1], 2)
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141
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142 julia> c(0)
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143 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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144 3.0
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145 1.0
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146
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147 julia> c(π/2)
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148 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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149 1.0000000000000002
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150 3.0
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151 ```
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152 """
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153 function Circle(c,r)
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154 c = SVector{2}(c)
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155 return Circle{typeof(c), typeof(r)}(c,r)
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156 end
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157
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158 function (C::Circle)(θ)
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159 (;c, r) = C
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160 c + r*@SVector[cos(θ), sin(θ)]
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161 end
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162
1976
34a7e3919e9a Implement Grids.jacobian for Circle
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163 function Grids.jacobian(C::Circle, θ)
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164 (;r) = C
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165 r*@SVector[-sin(θ), cos(θ)]
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166 end
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167
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168
2011
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169 struct Arc{PT,T}
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170 c::Circle{PT,T}
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171 θ₀::T
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172 θ₁::T
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173 end
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174
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175 """
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176 Arc(C::Circle, θ₀, θ₁)
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177
2014
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178 A circular arc as a callable object. The arc is around the circle `C` between
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179 angles `θ₀` and `θ₁` and is paramatrized between 0 and 1.
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180
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181 See also: [`arc`](@ref), [`Circle`](@ref).
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182 """
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183 function Arc(C, θ₀, θ₁)
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184 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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185
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186 return Arc(Circle(C.c, r), θ₀, θ₁)
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187 end
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188
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189 function (A::Arc)(t)
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190 (; θ₀, θ₁) = A
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191 return A.c((1-t)*θ₀ + t*θ₁)
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192 end
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193
2013
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194 function Grids.jacobian(A::Arc, t)
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195 (;c, θ₀, θ₁) = A
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196 return (θ₁-θ₀)*jacobian(c, t)
2011
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197 end
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198
2012
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199
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200 """
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201 arc(a,b,r)
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202
2014
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203 A circular arc between the points `a` and `b` with radius `abs(r)`. If `r > 0`
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204 the arc goes counter clockwise and if `r<0` the arc goes clockwise. The arc is
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205 parametrized such that if `A = arc(a,b,r)` then `A(0)` corresponds to `a` and
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206 `A(1)` to `b`.
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207
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208 See also: [`Arc`](@ref), [`Circle`](@ref).
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209 """
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210 function arc(a,b,r)
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211 if abs(r) < norm(b-a)/2
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212 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
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213 end
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214
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215 R̂ = @SMatrix[0 -1; 1 0]
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216
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217 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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218 t̂ = R̂*(b-a)/norm(b-a)
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219
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220 c = (a+b)/2 + α*t̂
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221
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222 ca = a-c
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223 cb = b-c
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224 θₐ = atan(ca[2],ca[1])
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225 θᵦ = atan(cb[2],cb[1])
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226
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227 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
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228
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229 if r > 0
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230 Δθ = abs(Δθ)
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231 else
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232 Δθ = -abs(Δθ)
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233 end
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234
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235 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
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236 end
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237
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238 # REVIEW:
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239 # 1. Explain parametrisation
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240 # 2. Boundscheck for the parametrisation argumetns, i.e. within [0,1]?
1978
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241 """
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242 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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243
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244 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
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245 """
1916
6859089b361e Remove abstract types for Curve and surface
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diff changeset
246 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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247 c₁::T1
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248 c₂::T2
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249 c₃::T3
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250 c₄::T4
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251 end
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252
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253 function (s::TransfiniteInterpolationSurface)(u,v)
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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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261 )
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262 end
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263
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diff changeset
264 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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265 s(ξ̄...)
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266 end
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267
1978
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268 """
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269 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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diff changeset
270
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diff changeset
271 Throw an error if the ends of the curves in the transfinite interpolation do not match.
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diff changeset
272 """
1973
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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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diff changeset
276 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
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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
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diff changeset
278 end
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Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
279 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
280
1978
d7a5129517d9 Add docstrings
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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
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parents: 1977
diff changeset
283
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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)
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parents: 1971
diff changeset
287 if !isapprox(s.c₁(1), s.c₂(0))
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diff changeset
288 return false
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parents: 1971
diff changeset
289 end
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parents: 1971
diff changeset
290
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parents: 1971
diff changeset
291 if !isapprox(s.c₂(1), s.c₃(0))
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diff changeset
292 return false
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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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diff changeset
295 if !isapprox(s.c₃(1), s.c₄(0))
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diff changeset
296 return false
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parents: 1971
diff changeset
297 end
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parents: 1971
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298
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299 if !isapprox(s.c₄(1), s.c₁(0))
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300 return false
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301 end
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302
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303 return true
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304 end
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305
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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306 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
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307 u, v = ξ̄
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308
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309 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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310 P₀₀ = c₁(0)
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311 P₁₀ = c₂(0)
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312 P₁₁ = c₃(0)
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313 P₀₁ = c₄(0)
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314
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315 ∂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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316 -(1-v)*P₀₀ + (1-v)*P₁₀ + v*P₁₁ - v*P₀₁
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317 )
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318
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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319 ∂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>
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320 -(1-u)*P₀₀ - u*P₁₀ + u*P₁₁ + (1-u)*P₀₁
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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321 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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322
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
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323 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
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324 end