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annotate src/Grids/geometry.jl @ 2014:6478c29effce feature/grids/geometry_functions

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Add docstring for Arc and arc
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 09 May 2025 07:42:21 +0200
parents 7895b509f9bf
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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 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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diff changeset
157
2011
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diff changeset
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
2014
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167 A circular arc as a callable object. The arc is around the circle `C` between
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168 angles `θ₀` and `θ₁` and is paramatrized between 0 and 1.
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169
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170 See also: [`arc`](@ref), [`Circle`](@ref).
2011
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171 """
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172 function Arc(C, θ₀, θ₁)
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173 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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174
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175 return Arc(Circle(C.c, r), θ₀, θ₁)
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176 end
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177
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178 function (A::Arc)(t)
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179 (; θ₀, θ₁) = A
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180 return A.c((1-t)*θ₀ + t*θ₁)
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181 end
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182
2013
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183 function Grids.jacobian(A::Arc, t)
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184 (;c, θ₀, θ₁) = A
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185 return (θ₁-θ₀)*jacobian(c, t)
2011
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186 end
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187
2012
4617e4b74b82 Add arc() for constructing circle arcs between two points
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188
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189 """
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diff changeset
190 arc(a,b,r)
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diff changeset
191
2014
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192 A circular arc between the points `a` and `b` with radius `abs(r)`. If `r > 0`
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193 the arc goes counter clockwise and if `r<0` the arc goes clockwise. The arc is
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diff changeset
194 parametrized such that if `A = arc(a,b,r)` then `A(0)` corresponds to `a` and
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195 `A(1)` to `b`.
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196
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197 See also: [`Arc`](@ref), [`Circle`](@ref).
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198 """
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199 function arc(a,b,r)
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200 if abs(r) < norm(b-a)/2
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201 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
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diff changeset
202 end
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diff changeset
203
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
204 R̂ = @SMatrix[0 -1; 1 0]
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205
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206 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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diff changeset
207 t̂ = R̂*(b-a)/norm(b-a)
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diff changeset
208
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diff changeset
209 c = (a+b)/2 + α*t̂
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diff changeset
210
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diff changeset
211 ca = a-c
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212 cb = b-c
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213 θₐ = atan(ca[2],ca[1])
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214 θᵦ = atan(cb[2],cb[1])
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215
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diff changeset
216 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
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217
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diff changeset
218 if r > 0
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219 Δθ = abs(Δθ)
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220 else
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221 Δθ = -abs(Δθ)
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222 end
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223
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224 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
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225 end
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226
1978
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227 """
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228 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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229
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diff changeset
230 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
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diff changeset
231 """
1916
6859089b361e Remove abstract types for Curve and surface
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diff changeset
232 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
c003685d9926 Add geometry functions removed from feature/grids/manifolds
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233 c₁::T1
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parents:
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234 c₂::T2
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235 c₃::T3
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236 c₄::T4
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diff changeset
237 end
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parents:
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238
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parents:
diff changeset
239 function (s::TransfiniteInterpolationSurface)(u,v)
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240 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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241 P₀₀ = c₁(0)
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diff changeset
242 P₁₀ = c₂(0)
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243 P₁₁ = c₃(0)
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244 P₀₁ = c₄(0)
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245 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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parents:
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246 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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247 )
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parents:
diff changeset
248 end
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parents:
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249
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parents:
diff changeset
250 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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251 s(ξ̄...)
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252 end
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253
1978
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254 """
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diff changeset
255 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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diff changeset
256
d7a5129517d9 Add docstrings
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diff changeset
257 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
258 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
259 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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parents: 1971
diff changeset
260 if check_transfiniteinterpolation(Bool, s)
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parents: 1971
diff changeset
261 return nothing
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
262 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
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parents: 1979
diff changeset
263 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
264 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
265 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
266
1978
d7a5129517d9 Add docstrings
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diff changeset
267 """
1983
730c9848ad0b Update docstring for check_transfiniteinterpolation
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parents: 1982
diff changeset
268 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
1978
d7a5129517d9 Add docstrings
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diff changeset
269
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diff changeset
270 Return true if the ends of the curves in the transfinite interpolation match.
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diff changeset
271 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
272 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
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parents: 1971
diff changeset
273 if !isapprox(s.c₁(1), s.c₂(0))
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diff changeset
274 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
275 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
276
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
277 if !isapprox(s.c₂(1), s.c₃(0))
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diff changeset
278 return false
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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
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
281 if !isapprox(s.c₃(1), s.c₄(0))
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parents: 1971
diff changeset
282 return false
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parents: 1971
diff changeset
283 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
284
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
285 if !isapprox(s.c₄(1), s.c₁(0))
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parents: 1971
diff changeset
286 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
287 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
288
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
289 return true
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parents: 1971
diff changeset
290 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
291
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
292 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
293 u, v = ξ̄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
294
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
295 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
296 P₀₀ = c₁(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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297 P₁₀ = c₂(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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298 P₁₁ = c₃(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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299 P₀₁ = c₄(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
300
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
301 ∂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
302 -(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
303 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
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304
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
305 ∂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
306 -(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
307 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
308
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
309 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
310 end