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annotate src/Grids/geometry.jl @ 2012:4617e4b74b82 feature/grids/geometry_functions

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Add arc() for constructing circle arcs between two points
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 07 May 2025 08:39:06 +0200
parents d0b6c63c506e
children 7895b509f9bf
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 struct Line{PT}
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2 p::PT
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3 tangent::PT
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4
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5 Line{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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6 end
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7
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8 """
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9 Line(p,t)
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10
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11 A line, as a callable object, starting at `p` with tangent `t`.
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12
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13 # Example
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14 ```julia-repl
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15 julia> l = Grids.Line([1,1],[2,1])
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16 Diffinitive.Grids.Line{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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17
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18 julia> l(0)
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19 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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20 1
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21 1
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22
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23 julia> l(1)
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24 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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25 3
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26 2
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27 ```
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28
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29 See also: [`LineSegment`](@ref).
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30 """
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31 function Line(p, t)
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32 p = SVector{length(p)}(p)
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33 t = SVector{length(t)}(t)
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34 p, t = promote(p, t)
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35
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36 return Line{typeof(p)}(p,t)
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37 end
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38
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39 (c::Line)(s) = c.p + s*c.tangent
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40
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41 Grids.jacobian(l::Line, t) = l.tangent
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42
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43 struct LineSegment{PT}
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44 a::PT
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45 b::PT
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46
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47 LineSegment{PT}(p::PT, tangent::PT) where PT = new{PT}(p,tangent)
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48 end
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49
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50 """
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51 LineSegment(a,b)
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52
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53 A line segment, as a callable object, from `a` to `b`.
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54
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55 # Example
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56 ```julia-repl
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57 julia> l = Grids.LineSegment([1,1],[2,1])
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58 Diffinitive.Grids.LineSegment{StaticArraysCore.SVector{2, Int64}}([1, 1], [2, 1])
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59
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60 julia> l(0)
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61 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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62 1
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63 1
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64
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65 julia> l(0.5)
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66 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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67 1.5
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68 1.0
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69
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70 julia> l(1)
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71 2-element StaticArraysCore.SVector{2, Int64} with indices SOneTo(2):
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72 2
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73 1
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74 ```
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75
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76 See also: [`Line`](@ref).
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77 """
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78 function LineSegment(a, b)
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79 a = SVector{length(a)}(a)
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80 b = SVector{length(b)}(b)
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81 a, b = promote(a, b)
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82
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83 return LineSegment{typeof(a)}(a,b)
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84 end
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85
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86 (c::LineSegment)(s) = (1-s)*c.a + s*c.b
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87
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88 Grids.jacobian(c::LineSegment, s) = c.b - c.a
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89
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90 """
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91 linesegments(ps...)
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92
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93 An array of line segments between the points `ps[1]`, `ps[2]`, and so on.
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94
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95 See also: [`polygon_edges`](@ref).
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96 """
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97 function linesegments(ps...)
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98 return [LineSegment(ps[i], ps[i+1]) for i ∈ 1:length(ps)-1]
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99 end
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100
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101
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102 """
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103 polygon_edges(ps...)
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104
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105 An array of line segments between the points `ps[1]`, `ps[2]`, and so on
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106 including the segment between `ps[end]` and `ps[1]`.
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107
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108 See also: [`linesegments`](@ref).
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109 """
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110 function polygon_edges(ps...)
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111 n = length(ps)
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112 return [LineSegment(ps[i], ps[mod1(i+1,n)]) for i ∈ eachindex(ps)]
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113 end
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114
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115 struct Circle{PT,T}
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116 c::PT
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117 r::T
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118
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119 Circle{PT,T}(c,r) where {PT,T} = new{PT,T}(c,r)
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120 end
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121
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122 """
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123 Circle(c,r)
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124
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125 A circle with center `c` and radius `r` paramatrized with the angle to the x-axis.
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126
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127 # Example
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128 ```julia-repl
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129 julia> c = Grids.Circle([1,1], 2)
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130 Diffinitive.Grids.Circle{StaticArraysCore.SVector{2, Int64}, Int64}([1, 1], 2)
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131
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132 julia> c(0)
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133 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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134 3.0
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135 1.0
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136
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137 julia> c(π/2)
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138 2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
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139 1.0000000000000002
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140 3.0
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141 ```
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142 """
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143 function Circle(c,r)
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144 c = SVector{2}(c)
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145 return Circle{typeof(c), typeof(r)}(c,r)
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146 end
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147
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148 function (C::Circle)(θ)
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149 (;c, r) = C
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150 c + r*@SVector[cos(θ), sin(θ)]
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151 end
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152
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153 function Grids.jacobian(C::Circle, θ)
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154 (;r) = C
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155 r*@SVector[-sin(θ), cos(θ)]
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156 end
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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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diff changeset
161 θ₁::T
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diff changeset
162 end
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
163
d0b6c63c506e Add Arc type for representing partial circles
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parents: 1983
diff changeset
164 """
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165 Arc(C::Circle, θ₀, θ₁)
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diff changeset
166
d0b6c63c506e Add Arc type for representing partial circles
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diff changeset
167 # TODO
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168 """
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diff changeset
169 function Arc(C, θ₀, θ₁)
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diff changeset
170 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁)
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171
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172 return Arc(Circle(C.c, r), θ₀, θ₁)
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173 end
d0b6c63c506e Add Arc type for representing partial circles
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diff changeset
174
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175 function (A::Arc)(t)
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176 (; θ₀, θ₁) = A
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177 return A.c((1-t)*θ₀ + t*θ₁)
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diff changeset
178 end
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diff changeset
179
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180 function Grids.jacobian(a::Arc, t)
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181 return nothing
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182 end
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183
2012
4617e4b74b82 Add arc() for constructing circle arcs between two points
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184
4617e4b74b82 Add arc() for constructing circle arcs between two points
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185 """
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186 arc(a,b,r)
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187
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188 # TODO
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189 """
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190 function arc(a,b,r)
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191 if abs(r) < norm(b-a)/2
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192 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points."))
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193 end
4617e4b74b82 Add arc() for constructing circle arcs between two points
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194
4617e4b74b82 Add arc() for constructing circle arcs between two points
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195 R̂ = @SMatrix[0 -1; 1 0]
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196
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197 α = sign(r)*√(r^2 - norm((b-a)/2)^2)
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198 t̂ = R̂*(b-a)/norm(b-a)
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199
4617e4b74b82 Add arc() for constructing circle arcs between two points
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200 c = (a+b)/2 + α*t̂
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201
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202 ca = a-c
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203 cb = b-c
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204 θₐ = atan(ca[2],ca[1])
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205 θᵦ = atan(cb[2],cb[1])
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diff changeset
206
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diff changeset
207 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π)
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diff changeset
208
4617e4b74b82 Add arc() for constructing circle arcs between two points
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diff changeset
209 if r > 0
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diff changeset
210 Δθ = abs(Δθ)
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diff changeset
211 else
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diff changeset
212 Δθ = -abs(Δθ)
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213 end
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214
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215 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ)
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216 end
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217
1978
d7a5129517d9 Add docstrings
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218 """
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219 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄)
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220
d7a5129517d9 Add docstrings
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221 A surface defined by the transfinite interpolation of the curves `c₁`, `c₂`, `c₃`, and `c₄`.
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222 """
1916
6859089b361e Remove abstract types for Curve and surface
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223 struct TransfiniteInterpolationSurface{T1,T2,T3,T4}
1915
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224 c₁::T1
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225 c₂::T2
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226 c₃::T3
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227 c₄::T4
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228 end
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229
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230 function (s::TransfiniteInterpolationSurface)(u,v)
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231 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
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232 P₀₀ = c₁(0)
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233 P₁₀ = c₂(0)
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234 P₁₁ = c₃(0)
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235 P₀₁ = c₄(0)
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236 return (1-v)*c₁(u) + u*c₂(v) + v*c₃(1-u) + (1-u)*c₄(1-v) - (
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237 (1-u)*(1-v)*P₀₀ + u*(1-v)*P₁₀ + u*v*P₁₁ + (1-u)*v*P₀₁
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238 )
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parents:
diff changeset
239 end
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parents:
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240
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parents:
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241 function (s::TransfiniteInterpolationSurface)(ξ̄::AbstractArray)
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242 s(ξ̄...)
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243 end
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244
1978
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245 """
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246 check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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247
d7a5129517d9 Add docstrings
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diff changeset
248 Throw an error if the ends of the curves in the transfinite interpolation do not match.
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diff changeset
249 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
250 function check_transfiniteinterpolation(s::TransfiniteInterpolationSurface)
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diff changeset
251 if check_transfiniteinterpolation(Bool, s)
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diff changeset
252 return nothing
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diff changeset
253 else
1982
486b3c6f919e Throw better error type for transfinite interpolation check
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diff changeset
254 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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diff changeset
255 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
256 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
257
1978
d7a5129517d9 Add docstrings
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diff changeset
258 """
1983
730c9848ad0b Update docstring for check_transfiniteinterpolation
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parents: 1982
diff changeset
259 check_transfiniteinterpolation(Bool, s::TransfiniteInterpolationSurface)
1978
d7a5129517d9 Add docstrings
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diff changeset
260
d7a5129517d9 Add docstrings
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diff changeset
261 Return true if the ends of the curves in the transfinite interpolation match.
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diff changeset
262 """
1973
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
263 function check_transfiniteinterpolation(::Type{Bool}, s::TransfiniteInterpolationSurface)
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
264 if !isapprox(s.c₁(1), s.c₂(0))
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
265 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
266 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
267
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
268 if !isapprox(s.c₂(1), s.c₃(0))
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diff changeset
269 return false
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parents: 1971
diff changeset
270 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
271
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
272 if !isapprox(s.c₃(1), s.c₄(0))
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diff changeset
273 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
274 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
275
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
276 if !isapprox(s.c₄(1), s.c₁(0))
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diff changeset
277 return false
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
278 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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parents: 1971
diff changeset
279
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
280 return true
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
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diff changeset
281 end
8e9575b518a1 Add tests for TransfiniteInterpolationSurface and implemnet check_tranfiniteinterpolation
Jonatan Werpers <jonatan@werpers.com>
parents: 1971
diff changeset
282
1977
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
283 function Grids.jacobian(s::TransfiniteInterpolationSurface, ξ̄)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
284 u, v = ξ̄
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diff changeset
285
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
286 c₁, c₂, c₃, c₄ = s.c₁, s.c₂, s.c₃, s.c₄
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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diff changeset
287 P₀₀ = c₁(0)
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diff changeset
288 P₁₀ = c₂(0)
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diff changeset
289 P₁₁ = c₃(0)
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diff changeset
290 P₀₁ = c₄(0)
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
291
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
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parents: 1976
diff changeset
292 ∂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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parents: 1976
diff changeset
293 -(1-v)*P₀₀ + (1-v)*P₁₀ + v*P₁₁ - v*P₀₁
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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parents: 1976
diff changeset
295
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
296 ∂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
297 -(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
298 )
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
299
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
300 return [∂x̄∂ξ₁ ∂x̄∂ξ₂]
270675bb97be Implement Grids.jacobian for TransfiniteInterpolationSurface
Jonatan Werpers <jonatan@werpers.com>
parents: 1976
diff changeset
301 end