Mercurial > repos > public > sbplib_julia
comparison src/Grids/geometry.jl @ 2037:e1ce0697caf5 feature/sbp_operators/laplace_curvilinear
Merge feature/grids/geometry_functions
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Wed, 04 Feb 2026 09:44:55 +0100 |
| parents | 6478c29effce |
| children | 00b274a118e0 |
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| 2003:524a52f190d7 | 2037:e1ce0697caf5 |
|---|---|
| 151 end | 151 end |
| 152 | 152 |
| 153 function Grids.jacobian(C::Circle, θ) | 153 function Grids.jacobian(C::Circle, θ) |
| 154 (;r) = C | 154 (;r) = C |
| 155 r*@SVector[-sin(θ), cos(θ)] | 155 r*@SVector[-sin(θ), cos(θ)] |
| 156 end | |
| 157 | |
| 158 struct Arc{PT,T} | |
| 159 c::Circle{PT,T} | |
| 160 θ₀::T | |
| 161 θ₁::T | |
| 162 end | |
| 163 | |
| 164 """ | |
| 165 Arc(C::Circle, θ₀, θ₁) | |
| 166 | |
| 167 A circular arc as a callable object. The arc is around the circle `C` between | |
| 168 angles `θ₀` and `θ₁` and is paramatrized between 0 and 1. | |
| 169 | |
| 170 See also: [`arc`](@ref), [`Circle`](@ref). | |
| 171 """ | |
| 172 function Arc(C, θ₀, θ₁) | |
| 173 r, θ₀, θ₁ = promote(C.r, θ₀, θ₁) | |
| 174 | |
| 175 return Arc(Circle(C.c, r), θ₀, θ₁) | |
| 176 end | |
| 177 | |
| 178 function (A::Arc)(t) | |
| 179 (; θ₀, θ₁) = A | |
| 180 return A.c((1-t)*θ₀ + t*θ₁) | |
| 181 end | |
| 182 | |
| 183 function Grids.jacobian(A::Arc, t) | |
| 184 (;c, θ₀, θ₁) = A | |
| 185 return (θ₁-θ₀)*jacobian(c, t) | |
| 186 end | |
| 187 | |
| 188 | |
| 189 """ | |
| 190 arc(a,b,r) | |
| 191 | |
| 192 A circular arc between the points `a` and `b` with radius `abs(r)`. If `r > 0` | |
| 193 the arc goes counter clockwise and if `r<0` the arc goes clockwise. The arc is | |
| 194 parametrized such that if `A = arc(a,b,r)` then `A(0)` corresponds to `a` and | |
| 195 `A(1)` to `b`. | |
| 196 | |
| 197 See also: [`Arc`](@ref), [`Circle`](@ref). | |
| 198 """ | |
| 199 function arc(a,b,r) | |
| 200 if abs(r) < norm(b-a)/2 | |
| 201 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points.")) | |
| 202 end | |
| 203 | |
| 204 R̂ = @SMatrix[0 -1; 1 0] | |
| 205 | |
| 206 α = sign(r)*√(r^2 - norm((b-a)/2)^2) | |
| 207 t̂ = R̂*(b-a)/norm(b-a) | |
| 208 | |
| 209 c = (a+b)/2 + α*t̂ | |
| 210 | |
| 211 ca = a-c | |
| 212 cb = b-c | |
| 213 θₐ = atan(ca[2],ca[1]) | |
| 214 θᵦ = atan(cb[2],cb[1]) | |
| 215 | |
| 216 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π) | |
| 217 | |
| 218 if r > 0 | |
| 219 Δθ = abs(Δθ) | |
| 220 else | |
| 221 Δθ = -abs(Δθ) | |
| 222 end | |
| 223 | |
| 224 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ) | |
| 156 end | 225 end |
| 157 | 226 |
| 158 """ | 227 """ |
| 159 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄) | 228 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄) |
| 160 | 229 |