Mercurial > repos > public > sbplib_julia
comparison src/Grids/geometry.jl @ 2012:4617e4b74b82 feature/grids/geometry_functions
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 |
comparison
equal
deleted
inserted
replaced
| 2011:d0b6c63c506e | 2012:4617e4b74b82 |
|---|---|
| 177 return A.c((1-t)*θ₀ + t*θ₁) | 177 return A.c((1-t)*θ₀ + t*θ₁) |
| 178 end | 178 end |
| 179 | 179 |
| 180 function Grids.jacobian(a::Arc, t) | 180 function Grids.jacobian(a::Arc, t) |
| 181 return nothing | 181 return nothing |
| 182 end | |
| 183 | |
| 184 | |
| 185 """ | |
| 186 arc(a,b,r) | |
| 187 | |
| 188 # TODO | |
| 189 """ | |
| 190 function arc(a,b,r) | |
| 191 if abs(r) < norm(b-a)/2 | |
| 192 throw(DomainError(r, "arc was called with radius r = $r smaller than half the distance between the points.")) | |
| 193 end | |
| 194 | |
| 195 R̂ = @SMatrix[0 -1; 1 0] | |
| 196 | |
| 197 α = sign(r)*√(r^2 - norm((b-a)/2)^2) | |
| 198 t̂ = R̂*(b-a)/norm(b-a) | |
| 199 | |
| 200 c = (a+b)/2 + α*t̂ | |
| 201 | |
| 202 ca = a-c | |
| 203 cb = b-c | |
| 204 θₐ = atan(ca[2],ca[1]) | |
| 205 θᵦ = atan(cb[2],cb[1]) | |
| 206 | |
| 207 Δθ = mod(θᵦ-θₐ+π, 2π)-π # Δθ in the interval (-π,π) | |
| 208 | |
| 209 if r > 0 | |
| 210 Δθ = abs(Δθ) | |
| 211 else | |
| 212 Δθ = -abs(Δθ) | |
| 213 end | |
| 214 | |
| 215 return Arc(Circle(c,abs(r)), θₐ, θₐ+Δθ) | |
| 182 end | 216 end |
| 183 | 217 |
| 184 """ | 218 """ |
| 185 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄) | 219 TransfiniteInterpolationSurface(c₁, c₂, c₃, c₄) |
| 186 | 220 |